phit

Verification

Each report compares phit with a reference implementation on the same inputs, at a stated tolerance.

reports

1,529

comparisons

All pass

within tolerance

OLS: agreement with R
Logistic regression: agreement with R
Probit regression: agreement with R
Poisson regression: agreement with R
Gaussian random intercept: agreement with R
Mixed models on published data sets: agreement with R
Binomial random intercept: agreement with lme4
Weights, offsets and mixed models: agreement with R and lme4
Distributions: accuracy against 60-digit references

OLS: agreement with R

105/105 pass

Largest absolute difference from R for every reported quantity, alongside statsmodels. Every case also passes the release gate (scripts/check).

Reference: R version 4.6.1 (2026-06-24), statsmodels 0.15.0, numpy 2.5.4, Python 3.14.7, PHP 8.5.10
Tolerance: release gate: 1e-9 + 1e-7*|reference| (fixed models), 1e-7 + 1e-6*|reference| (mixed models)
Result: 105 of 105 comparisons pass, across 7 cases.

✓ simulated_housing 15 quantities worst abs. 3.5e-10

Quantity	Max abs. error	statsmodels	Pass
coefficients	2.0e-12	1.7e-13	✓
covariance	6.5e-11	1.5e-11	✓
std_errors	1.4e-13	2.8e-14	✓
t_statistics	1.0e-14	1.8e-15	✓
p_values	2.5e-15	2.8e-16	✓
conf_int	2.7e-12	2.4e-12	✓
fitted	9.1e-13	6.8e-13	✓
residuals	9.4e-13	5.7e-13	✓
rss	3.5e-10	8.7e-11	✓
residual_variance	5.8e-11	1.5e-11	✓
sigma	1.7e-13	2.8e-14	✓
r_squared	1.1e-16	0	✓
adj_r_squared	1.1e-16	1.1e-16	✓
df_residual	0	0	✓
log_likelihood	7.1e-15	7.1e-15	✓

✓ simulated_housing_multiple 15 quantities worst abs. 1.9e-10

Quantity	Max abs. error	statsmodels	Pass
coefficients	2.0e-13	4.5e-13	✓
covariance	1.9e-10	1.5e-11	✓
std_errors	2.8e-13	5.7e-14	✓
t_statistics	1.3e-15	2.0e-15	✓
p_values	1.4e-16	5.0e-16	✓
conf_int	2.3e-13	6.8e-13	✓
fitted	1.8e-12	2.3e-12	✓
residuals	1.7e-12	2.4e-12	✓
rss	1.2e-10	2.9e-11	✓
residual_variance	2.2e-11	7.3e-12	✓
sigma	5.7e-14	2.8e-14	✓
r_squared	0	0	✓
adj_r_squared	0	0	✓
df_residual	0	0	✓
log_likelihood	7.1e-15	7.1e-15	✓

✓ simple 15 quantities worst abs. 8.5e-14

Quantity	Max abs. error	statsmodels	Pass
coefficients	5.2e-15	4.7e-15	✓
covariance	1.8e-16	2.9e-16	✓
std_errors	4.4e-16	7.2e-16	✓
t_statistics	8.5e-14	1.1e-13	✓
p_values	1.8e-14	1.7e-14	✓
conf_int	6.2e-15	7.0e-15	✓
fitted	5.8e-15	4.4e-15	✓
residuals	5.9e-15	4.1e-15	✓
rss	2.1e-16	7.5e-16	✓
residual_variance	6.9e-17	2.5e-16	✓
sigma	1.9e-16	6.7e-16	✓
r_squared	0	1.1e-16	✓
adj_r_squared	0	2.2e-16	✓
df_residual	0	0	✓
log_likelihood	5.3e-15	1.6e-14	✓

✓ multiple 15 quantities worst abs. 7.1e-15

Quantity	Max abs. error	statsmodels	Pass
coefficients	3.6e-15	1.3e-15	✓
covariance	1.9e-16	3.6e-16	✓
std_errors	1.7e-16	4.4e-16	✓
t_statistics	7.1e-15	1.8e-14	✓
p_values	1.2e-16	1.4e-17	✓
conf_int	4.0e-15	2.2e-15	✓
fitted	4.0e-15	3.6e-15	✓
residuals	3.9e-15	2.1e-15	✓
rss	1.8e-15	3.1e-15	✓
residual_variance	2.2e-16	4.4e-16	✓
sigma	2.2e-16	3.3e-16	✓
r_squared	0	0	✓
adj_r_squared	0	0	✓
df_residual	0	0	✓
log_likelihood	3.6e-15	6.2e-15	✓

✓ no_intercept 15 quantities worst abs. 7.1e-15

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.7e-15	2.1e-15	✓
covariance	5.2e-18	9.7e-17	✓
std_errors	1.4e-17	2.2e-16	✓
t_statistics	7.1e-15	4.3e-14	✓
p_values	2.2e-15	1.2e-15	✓
conf_int	3.2e-15	2.5e-15	✓
fitted	5.3e-15	1.1e-14	✓
residuals	5.3e-15	1.1e-14	✓
rss	1.8e-15	8.0e-15	✓
residual_variance	2.2e-16	1.0e-15	✓
sigma	1.1e-16	6.7e-16	✓
r_squared	0	0	✓
adj_r_squared	0	0	✓
df_residual	0	0	✓
log_likelihood	3.6e-15	8.9e-15	✓

✓ correlated 15 quantities worst abs. 6.5e-13

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.0e-13	8.9e-14	✓
covariance	6.5e-13	2.9e-12	✓
std_errors	2.7e-14	1.2e-13	✓
t_statistics	1.2e-13	1.7e-13	✓
p_values	8.9e-14	1.3e-13	✓
conf_int	1.6e-13	2.9e-13	✓
fitted	5.5e-14	2.9e-13	✓
residuals	5.5e-14	2.9e-13	✓
rss	2.3e-14	5.9e-14	✓
residual_variance	3.3e-15	8.4e-15	✓
sigma	2.2e-15	5.6e-15	✓
r_squared	1.1e-16	1.1e-16	✓
adj_r_squared	1.1e-16	1.1e-16	✓
df_residual	0	0	✓
log_likelihood	3.0e-14	7.3e-14	✓

✓ listwise_missing 15 quantities worst abs. 1.0e-12

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.8e-15	3.6e-15	✓
covariance	1.1e-16	1.4e-17	✓
std_errors	7.5e-16	9.7e-17	✓
t_statistics	1.0e-12	1.4e-13	✓
p_values	2.0e-15	8.9e-15	✓
conf_int	4.4e-15	3.9e-15	✓
fitted	5.3e-15	4.4e-15	✓
residuals	5.5e-15	4.3e-15	✓
rss	1.8e-16	2.9e-17	✓
residual_variance	9.2e-17	1.5e-17	✓
sigma	6.8e-16	1.1e-16	✓
r_squared	0	0	✓
adj_r_squared	0	0	✓
df_residual	0	0	✓
log_likelihood	3.9e-14	7.1e-15	✓

Peer columns give the same error measure for statsmodels against the reference.

Logistic regression: agreement with R

91/91 pass

Largest absolute difference from R for every reported quantity, alongside statsmodels. Every case also passes the release gate (scripts/check).

Reference: R version 4.6.1 (2026-06-24), statsmodels 0.15.0, numpy 2.5.4, Python 3.14.7, PHP 8.5.10
Tolerance: release gate: 1e-9 + 1e-7*|reference| (fixed models), 1e-7 + 1e-6*|reference| (mixed models)
Result: 91 of 91 comparisons pass, across 7 cases.

✓ simulated_learning 13 quantities worst abs. 1.1e-11

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.1e-14	2.5e-16	✓
covariance	8.6e-13	9.0e-13	✓
std_errors	2.9e-13	3.0e-13	✓
z_statistics	4.1e-13	4.4e-13	✓
p_values	1.1e-11	6.7e-14	✓
conf_int	5.8e-13	6.0e-13	✓
fitted	1.0e-15	7.8e-16	✓
residuals	1.0e-15	7.8e-16	✓
log_likelihood	1.4e-14	2.1e-14	✓
deviance	2.8e-14	4.3e-14	✓
null_deviance	0	1.3e-13	✓
aic	2.8e-14	4.3e-14	✓
df_residual	0	0	✓

✓ simple 13 quantities worst abs. 1.8e-12

Quantity	Max abs. error	statsmodels	Pass
coefficients	6.7e-16	2.2e-16	✓
covariance	3.2e-13	3.2e-13	✓
std_errors	2.8e-13	2.8e-13	✓
z_statistics	1.4e-12	1.4e-12	✓
p_values	1.8e-12	6.9e-14	✓
conf_int	5.6e-13	5.6e-13	✓
fitted	1.7e-16	1.1e-16	✓
residuals	2.2e-16	1.1e-16	✓
log_likelihood	7.1e-15	1.4e-14	✓
deviance	0	4.3e-14	✓
null_deviance	0	1.3e-13	✓
aic	1.4e-14	2.8e-14	✓
df_residual	0	0	✓

✓ no_intercept 13 quantities worst abs. 3.8e-12

Quantity	Max abs. error	statsmodels	Pass
coefficients	8.3e-17	3.5e-18	✓
covariance	3.0e-15	3.0e-15	✓
std_errors	1.5e-14	1.5e-14	✓
z_statistics	4.4e-13	4.3e-13	✓
p_values	3.8e-12	4.7e-14	✓
conf_int	3.0e-14	2.9e-14	✓
fitted	2.2e-16	1.7e-16	✓
residuals	2.2e-16	2.2e-16	✓
log_likelihood	1.4e-14	7.1e-15	✓
deviance	2.8e-14	1.4e-14	✓
null_deviance	0	0	✓
aic	2.8e-14	1.4e-14	✓
df_residual	0	0	✓

✓ intercept_only 13 quantities worst abs. 6.5e-13

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.1e-16	1.1e-16	✓
covariance	3.0e-16	3.3e-16	✓
std_errors	6.4e-16	6.9e-16	✓
z_statistics	6.2e-15	7.1e-15	✓
p_values	6.5e-13	3.0e-16	✓
conf_int	1.6e-15	1.6e-15	✓
fitted	0	0	✓
residuals	0	0	✓
log_likelihood	0	6.4e-14	✓
deviance	4.3e-14	1.7e-13	✓
null_deviance	0	1.3e-13	✓
aic	0	1.3e-13	✓
df_residual	0	0	✓

✓ correlated 13 quantities worst abs. 1.0e-12

Quantity	Max abs. error	statsmodels	Pass
coefficients	2.1e-14	3.8e-14	✓
covariance	9.6e-13	1.3e-12	✓
std_errors	2.8e-13	3.8e-13	✓
z_statistics	1.0e-12	1.1e-12	✓
p_values	1.9e-13	7.8e-14	✓
conf_int	5.8e-13	7.8e-13	✓
fitted	2.1e-15	2.1e-15	✓
residuals	2.1e-15	2.1e-15	✓
log_likelihood	7.1e-15	7.1e-15	✓
deviance	1.4e-14	1.4e-14	✓
null_deviance	0	1.3e-13	✓
aic	1.4e-14	1.4e-14	✓
df_residual	0	0	✓

✓ imbalanced 13 quantities worst abs. 3.5e-8

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.1e-16	1.8e-15	✓
covariance	3.5e-8	3.5e-8	✓
std_errors	5.3e-9	5.3e-9	✓
z_statistics	2.7e-9	2.7e-9	✓
p_values	7.5e-10	7.4e-10	✓
conf_int	1.0e-8	1.0e-8	✓
fitted	1.4e-16	3.3e-16	✓
residuals	1.4e-16	3.3e-16	✓
log_likelihood	3.6e-15	7.1e-15	✓
deviance	7.1e-15	1.4e-14	✓
null_deviance	0	4.6e-14	✓
aic	7.1e-15	1.4e-14	✓
df_residual	0	0	✓

✓ listwise_missing 13 quantities worst abs. 1.4e-11

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.3e-15	1.6e-14	✓
covariance	1.1e-12	1.2e-12	✓
std_errors	3.8e-13	4.1e-13	✓
z_statistics	5.2e-13	5.6e-13	✓
p_values	1.4e-11	9.3e-14	✓
conf_int	7.5e-13	8.1e-13	✓
fitted	3.3e-16	2.4e-15	✓
residuals	3.3e-16	2.4e-15	✓
log_likelihood	7.1e-15	1.4e-14	✓
deviance	1.4e-14	2.8e-14	✓
null_deviance	0	2.8e-14	✓
aic	1.4e-14	2.8e-14	✓
df_residual	0	0	✓

Peer columns give the same error measure for statsmodels against the reference.

Probit regression: agreement with R

91/91 pass

Largest absolute difference from R for every reported quantity, alongside statsmodels. Every case also passes the release gate (scripts/check).

Reference: R version 4.6.1 (2026-06-24), statsmodels 0.15.0, numpy 2.5.4, Python 3.14.7, PHP 8.5.10
Tolerance: release gate: 1e-9 + 1e-7*|reference| (fixed models), 1e-7 + 1e-6*|reference| (mixed models)
Result: 91 of 91 comparisons pass, across 7 cases.

✓ simulated_learning 13 quantities worst abs. 6.4e-10

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.9e-10	1.3e-10	✓
covariance	1.7e-10	1.5e-10	✓
std_errors	1.2e-10	1.1e-10	✓
z_statistics	6.4e-10	5.8e-10	✓
p_values	1.9e-10	1.8e-10	✓
conf_int	4.2e-10	3.3e-10	✓
fitted	3.3e-11	3.5e-11	✓
residuals	3.3e-11	3.5e-11	✓
log_likelihood	1.4e-10	1.4e-14	✓
deviance	2.7e-10	0	✓
null_deviance	0	5.7e-14	✓
aic	2.7e-10	2.8e-14	✓
df_residual	0	0	✓

✓ simple 13 quantities worst abs. 2.7e-10

Quantity	Max abs. error	statsmodels	Pass
coefficients	5.6e-11	1.5e-13	✓
covariance	4.2e-12	1.3e-12	✓
std_errors	7.1e-12	2.2e-12	✓
z_statistics	8.9e-11	3.3e-11	✓
p_values	2.5e-14	7.2e-15	✓
conf_int	7.0e-11	4.5e-12	✓
fitted	1.2e-11	3.1e-14	✓
residuals	1.2e-11	3.1e-14	✓
log_likelihood	1.4e-10	0	✓
deviance	2.7e-10	2.8e-14	✓
null_deviance	0	5.7e-14	✓
aic	2.7e-10	0	✓
df_residual	0	0	✓

✓ no_intercept 13 quantities worst abs. 5.6e-11

Quantity	Max abs. error	statsmodels	Pass
coefficients	7.7e-12	2.8e-15	✓
covariance	1.3e-13	1.9e-15	✓
std_errors	1.2e-12	1.8e-14	✓
z_statistics	5.6e-11	1.3e-12	✓
p_values	2.0e-14	6.7e-16	✓
conf_int	1.0e-11	3.7e-14	✓
fitted	1.7e-11	5.2e-15	✓
residuals	1.7e-11	5.2e-15	✓
log_likelihood	7.9e-12	4.3e-14	✓
deviance	1.6e-11	5.7e-14	✓
null_deviance	0	0	✓
aic	1.6e-11	8.5e-14	✓
df_residual	0	0	✓

✓ intercept_only 13 quantities worst abs. 2.0e-12

Quantity	Max abs. error	statsmodels	Pass
coefficients	2.5e-16	1.9e-16	✓
covariance	0	1.0e-17	✓
std_errors	0	4.2e-17	✓
z_statistics	2.2e-15	2.7e-15	✓
p_values	2.0e-12	2.9e-16	✓
conf_int	3.1e-16	3.6e-16	✓
fitted	1.1e-16	5.6e-17	✓
residuals	2.2e-16	1.1e-16	✓
log_likelihood	1.4e-14	4.3e-14	✓
deviance	2.8e-14	8.5e-14	✓
null_deviance	0	5.7e-14	✓
aic	2.8e-14	8.5e-14	✓
df_residual	0	0	✓

✓ correlated 13 quantities worst abs. 2.7e-10

Quantity	Max abs. error	statsmodels	Pass
coefficients	5.6e-11	3.2e-11	✓
covariance	2.2e-11	3.9e-11	✓
std_errors	1.2e-11	2.2e-11	✓
z_statistics	1.8e-10	1.3e-10	✓
p_values	4.5e-11	2.0e-11	✓
conf_int	7.6e-11	7.6e-11	✓
fitted	1.3e-11	4.3e-12	✓
residuals	1.3e-11	4.3e-12	✓
log_likelihood	1.4e-10	1.4e-14	✓
deviance	2.7e-10	0	✓
null_deviance	0	5.7e-14	✓
aic	2.7e-10	2.8e-14	✓
df_residual	0	0	✓

✓ imbalanced 13 quantities worst abs. 1.4e-10

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.0e-10	6.6e-13	✓
covariance	5.7e-11	3.8e-12	✓
std_errors	1.7e-11	1.2e-12	✓
z_statistics	1.0e-10	1.3e-12	✓
p_values	2.0e-11	9.1e-14	✓
conf_int	1.4e-10	2.9e-12	✓
fitted	3.8e-12	3.8e-14	✓
residuals	3.8e-12	3.8e-14	✓
log_likelihood	3.4e-11	3.6e-15	✓
deviance	6.7e-11	7.1e-15	✓
null_deviance	0	1.6e-13	✓
aic	6.7e-11	7.1e-15	✓
df_residual	0	0	✓

✓ listwise_missing 13 quantities worst abs. 3.7e-10

Quantity	Max abs. error	statsmodels	Pass
coefficients	5.9e-11	3.9e-14	✓
covariance	1.9e-11	7.0e-15	✓
std_errors	1.3e-11	6.1e-15	✓
z_statistics	5.6e-11	1.6e-13	✓
p_values	7.1e-12	5.4e-14	✓
conf_int	8.5e-11	4.9e-14	✓
fitted	1.5e-11	1.2e-14	✓
residuals	1.5e-11	1.2e-14	✓
log_likelihood	1.9e-10	1.4e-14	✓
deviance	3.7e-10	2.8e-14	✓
null_deviance	0	2.3e-13	✓
aic	3.7e-10	2.8e-14	✓
df_residual	0	0	✓

Peer columns give the same error measure for statsmodels against the reference.

Poisson regression: agreement with R

91/91 pass

Largest absolute difference from R for every reported quantity, alongside statsmodels. Every case also passes the release gate (scripts/check).

Reference: R version 4.6.1 (2026-06-24), statsmodels 0.15.0, numpy 2.5.4, Python 3.14.7, PHP 8.5.10
Tolerance: release gate: 1e-9 + 1e-7*|reference| (fixed models), 1e-7 + 1e-6*|reference| (mixed models)
Result: 91 of 91 comparisons pass, across 7 cases.

✓ simulated_clinic 13 quantities worst abs. 6.5e-12

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.8e-15	8.9e-16	✓
covariance	6.2e-17	4.2e-17	✓
std_errors	1.4e-16	1.1e-16	✓
z_statistics	8.2e-15	4.9e-15	✓
p_values	6.5e-12	1.3e-15	✓
conf_int	1.9e-15	9.4e-16	✓
fitted	2.2e-15	1.8e-15	✓
residuals	2.2e-15	1.8e-15	✓
log_likelihood	1.1e-13	5.7e-14	✓
deviance	2.8e-14	2.8e-14	✓
null_deviance	0	2.8e-14	✓
aic	2.3e-13	1.1e-13	✓
df_residual	0	0	✓

✓ simple 13 quantities worst abs. 3.0e-11

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.7e-16	6.4e-16	✓
covariance	6.9e-18	4.9e-17	✓
std_errors	2.8e-17	1.1e-16	✓
z_statistics	8.9e-16	3.1e-15	✓
p_values	3.0e-11	1.7e-15	✓
conf_int	2.2e-16	6.9e-16	✓
fitted	4.4e-16	8.9e-16	✓
residuals	8.9e-16	8.9e-16	✓
log_likelihood	8.5e-14	5.7e-14	✓
deviance	0	5.7e-14	✓
null_deviance	0	2.8e-14	✓
aic	1.7e-13	1.1e-13	✓
df_residual	0	0	✓

✓ no_intercept 13 quantities worst abs. 6.2e-13

Quantity	Max abs. error	statsmodels	Pass
coefficients	1.4e-16	8.3e-17	✓
covariance	2.6e-18	8.7e-18	✓
std_errors	1.4e-17	5.6e-17	✓
z_statistics	1.3e-15	1.8e-15	✓
p_values	6.2e-13	2.6e-17	✓
conf_int	1.4e-16	1.1e-16	✓
fitted	3.1e-15	4.4e-15	✓
residuals	3.1e-15	4.4e-15	✓
log_likelihood	1.4e-13	5.7e-14	✓
deviance	0	2.8e-14	✓
null_deviance	5.7e-14	2.8e-14	✓
aic	2.8e-13	1.1e-13	✓
df_residual	0	0	✓

✓ intercept_only 13 quantities worst abs. 5.7e-14

Quantity	Max abs. error	statsmodels	Pass
coefficients	3.3e-16	1.1e-16	✓
covariance	2.6e-18	3.1e-14	✓
std_errors	1.4e-17	2.3e-13	✓
z_statistics	7.1e-15	3.0e-11	✓
p_values	6.3e-29	3.2e-28	✓
conf_int	3.3e-16	4.5e-13	✓
fitted	6.7e-16	2.2e-16	✓
residuals	8.9e-16	2.2e-16	✓
log_likelihood	2.8e-14	1.4e-13	✓
deviance	2.8e-14	0	✓
null_deviance	0	2.8e-14	✓
aic	5.7e-14	2.8e-13	✓
df_residual	0	0	✓

✓ correlated 13 quantities worst abs. 1.1e-11

Quantity	Max abs. error	statsmodels	Pass
coefficients	8.0e-15	5.5e-15	✓
covariance	2.9e-16	3.9e-16	✓
std_errors	6.1e-16	3.2e-16	✓
z_statistics	7.5e-14	5.8e-14	✓
p_values	1.1e-11	1.9e-14	✓
conf_int	8.9e-15	6.0e-15	✓
fitted	5.4e-14	1.7e-13	✓
residuals	5.4e-14	1.7e-13	✓
log_likelihood	1.1e-13	5.7e-14	✓
deviance	8.5e-14	5.7e-14	✓
null_deviance	0	2.8e-14	✓
aic	2.3e-13	1.1e-13	✓
df_residual	0	0	✓

✓ sparse 13 quantities worst abs. 9.9e-13

Quantity	Max abs. error	statsmodels	Pass
coefficients	8.3e-16	6.9e-16	✓
covariance	2.4e-16	5.6e-16	✓
std_errors	1.7e-16	4.4e-16	✓
z_statistics	2.6e-15	2.1e-15	✓
p_values	9.9e-13	1.6e-15	✓
conf_int	1.4e-15	1.3e-15	✓
fitted	6.9e-16	4.2e-16	✓
residuals	6.9e-16	4.2e-16	✓
log_likelihood	2.8e-14	7.1e-15	✓
deviance	0	1.4e-14	✓
null_deviance	0	8.5e-14	✓
aic	5.7e-14	1.4e-14	✓
df_residual	0	0	✓

✓ listwise_missing 13 quantities worst abs. 5.7e-12

Quantity	Max abs. error	statsmodels	Pass
coefficients	3.3e-16	1.3e-15	✓
covariance	3.5e-17	1.2e-16	✓
std_errors	8.3e-17	2.5e-16	✓
z_statistics	3.1e-15	6.7e-15	✓
p_values	5.7e-12	1.7e-15	✓
conf_int	4.4e-16	1.9e-15	✓
fitted	3.1e-15	1.3e-15	✓
residuals	3.1e-15	1.3e-15	✓
log_likelihood	2.8e-14	5.7e-14	✓
deviance	0	0	✓
null_deviance	0	1.1e-13	✓
aic	5.7e-14	1.1e-13	✓
df_residual	0	0	✓

Peer columns give the same error measure for statsmodels against the reference.

Gaussian random intercept: agreement with R

126/126 pass

Largest absolute difference from R for every reported quantity, alongside statsmodels. Every case also passes the release gate (scripts/check).

Reference: R version 4.6.1 (2026-06-24), lme4 2.0.6, statsmodels 0.15.0, PHP 8.5.10, Python 3.14.7
Tolerance: release gate: 1e-9 + 1e-7*|reference| (fixed models), 1e-7 + 1e-6*|reference| (mixed models)
Result: 126 of 126 comparisons pass, across 7 cases.

✓ simulated_schools 18 quantities worst abs. 4.8e-7

Quantity	Max abs. error	Python	Pass
coefficients	2.5e-9	2.5e-9	✓
covariance	3.6e-8	3.6e-8	✓
std_errors	8.2e-9	8.2e-9	✓
z_statistics	7.7e-8	7.7e-8	✓
p_values	5.3e-17	5.3e-17	✓
conf_int	1.9e-8	1.9e-8	✓
fixed_fitted	1.4e-9	1.4e-9	✓
fitted	2.1e-8	2.0e-8	✓
residuals	2.1e-8	2.0e-8	✓
marginal_residuals	1.4e-9	1.4e-9	✓
random_effects	2.0e-8	2.0e-8	✓
residual_variance	3.1e-8	3.1e-8	✓
random_intercept_variance	4.8e-7	4.8e-7	✓
sigma	3.1e-9	3.1e-9	✓
icc	6.7e-9	6.7e-9	✓
log_likelihood	0	1.1e-13	✓
aic	0	2.3e-13	✓
df_residual	0	0	✓

✓ simple 18 quantities worst abs. 1.5e-6

Quantity	Max abs. error	Python	Pass
coefficients	1.9e-9	1.9e-9	✓
covariance	1.2e-7	1.2e-7	✓
std_errors	4.1e-8	4.1e-8	✓
z_statistics	1.0e-6	1.0e-6	✓
p_values	2.6e-109	2.6e-109	✓
conf_int	8.2e-8	8.1e-8	✓
fixed_fitted	1.7e-9	1.6e-9	✓
fitted	6.2e-8	6.2e-8	✓
residuals	6.2e-8	6.2e-8	✓
marginal_residuals	1.7e-9	1.6e-9	✓
random_effects	6.1e-8	6.0e-8	✓
residual_variance	1.1e-7	1.1e-7	✓
random_intercept_variance	1.5e-6	1.5e-6	✓
sigma	9.9e-9	9.8e-9	✓
icc	2.0e-8	1.9e-8	✓
log_likelihood	1.1e-13	2.3e-13	✓
aic	2.3e-13	4.5e-13	✓
df_residual	0	0	✓

✓ no_intercept 18 quantities worst abs. 1.6e-4

Quantity	Max abs. error	Python	Pass
coefficients	2.8e-9	2.9e-9	✓
covariance	8.9e-11	9.1e-11	✓
std_errors	2.8e-10	2.8e-10	✓
z_statistics	3.5e-8	3.6e-8	✓
p_values	4.7e-17	4.8e-17	✓
conf_int	3.4e-9	3.4e-9	✓
fixed_fitted	9.7e-8	9.9e-8	✓
fitted	4.1e-8	4.2e-8	✓
residuals	4.1e-8	4.2e-8	✓
marginal_residuals	9.7e-8	9.9e-8	✓
random_effects	7.3e-8	7.5e-8	✓
residual_variance	9.6e-8	9.9e-8	✓
random_intercept_variance	1.6e-4	1.6e-4	✓
sigma	9.6e-9	9.8e-9	✓
icc	9.2e-10	9.5e-10	✓
log_likelihood	1.1e-13	0	✓
aic	2.3e-13	0	✓
df_residual	0	0	✓

✓ intercept_only 18 quantities worst abs. 4.1e-7

Quantity	Max abs. error	Python	Pass
coefficients	6.6e-11	6.6e-11	✓
covariance	3.4e-8	3.4e-8	✓
std_errors	1.2e-8	1.2e-8	✓
z_statistics	4.0e-7	4.0e-7	✓
p_values	0	0	✓
conf_int	2.3e-8	2.3e-8	✓
fixed_fitted	6.6e-11	6.6e-11	✓
fitted	3.3e-8	3.3e-8	✓
residuals	3.3e-8	3.3e-8	✓
marginal_residuals	6.6e-11	6.6e-11	✓
random_effects	3.3e-8	3.3e-8	✓
residual_variance	6.9e-8	6.9e-8	✓
random_intercept_variance	4.1e-7	4.1e-7	✓
sigma	3.7e-9	3.7e-9	✓
icc	3.2e-9	3.2e-9	✓
log_likelihood	0	1.1e-13	✓
aic	0	2.3e-13	✓
df_residual	0	0	✓

✓ singleton_groups 18 quantities worst abs. 5.8e-7

Quantity	Max abs. error	Python	Pass
coefficients	1.6e-9	1.6e-9	✓
covariance	4.1e-8	4.1e-8	✓
std_errors	9.4e-9	9.4e-9	✓
z_statistics	9.2e-8	9.2e-8	✓
p_values	7.5e-17	7.5e-17	✓
conf_int	2.0e-8	2.0e-8	✓
fixed_fitted	4.8e-9	4.8e-9	✓
fitted	5.0e-8	5.1e-8	✓
residuals	5.0e-8	5.1e-8	✓
marginal_residuals	4.8e-9	4.8e-9	✓
random_effects	4.7e-8	4.7e-8	✓
residual_variance	4.0e-8	4.0e-8	✓
random_intercept_variance	5.8e-7	5.8e-7	✓
sigma	3.9e-9	3.9e-9	✓
icc	8.2e-9	8.2e-9	✓
log_likelihood	0	1.1e-13	✓
aic	0	2.3e-13	✓
df_residual	0	0	✓

✓ boundary 18 quantities worst abs. 7.1e-15

Quantity	Max abs. error	Python	Pass
coefficients	6.4e-17	7.1e-19	✓
covariance	6.9e-18	0	✓
std_errors	2.8e-17	0	✓
z_statistics	2.7e-16	3.0e-18	✓
p_values	2.2e-16	0	✓
conf_int	1.1e-16	1.7e-16	✓
fixed_fitted	6.4e-17	7.1e-19	✓
fitted	6.4e-17	7.1e-19	✓
residuals	1.1e-16	7.1e-19	✓
marginal_residuals	1.1e-16	7.1e-19	✓
random_effects	0	0	✓
residual_variance	0	0	✓
random_intercept_variance	0	0	✓
sigma	0	0	✓
icc	0	0	✓
log_likelihood	3.6e-15	1.8e-15	✓
aic	7.1e-15	7.1e-15	✓
df_residual	0	0	✓

✓ listwise_missing 18 quantities worst abs. 1.1e-6

Quantity	Max abs. error	Python	Pass
coefficients	6.3e-9	6.3e-9	✓
covariance	8.5e-8	8.5e-8	✓
std_errors	1.9e-8	1.9e-8	✓
z_statistics	1.8e-7	1.8e-7	✓
p_values	1.6e-16	1.6e-16	✓
conf_int	4.4e-8	4.4e-8	✓
fixed_fitted	3.4e-9	3.4e-9	✓
fitted	4.8e-8	4.8e-8	✓
residuals	4.8e-8	4.8e-8	✓
marginal_residuals	3.4e-9	3.4e-9	✓
random_effects	4.6e-8	4.6e-8	✓
residual_variance	7.5e-8	7.5e-8	✓
random_intercept_variance	1.1e-6	1.1e-6	✓
sigma	7.4e-9	7.4e-9	✓
icc	1.6e-8	1.6e-8	✓
log_likelihood	2.3e-13	3.4e-13	✓
aic	4.5e-13	6.8e-13	✓
df_residual	0	0	✓

Peer columns give the same error measure for Python against the reference.

Mixed models on published data sets: agreement with R

72/72 pass

Largest absolute difference from R for every reported quantity, alongside nlme and statsmodels. Every case also passes the release gate (scripts/check).

Reference: R version 4.6.1 (2026-06-24), lme4 2.0.6, statsmodels 0.15.0, PHP 8.5.10, Python 3.14.7, nlme 3.1.169
Tolerance: release gate: 1e-9 + 1e-7*|reference| (fixed models), 1e-7 + 1e-6*|reference| (mixed models)
Result: 72 of 72 comparisons pass, across 4 cases.

✓ sleepstudy 18 quantities worst abs. 1.5e-5

Quantity	Max abs. error	nlme	Python	Pass
coefficients	1.3e-12	1.2e-12	4.8e-13	✓
covariance	8.3e-7	6.3e-7	8.4e-7	✓
std_errors	4.4e-8	3.3e-8	4.4e-8	✓
z_statistics	1.2e-7	9.2e-8	1.2e-7	✓
p_values	6.1e-46	4.6e-46	6.2e-46	✓
conf_int	8.6e-8	6.5e-8	8.6e-8	✓
fixed_fitted	1.3e-12	1.2e-12	4.8e-13	✓
fitted	7.0e-8	5.2e-8	7.0e-8	✓
residuals	7.0e-8	5.2e-8	7.0e-8	✓
marginal_residuals	1.3e-12	1.2e-12	4.8e-13	✓
random_effects	7.0e-8	5.2e-8	7.0e-8	✓
residual_variance	1.2e-6	8.7e-7	1.2e-6	✓
random_intercept_variance	1.5e-5	1.2e-5	1.5e-5	✓
sigma	1.9e-8	1.4e-8	1.9e-8	✓
icc	3.2e-9	2.4e-9	3.2e-9	✓
log_likelihood	1.1e-13	2.3e-13	1.1e-13	✓
aic	2.3e-13	4.5e-13	2.3e-13	✓
df_residual	0	0	0	✓

✓ Orthodont 18 quantities worst abs. 5.8e-8

Quantity	Max abs. error	nlme	Python	Pass
coefficients	1.2e-13	1.3e-13	1.8e-13	✓
covariance	8.3e-10	5.1e-9	8.3e-10	✓
std_errors	3.1e-10	2.0e-9	3.1e-10	✓
z_statistics	2.7e-8	1.7e-7	2.7e-8	✓
p_values	2.1e-10	1.3e-9	2.1e-10	✓
conf_int	6.2e-10	3.8e-9	6.2e-10	✓
fixed_fitted	3.6e-14	4.3e-14	6.4e-14	✓
fitted	1.3e-8	7.9e-8	1.3e-8	✓
residuals	1.3e-8	7.9e-8	1.3e-8	✓
marginal_residuals	3.6e-14	4.3e-14	6.4e-14	✓
random_effects	1.3e-8	7.9e-8	1.3e-8	✓
residual_variance	9.8e-9	6.1e-8	9.8e-9	✓
random_intercept_variance	5.8e-8	3.6e-7	5.8e-8	✓
sigma	3.6e-9	2.2e-8	3.6e-9	✓
icc	5.7e-9	3.5e-8	5.7e-9	✓
log_likelihood	8.5e-14	1.7e-13	1.1e-13	✓
aic	1.7e-13	3.4e-13	2.3e-13	✓
df_residual	0	0	0	✓

✓ Machines 18 quantities worst abs. 3.6e-7

Quantity	Max abs. error	nlme	Python	Pass
coefficients	7.8e-14	8.9e-15	7.1e-14	✓
covariance	6.0e-8	1.6e-7	5.9e-8	✓
std_errors	1.5e-8	3.9e-8	1.4e-8	✓
z_statistics	1.8e-7	4.9e-7	1.8e-7	✓
p_values	6.8e-22	1.8e-21	6.8e-22	✓
conf_int	2.9e-8	7.7e-8	2.8e-8	✓
fixed_fitted	8.5e-14	1.4e-14	7.1e-14	✓
fitted	7.4e-9	2.0e-8	7.4e-9	✓
residuals	7.4e-9	2.0e-8	7.4e-9	✓
marginal_residuals	8.5e-14	1.4e-14	7.1e-14	✓
random_effects	7.4e-9	2.0e-8	7.4e-9	✓
residual_variance	1.9e-8	5.0e-8	1.9e-8	✓
random_intercept_variance	3.6e-7	9.8e-7	3.6e-7	✓
sigma	3.0e-9	8.2e-9	3.0e-9	✓
icc	3.9e-9	1.1e-8	3.9e-9	✓
log_likelihood	2.8e-14	0	2.8e-14	✓
aic	5.7e-14	0	5.7e-14	✓
df_residual	0	0	0	✓

✓ Hsb82 18 quantities worst abs. 2.7e-6

Quantity	Max abs. error	nlme	Python	Pass
coefficients	5.4e-9	9.8e-9	5.4e-9	✓
covariance	1.2e-8	2.2e-8	1.2e-8	✓
std_errors	1.6e-8	2.9e-8	1.6e-8	✓
z_statistics	2.7e-6	4.9e-6	2.7e-6	✓
p_values	4.2e-11	7.7e-11	4.2e-11	✓
conf_int	3.6e-8	6.6e-8	3.6e-8	✓
fixed_fitted	6.5e-9	1.2e-8	6.5e-9	✓
fitted	2.4e-7	4.4e-7	2.4e-7	✓
residuals	2.4e-7	4.4e-7	2.4e-7	✓
marginal_residuals	6.5e-9	1.2e-8	6.5e-9	✓
random_effects	2.4e-7	4.4e-7	2.4e-7	✓
residual_variance	7.5e-8	1.4e-7	7.5e-8	✓
random_intercept_variance	2.9e-7	5.2e-7	2.9e-7	✓
sigma	6.2e-9	1.1e-8	6.2e-9	✓
icc	7.0e-9	1.3e-8	7.0e-9	✓
log_likelihood	7.3e-12	3.6e-12	7.3e-12	✓
aic	1.5e-11	7.3e-12	1.5e-11	✓
df_residual	0	0	0	✓

Peer columns give the same error measure for nlme and Python against the reference.

Binomial random intercept: agreement with lme4

28/28 pass

Largest coefficient difference from lme4::glmer for Laplace and adaptive quadrature fits.

Reference: R version 4.6.1 (2026-06-24), lme4 2.0.6, PHP 8.5.10, python 3.14.7, numpy 2.5.4, scipy 1.18.1, statsmodels 0.15.0
Tolerance: 2e-05 + 0.0002*|reference|
Result: 28 of 28 comparisons pass, across 28 cases.

✓ binary_1 1 quantity worst abs. 3.1e-7

Quantity	Max abs. error	Pass
coefficients	3.1e-7	✓

✓ binary_9 1 quantity worst abs. 8.4e-8

Quantity	Max abs. error	Pass
coefficients	8.4e-8	✓

✓ binary_25 1 quantity worst abs. 1.3e-7

Quantity	Max abs. error	Pass
coefficients	1.3e-7	✓

✓ binary_61 1 quantity worst abs. 4.0e-8

Quantity	Max abs. error	Pass
coefficients	4.0e-8	✓

✓ no_intercept_1 1 quantity worst abs. 3.0e-8

Quantity	Max abs. error	Pass
coefficients	3.0e-8	✓

✓ no_intercept_9 1 quantity worst abs. 7.6e-9

Quantity	Max abs. error	Pass
coefficients	7.6e-9	✓

✓ no_intercept_25 1 quantity worst abs. 2.7e-8

Quantity	Max abs. error	Pass
coefficients	2.7e-8	✓

✓ no_intercept_61 1 quantity worst abs. 2.2e-8

Quantity	Max abs. error	Pass
coefficients	2.2e-8	✓

✓ grouped_offset_1 1 quantity worst abs. 1.8e-6

Quantity	Max abs. error	Pass
coefficients	1.8e-6	✓

✓ grouped_offset_9 1 quantity worst abs. 1.4e-6

Quantity	Max abs. error	Pass
coefficients	1.4e-6	✓

✓ grouped_offset_25 1 quantity worst abs. 7.4e-7

Quantity	Max abs. error	Pass
coefficients	7.4e-7	✓

✓ grouped_offset_61 1 quantity worst abs. 8.2e-8

Quantity	Max abs. error	Pass
coefficients	8.2e-8	✓

✓ rare_events_1 1 quantity worst abs. 1.2e-6

Quantity	Max abs. error	Pass
coefficients	1.2e-6	✓

✓ rare_events_9 1 quantity worst abs. 4.1e-8

Quantity	Max abs. error	Pass
coefficients	4.1e-8	✓

✓ rare_events_25 1 quantity worst abs. 1.3e-7

Quantity	Max abs. error	Pass
coefficients	1.3e-7	✓

✓ rare_events_61 1 quantity worst abs. 2.8e-8

Quantity	Max abs. error	Pass
coefficients	2.8e-8	✓

✓ large_group_variation_1 1 quantity worst abs. 1.5e-6

Quantity	Max abs. error	Pass
coefficients	1.5e-6	✓

✓ large_group_variation_9 1 quantity worst abs. 5.2e-8

Quantity	Max abs. error	Pass
coefficients	5.2e-8	✓

✓ large_group_variation_25 1 quantity worst abs. 4.2e-8

Quantity	Max abs. error	Pass
coefficients	4.2e-8	✓

✓ large_group_variation_61 1 quantity worst abs. 4.6e-8

Quantity	Max abs. error	Pass
coefficients	4.6e-8	✓

✓ boundary_1 1 quantity worst abs. 8.2e-9

Quantity	Max abs. error	Pass
coefficients	8.2e-9	✓

✓ boundary_9 1 quantity worst abs. 4.8e-9

Quantity	Max abs. error	Pass
coefficients	4.8e-9	✓

✓ boundary_25 1 quantity worst abs. 4.8e-9

Quantity	Max abs. error	Pass
coefficients	4.8e-9	✓

✓ boundary_61 1 quantity worst abs. 4.8e-9

Quantity	Max abs. error	Pass
coefficients	4.8e-9	✓

✓ cbpp_1 1 quantity worst abs. 7.6e-8

Quantity	Max abs. error	Pass
coefficients	7.6e-8	✓

✓ cbpp_9 1 quantity worst abs. 5.2e-8

Quantity	Max abs. error	Pass
coefficients	5.2e-8	✓

✓ cbpp_25 1 quantity worst abs. 7.1e-8

Quantity	Max abs. error	Pass
coefficients	7.1e-8	✓

✓ cbpp_61 1 quantity worst abs. 8.6e-8

Quantity	Max abs. error	Pass
coefficients	8.6e-8	✓

Weights, offsets and mixed models: agreement with R and lme4

372/372 pass

Weighted and offset GLMs against base R, and mixed models against all four lme4 optimizers.

Reference: R version 4.6.1 (2026-06-24), lme4 2.0.6, PHP 8.5.10, python 3.14.7, numpy 2.5.4, scipy 1.18.1, statsmodels 0.15.0
Tolerance: fixed: 1e-07 + 1e-06*|reference|; mixed_bobyqa: 1e-05 + 1e-05*|reference|; mixed_other_optimizers: 0.001 + 0.0003*|reference|; mixed_likelihood: 5e-06 + 1e-09*|reference|
Result: 372 of 372 comparisons pass, across 27 cases.

✓ ols_intercept_individual 1 quantity worst abs. 4.5e-13

Quantity	Max abs. error	Pass
ols: all quantities	4.5e-13	✓

✓ ols_no_intercept_individual 1 quantity worst abs. 1.1e-11

Quantity	Max abs. error	Pass
ols: all quantities	1.1e-11	✓

✓ logistic_intercept_individual 1 quantity worst abs. 1.4e-6

Quantity	Max abs. error	Pass
logistic: all quantities	1.4e-6	✓

✓ logistic_intercept_grouped 1 quantity worst abs. 2.1e-11

Quantity	Max abs. error	Pass
logistic: all quantities	2.1e-11	✓

✓ logistic_no_intercept_individual 1 quantity worst abs. 8.9e-7

Quantity	Max abs. error	Pass
logistic: all quantities	8.9e-7	✓

✓ logistic_no_intercept_grouped 1 quantity worst abs. 1.0e-6

Quantity	Max abs. error	Pass
logistic: all quantities	1.0e-6	✓

✓ probit_intercept_individual 1 quantity worst abs. 1.6e-6

Quantity	Max abs. error	Pass
probit: all quantities	1.6e-6	✓

✓ probit_intercept_grouped 1 quantity worst abs. 1.1e-7

Quantity	Max abs. error	Pass
probit: all quantities	1.1e-7	✓

✓ probit_no_intercept_individual 1 quantity worst abs. 6.0e-7

Quantity	Max abs. error	Pass
probit: all quantities	6.0e-7	✓

✓ probit_no_intercept_grouped 1 quantity worst abs. 6.6e-7

Quantity	Max abs. error	Pass
probit: all quantities	6.6e-7	✓

✓ poisson_intercept_individual 1 quantity worst abs. 3.9e-6

Quantity	Max abs. error	Pass
poisson: all quantities	3.9e-6	✓

✓ poisson_no_intercept_individual 1 quantity worst abs. 1.9e-8

Quantity	Max abs. error	Pass
poisson: all quantities	1.9e-8	✓

✓ random_slopes_ml (ML) 24 quantities worst abs. 1.0e-5

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	5.7e-14	✓
phit bobyqa vs lme4 bobyqa: max fitted	3.8e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	1.1e-8	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.3e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	3.1e-7	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	2.4e-7	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	1.6e-10	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	5.4e-6	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	1.6e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	1.5e-10	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	5.0e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	1.4e-6	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	4.0e-12	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	6.0e-7	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.1e-6	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	2.8e-12	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	9.4e-7	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	9.2e-7	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	5.7e-10	✓
phit bobyqa vs lme4 nloptwrap: max fitted	9.9e-6	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	9.0e-6	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	5.7e-10	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	1.0e-5	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	8.8e-6	✓

✓ random_slopes_reml (REML) 24 quantities worst abs. 4.7e-4

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	5.7e-14	✓
phit bobyqa vs lme4 bobyqa: max fitted	2.6e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	2.6e-8	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.5e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	3.1e-7	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	7.6e-7	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	5.6e-11	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	9.0e-7	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	5.4e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	5.4e-11	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	8.6e-7	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	6.1e-6	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	6.6e-11	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	3.4e-6	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	3.6e-6	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	6.4e-11	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	3.6e-6	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	4.4e-6	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	4.3e-7	✓
phit bobyqa vs lme4 nloptwrap: max fitted	7.3e-5	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	4.7e-4	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	4.3e-7	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	7.3e-5	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	4.7e-4	✓

✓ independent_slopes (ML) 24 quantities worst abs. 1.4e-4

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	5.7e-14	✓
phit bobyqa vs lme4 bobyqa: max fitted	9.6e-9	✓
phit bobyqa vs lme4 bobyqa: max random covariance	4.3e-8	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	5.1e-13	✓
phit nelder_mead vs lme4 bobyqa: max fitted	7.8e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	4.3e-7	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	8.4e-10	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.4e-5	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	5.1e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	8.4e-10	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	1.4e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	4.6e-6	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	6.2e-8	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	6.9e-5	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.4e-4	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	6.2e-8	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	6.8e-5	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.4e-4	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	5.1e-13	✓
phit bobyqa vs lme4 nloptwrap: max fitted	3.5e-7	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	1.8e-7	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	5.7e-14	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	3.4e-7	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	6.6e-7	✓

✓ crossed (ML) 24 quantities worst abs. 1.9e-5

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	2.8e-14	✓
phit bobyqa vs lme4 bobyqa: max fitted	3.1e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	5.8e-8	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	3.8e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	9.5e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	1.1e-6	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	2.4e-10	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	6.5e-7	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	9.6e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	2.4e-10	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	6.2e-7	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	9.8e-6	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	1.6e-8	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	1.8e-5	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.7e-5	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	1.6e-8	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	1.9e-5	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.7e-5	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	8.3e-10	✓
phit bobyqa vs lme4 nloptwrap: max fitted	1.2e-6	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	1.4e-5	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	8.3e-10	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	1.1e-6	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	1.4e-5	✓

✓ nested (ML) 24 quantities worst abs. 4.7e-6

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	8.5e-14	✓
phit bobyqa vs lme4 bobyqa: max fitted	4.3e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	8.2e-8	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	6.5e-13	✓
phit nelder_mead vs lme4 bobyqa: max fitted	7.9e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	1.7e-7	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	1.1e-10	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.1e-6	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	2.9e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	1.1e-10	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	9.8e-7	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	3.0e-6	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	1.2e-11	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	1.9e-7	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	2.3e-6	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	1.1e-11	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	9.5e-8	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	2.3e-6	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	5.4e-11	✓
phit bobyqa vs lme4 nloptwrap: max fitted	4.3e-7	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	4.7e-6	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	5.4e-11	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	5.4e-7	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	4.6e-6	✓

✓ weighted_offset (REML) 24 quantities worst abs. 4.9e-5

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	0	✓
phit bobyqa vs lme4 bobyqa: max fitted	1.8e-7	✓
phit bobyqa vs lme4 bobyqa: max random covariance	3.4e-8	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	6.5e-13	✓
phit nelder_mead vs lme4 bobyqa: max fitted	3.6e-7	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	4.4e-7	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	1.4e-11	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.6e-6	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	6.6e-7	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	1.4e-11	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	1.4e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	4.8e-7	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	4.0e-9	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	4.9e-5	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	5.1e-6	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	4.0e-9	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	4.9e-5	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	5.1e-6	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	6.1e-11	✓
phit bobyqa vs lme4 nloptwrap: max fitted	4.1e-6	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	4.5e-6	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	6.1e-11	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	4.3e-6	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	4.0e-6	✓

✓ no_intercept (ML) 24 quantities worst abs. 1.5e-4

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	0	✓
phit bobyqa vs lme4 bobyqa: max fitted	5.5e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	6.1e-7	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	5.7e-14	✓
phit nelder_mead vs lme4 bobyqa: max fitted	7.2e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	1.4e-7	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	3.4e-11	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.5e-6	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	1.7e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	3.4e-11	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	1.6e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	1.6e-5	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	2.2e-9	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	8.8e-6	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.5e-4	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	2.2e-9	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	8.9e-6	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.5e-4	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	2.1e-11	✓
phit bobyqa vs lme4 nloptwrap: max fitted	1.9e-6	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	3.4e-6	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	2.0e-11	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	1.9e-6	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	3.3e-6	✓

✓ random_slope_only (ML) 24 quantities worst abs. 1.9e-5

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	5.7e-14	✓
phit bobyqa vs lme4 bobyqa: max fitted	5.6e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	1.5e-8	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.7e-13	✓
phit nelder_mead vs lme4 bobyqa: max fitted	3.0e-7	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	8.3e-8	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	6.6e-10	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.9e-5	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	5.1e-6	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	6.6e-10	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	1.9e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	5.0e-6	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	2.0e-11	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	3.3e-6	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	8.9e-7	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	2.0e-11	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	3.0e-6	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	8.2e-7	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	1.3e-12	✓
phit bobyqa vs lme4 nloptwrap: max fitted	8.3e-7	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	2.3e-7	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	1.1e-12	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	1.1e-6	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	2.9e-7	✓

✓ sleepstudy_ml (ML) 24 quantities worst abs. 3.8e-2

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	0	✓
phit bobyqa vs lme4 bobyqa: max fitted	2.3e-6	✓
phit bobyqa vs lme4 bobyqa: max random covariance	2.7e-5	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.5e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	8.2e-6	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	4.7e-5	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	1.9e-10	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	6.2e-5	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	3.3e-3	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	1.9e-10	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	5.8e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	3.3e-3	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	3.9e-11	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	2.8e-5	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.8e-3	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	3.8e-11	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	3.1e-5	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.8e-3	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	1.3e-8	✓
phit bobyqa vs lme4 nloptwrap: max fitted	6.6e-4	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	3.8e-2	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	1.3e-8	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	6.5e-4	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	3.8e-2	✓

✓ sleepstudy_reml (REML) 24 quantities worst abs. 1.0e-2

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	1.1e-13	✓
phit bobyqa vs lme4 bobyqa: max fitted	3.7e-6	✓
phit bobyqa vs lme4 bobyqa: max random covariance	2.3e-4	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.5e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	8.5e-6	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	2.9e-4	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	4.7e-10	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.1e-4	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	7.5e-3	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	4.7e-10	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	1.1e-4	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	7.5e-3	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	6.8e-10	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	1.8e-4	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.6e-3	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	6.8e-10	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	1.7e-4	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.6e-3	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	7.3e-10	✓
phit bobyqa vs lme4 nloptwrap: max fitted	1.6e-4	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	1.0e-2	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	7.3e-10	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	1.6e-4	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	1.0e-2	✓

✓ boundary (REML) 24 quantities worst abs. 1.4e-14

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	1.4e-14	✓
phit bobyqa vs lme4 bobyqa: max fitted	1.9e-16	✓
phit bobyqa vs lme4 bobyqa: max random covariance	0	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.4e-14	✓
phit nelder_mead vs lme4 bobyqa: max fitted	1.9e-16	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	0	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	1.4e-14	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.9e-16	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	0	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	1.4e-14	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	1.9e-16	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	0	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	1.4e-14	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	1.9e-16	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	0	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	1.4e-14	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	1.9e-16	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	0	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	1.4e-14	✓
phit bobyqa vs lme4 nloptwrap: max fitted	1.9e-16	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	0	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	1.4e-14	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	1.9e-16	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	0	✓

✓ nested_3_grouping_levels_ml (ML) 24 quantities worst abs. 1.8e-3

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	7.4e-13	✓
phit bobyqa vs lme4 bobyqa: max fitted	6.6e-9	✓
phit bobyqa vs lme4 bobyqa: max random covariance	9.9e-6	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.7e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	1.8e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	2.9e-6	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	1.3e-11	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	1.4e-7	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	2.3e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	1.2e-11	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	1.6e-7	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	3.2e-5	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	2.1e-8	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	1.3e-6	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.8e-3	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	2.1e-8	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	1.4e-6	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.8e-3	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	1.1e-11	✓
phit bobyqa vs lme4 nloptwrap: max fitted	5.6e-8	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	5.6e-5	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	9.9e-12	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	7.6e-8	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	6.5e-5	✓

✓ nested_4_grouping_levels_ml (ML) 24 quantities worst abs. 1.7e-4

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	8.5e-13	✓
phit bobyqa vs lme4 bobyqa: max fitted	1.5e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	3.5e-5	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.4e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	7.6e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	2.2e-5	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	5.9e-12	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	8.1e-8	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	3.8e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	3.6e-12	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	4.3e-8	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	2.5e-5	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	1.7e-10	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	5.2e-7	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.4e-4	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	1.7e-10	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	4.7e-7	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.5e-4	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	2.5e-10	✓
phit bobyqa vs lme4 nloptwrap: max fitted	6.2e-7	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	1.7e-4	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	2.5e-10	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	6.6e-7	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	1.6e-4	✓

✓ nested_3_grouping_levels_reml (REML) 24 quantities worst abs. 1.2e-3

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	2.2e-12	✓
phit bobyqa vs lme4 bobyqa: max fitted	1.2e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	9.3e-7	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	4.7e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	5.1e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	2.9e-5	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	4.8e-12	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	9.0e-8	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	1.5e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	2.3e-12	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	5.3e-8	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	4.4e-5	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	8.1e-9	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	2.1e-6	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	1.0e-3	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	8.1e-9	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	2.2e-6	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	1.0e-3	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	2.6e-9	✓
phit bobyqa vs lme4 nloptwrap: max fitted	3.9e-7	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	1.2e-3	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	2.6e-9	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	3.9e-7	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	1.2e-3	✓

✓ nested_4_grouping_levels_reml (REML) 24 quantities worst abs. 2.1e-4

Quantity	Max abs. error	Pass
phit bobyqa vs lme4 bobyqa: log likelihood	8.0e-13	✓
phit bobyqa vs lme4 bobyqa: max fitted	2.2e-8	✓
phit bobyqa vs lme4 bobyqa: max random covariance	2.6e-5	✓
phit nelder_mead vs lme4 bobyqa: log likelihood	1.6e-12	✓
phit nelder_mead vs lme4 bobyqa: max fitted	6.8e-8	✓
phit nelder_mead vs lme4 bobyqa: max random covariance	2.5e-5	✓
phit bobyqa vs lme4 Nelder_Mead: log likelihood	9.4e-12	✓
phit bobyqa vs lme4 Nelder_Mead: max fitted	7.3e-8	✓
phit bobyqa vs lme4 Nelder_Mead: max random covariance	6.0e-5	✓
phit nelder_mead vs lme4 Nelder_Mead: log likelihood	8.5e-12	✓
phit nelder_mead vs lme4 Nelder_Mead: max fitted	3.5e-8	✓
phit nelder_mead vs lme4 Nelder_Mead: max random covariance	5.8e-5	✓
phit bobyqa vs lme4 nlminbwrap: log likelihood	1.6e-10	✓
phit bobyqa vs lme4 nlminbwrap: max fitted	4.6e-7	✓
phit bobyqa vs lme4 nlminbwrap: max random covariance	2.1e-4	✓
phit nelder_mead vs lme4 nlminbwrap: log likelihood	1.6e-10	✓
phit nelder_mead vs lme4 nlminbwrap: max fitted	4.2e-7	✓
phit nelder_mead vs lme4 nlminbwrap: max random covariance	2.1e-4	✓
phit bobyqa vs lme4 nloptwrap: log likelihood	3.8e-10	✓
phit bobyqa vs lme4 nloptwrap: max fitted	8.4e-7	✓
phit bobyqa vs lme4 nloptwrap: max random covariance	2.0e-4	✓
phit nelder_mead vs lme4 nloptwrap: log likelihood	3.8e-10	✓
phit nelder_mead vs lme4 nloptwrap: max fitted	8.8e-7	✓
phit nelder_mead vs lme4 nloptwrap: max random covariance	2.1e-4	✓

Distributions: accuracy against 60-digit references

553/553 pass

Relative error vs the rounded mpmath reference; for log values and quantiles the denominator is max(|reference|, 1) and max(|reference|, 1e-300). R and SciPy errors are shown for comparison.

Reference: mpmath (60 digits); R R version 4.6.1 (2026-06-24); SciPy 1.18.1
Tolerance: 1e-12 relative
Result: 553 of 553 comparisons pass, across 79 cases.

✓ normal(mean=0, sd=1) 7 quantities worst rel. 6.7e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	28	1.6e-16	1.6e-16	2.4e-16	✓
logpdf	28	0	0	1.6e-16	✓
cdf	28	2.8e-16	2.8e-16	1.1e-13	✓
logcdf	28	1.5e-16	1.1e-16	3.0e-16	✓
sf	28	2.8e-16	2.8e-16	1.1e-13	✓
logsf	28	1.5e-16	6.9e-18	3.0e-16	✓
quantile	15	6.7e-16	2.3e-16	2.2e-16	✓

✓ normal(mean=3, sd=2) 7 quantities worst rel. 1.8e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	28	1.8e-14	2.2e-16	2.4e-16	✓
logpdf	28	1.5e-16	1.5e-16	0	✓
cdf	28	2.8e-16	2.8e-16	1.1e-13	✓
logcdf	28	1.5e-16	1.1e-16	3.0e-16	✓
sf	28	2.8e-16	2.8e-16	1.1e-13	✓
logsf	28	1.5e-16	6.9e-18	3.0e-16	✓
quantile	15	1.3e-15	8.4e-16	6.0e-16	✓

✓ normal(mean=1000000, sd=1000) 7 quantities worst rel. 8.3e-15

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	28	8.3e-15	2.3e-16	3.5e-16	✓
logpdf	28	1.8e-16	1.8e-16	1.8e-16	✓
cdf	28	2.8e-16	2.8e-16	1.1e-13	✓
logcdf	28	1.5e-16	1.2e-16	3.0e-16	✓
sf	28	2.8e-16	2.8e-16	1.1e-13	✓
logsf	28	1.5e-16	1.2e-16	3.0e-16	✓
quantile	15	0	0	0	✓

✓ normal(mean=-2, sd=1e-08) 7 quantities worst rel. 2.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	28	2.8e-14	4.2e-9	4.3e-10	✓
logpdf	28	3.6e-16	3.6e-16	3.6e-16	✓
cdf	28	2.9e-14	2.9e-14	1.4e-13	✓
logcdf	28	1.6e-16	1.6e-16	3.3e-16	✓
sf	28	2.9e-14	2.9e-14	1.4e-13	✓
logsf	28	1.6e-16	1.6e-16	3.3e-16	✓
quantile	15	0	0	0	✓

✓ t(df=0.5) 7 quantities worst rel. 9.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	1.2e-15	1.1e-15	5.1e-16	✓
logpdf	19	2.0e-16	2.0e-16	1.7e-16	✓
cdf	19	2.8e-16	2.8e-16	2.2e-16	✓
logcdf	19	1.9e-16	1.9e-16	1.9e-16	✓
sf	19	2.4e-16	2.4e-16	3.8e-16	✓
logsf	19	1.9e-16	1.5e-16	1.9e-16	✓
quantile	15	9.2e-14	2.6e+284	1.0e+0	✓

✓ t(df=1) 7 quantities worst rel. 8.4e-15

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	1.5e-15	2.0e-15	1.5e-15	✓
logpdf	19	1.9e-16	1.7e-16	1.9e-16	✓
cdf	19	8.9e-16	8.9e-16	3.1e-9	✓
logcdf	19	6.4e-16	8.0e-16	3.1e-9	✓
sf	19	8.9e-16	8.9e-16	3.1e-9	✓
logsf	19	6.4e-16	8.0e-16	3.1e-9	✓
quantile	15	8.4e-15	1.8e-16	1.5e-16	✓

✓ t(df=2) 7 quantities worst rel. 6.0e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	4.1e-15	6.4e-16	4.1e-15	✓
logpdf	19	2.1e-16	2.1e-16	2.1e-16	✓
cdf	19	3.5e-16	1.8e-16	2.1e-16	✓
logcdf	19	2.8e-17	3.0e-16	1.6e-16	✓
sf	19	2.7e-16	1.6e-16	2.0e-16	✓
logsf	19	1.1e-16	3.0e-16	1.4e-16	✓
quantile	15	6.0e-14	2.1e-16	2.1e-16	✓

✓ t(df=3.5) 7 quantities worst rel. 1.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	3.6e-15	2.5e-15	3.6e-15	✓
logpdf	19	1.4e-16	1.9e-16	1.4e-16	✓
cdf	19	7.1e-15	7.1e-15	2.7e-16	✓
logcdf	19	2.7e-16	2.7e-16	1.1e-16	✓
sf	19	7.1e-15	7.1e-15	4.2e-16	✓
logsf	19	2.7e-16	1.8e-16	1.1e-16	✓
quantile	15	1.2e-14	4.4e-8	Inf	✓

✓ t(df=12) 7 quantities worst rel. 3.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	3.9e-14	7.9e-15	3.9e-14	✓
logpdf	19	5.6e-16	3.0e-16	7.8e-16	✓
cdf	19	5.6e-15	5.6e-15	1.0e-15	✓
logcdf	19	2.5e-16	2.1e-16	1.2e-16	✓
sf	19	5.6e-15	5.6e-15	1.1e-15	✓
logsf	19	2.5e-16	2.5e-16	2.0e-16	✓
quantile	15	2.4e-15	3.6e-12	Inf	✓

✓ t(df=30) 7 quantities worst rel. 1.2e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	1.2e-13	5.2e-14	1.2e-13	✓
logpdf	19	1.7e-16	3.5e-16	2.2e-15	✓
cdf	19	3.8e-14	2.7e-14	3.3e-15	✓
logcdf	19	1.9e-16	2.9e-16	1.2e-16	✓
sf	19	3.8e-14	2.7e-14	3.3e-15	✓
logsf	19	1.9e-16	2.3e-16	1.6e-16	✓
quantile	15	4.3e-15	3.7e-15	1.7e-16	✓

✓ t(df=100) 7 quantities worst rel. 2.7e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	1.1e-14	1.1e-14	3.1e-14	✓
logpdf	19	3.1e-16	2.0e-16	3.1e-14	✓
cdf	19	2.7e-14	2.5e-15	1.0e-15	✓
logcdf	19	4.8e-16	6.1e-16	Inf	✓
sf	19	2.7e-14	5.3e-15	4.4e-15	✓
logsf	19	4.8e-16	6.1e-16	Inf	✓
quantile	15	5.6e-16	2.9e-15	1.9e-16	✓

✓ t(df=10000) 7 quantities worst rel. 1.8e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	1.6e-14	2.8e-14	2.1e-12	✓
logpdf	19	6.7e-16	1.6e-16	2.1e-12	✓
cdf	19	8.7e-16	9.9e-15	4.5e-16	✓
logcdf	19	4.8e-16	6.0e-16	Inf	✓
sf	19	1.8e-13	7.8e-14	1.0e-13	✓
logsf	19	4.8e-16	6.0e-16	Inf	✓
quantile	15	6.5e-16	5.0e-16	2.2e-16	✓

✓ t(df=1000000) 7 quantities worst rel. 4.8e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	19	1.2e-14	2.6e-14	1.2e-14	✓
logpdf	19	6.7e-16	1.8e-16	3.3e-16	✓
cdf	19	8.8e-15	3.7e-15	5.0e-15	✓
logcdf	19	2.7e-16	3.5e-16	Inf	✓
sf	19	4.8e-14	8.8e-15	5.6e-14	✓
logsf	19	3.5e-16	1.2e-16	Inf	✓
quantile	15	3.5e-16	4.4e-16	1.9e-16	✓

✓ chisquare(df=0.5) 7 quantities worst rel. 1.4e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	22	1.4e-13	4.2e-16	3.5e-14	✓
logpdf	22	2.2e-16	2.2e-16	1.9e-16	✓
cdf	22	8.6e-15	1.7e-16	9.7e-15	✓
logcdf	22	1.4e-16	5.6e-17	3.9e-16	✓
sf	22	2.2e-14	1.4e-15	2.3e-14	✓
logsf	22	5.8e-16	2.2e-16	Inf	✓
quantile	15	1.4e-14	1.2e-14	7.9e-15	✓

✓ chisquare(df=1) 7 quantities worst rel. 7.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	22	7.9e-14	2.8e-16	3.4e-14	✓
logpdf	22	3.9e-16	2.1e-16	1.7e-16	✓
cdf	22	6.4e-16	1.3e-15	2.5e-14	✓
logcdf	22	6.7e-16	1.3e-15	4.8e-15	✓
sf	22	5.7e-14	7.2e-15	2.6e-14	✓
logsf	22	6.7e-16	3.8e-15	Inf	✓
quantile	15	1.1e-14	8.7e-15	1.9e-14	✓

✓ chisquare(df=2) 7 quantities worst rel. 3.4e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	23	1.8e-15	0	1.8e-15	✓
logpdf	23	1.1e-16	1.1e-16	1.1e-16	✓
cdf	23	3.4e-14	3.4e-14	3.4e-14	✓
logcdf	23	1.5e-16	1.5e-16	2.2e-16	✓
sf	23	2.6e-14	1.2e-16	2.6e-14	✓
logsf	23	1.1e-16	1.4e-17	Inf	✓
quantile	15	2.4e-14	3.1e-14	3.9e-15	✓

✓ chisquare(df=4) 7 quantities worst rel. 2.5e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	24	2.4e-14	3.8e-16	Inf	✓
logpdf	24	2.1e-16	2.1e-16	Inf	✓
cdf	24	2.5e-14	2.1e-16	2.5e-14	✓
logcdf	24	1.1e-16	2.2e-16	Inf	✓
sf	24	4.0e-15	4.3e-16	4.0e-15	✓
logsf	24	1.2e-16	2.1e-16	Inf	✓
quantile	15	1.5e-14	1.3e-14	1.5e-14	✓

✓ chisquare(df=5) 7 quantities worst rel. 9.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	23	3.6e-14	2.8e-16	Inf	✓
logpdf	23	2.2e-16	2.0e-16	Inf	✓
cdf	23	9.2e-14	2.5e-16	9.0e-14	✓
logcdf	23	2.7e-15	2.0e-16	Inf	✓
sf	23	7.5e-15	3.7e-16	7.5e-15	✓
logsf	23	2.2e-15	2.0e-16	Inf	✓
quantile	15	1.6e-14	1.8e-14	1.6e-14	✓

✓ chisquare(df=30) 7 quantities worst rel. 2.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	24	2.2e-14	1.2e-15	Inf	✓
logpdf	24	5.1e-16	2.0e-16	Inf	✓
cdf	24	2.0e-14	7.4e-16	2.7e-14	✓
logcdf	24	7.1e-16	2.2e-16	Inf	✓
sf	24	6.5e-15	1.3e-15	1.0e-14	✓
logsf	24	1.9e-16	2.2e-16	Inf	✓
quantile	15	1.5e-15	5.0e-15	1.8e-15	✓

✓ chisquare(df=1000) 7 quantities worst rel. 1.5e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	22	1.5e-13	2.7e-14	Inf	✓
logpdf	22	2.0e-15	1.3e-15	Inf	✓
cdf	22	3.1e-14	8.2e-14	3.0e-13	✓
logcdf	22	6.2e-16	1.6e-15	Inf	✓
sf	22	1.8e-14	2.0e-14	2.7e-13	✓
logsf	22	1.2e-15	1.5e-15	Inf	✓
quantile	15	7.1e-16	5.2e-16	1.8e-16	✓

✓ chisquare(df=1000000) 7 quantities worst rel. 8.3e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	24	2.7e-15	1.5e-11	Inf	✓
logpdf	24	6.0e-16	7.3e-13	Inf	✓
cdf	24	1.1e-13	2.4e-15	8.2e-9	✓
logcdf	24	7.4e-15	1.5e-16	Inf	✓
sf	24	4.2e-13	1.5e-14	2.8e-15	✓
logsf	24	8.3e-13	2.7e-16	Inf	✓
quantile	15	1.3e-14	1.2e-16	4.1e-14	✓

✓ f(df1=4, df2=40) 7 quantities worst rel. 2.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	14	2.9e-14	2.3e-14	Inf	✓
logpdf	14	5.1e-16	2.0e-16	Inf	✓
cdf	14	1.7e-15	1.3e-15	1.1e-15	✓
logcdf	14	5.0e-16	5.0e-16	Inf	✓
sf	14	2.4e-14	2.4e-14	1.0e-15	✓
logsf	14	6.7e-16	2.2e-16	Inf	✓
quantile	15	1.1e-14	1.0e+0	Inf	✓

✓ f(df1=1, df2=1) 7 quantities worst rel. 2.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	14	4.0e-15	Inf	2.4e-14	✓
logpdf	14	2.5e-16	Inf	2.2e-16	✓
cdf	14	8.9e-16	8.9e-16	6.4e-11	✓
logcdf	14	8.9e-16	1.0e-15	2.2e-16	✓
sf	14	8.9e-16	8.9e-16	2.6e-13	✓
logsf	14	8.9e-16	1.0e-15	2.2e-16	✓
quantile	15	2.9e-14	1.0e+0	1.8e-16	✓

✓ f(df1=0.5, df2=3) 7 quantities worst rel. 3.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	14	3.9e-14	Inf	1.8e-14	✓
logpdf	14	2.1e-16	Inf	2.7e-16	✓
cdf	14	2.6e-15	2.6e-15	5.2e-16	✓
logcdf	14	2.2e-16	2.2e-16	2.2e-16	✓
sf	14	4.3e-15	4.3e-15	6.5e-16	✓
logsf	14	4.7e-16	3.3e-16	3.0e-16	✓
quantile	15	1.5e-14	1.0e+0	9.9e-16	✓

✓ f(df1=10, df2=1000000) 7 quantities worst rel. 3.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	14	3.2e-14	3.3e-14	Inf	✓
logpdf	14	6.9e-16	4.1e-16	Inf	✓
cdf	14	1.1e-14	9.9e-15	2.1e-11	✓
logcdf	14	1.1e-14	3.6e-15	Inf	✓
sf	14	3.2e-14	8.1e-14	2.7e-11	✓
logsf	14	1.4e-14	3.0e-15	Inf	✓
quantile	15	5.9e-15	4.4e-5	Inf	✓

✓ f(df1=100, df2=100) 7 quantities worst rel. 3.5e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	14	2.4e-14	2.6e-14	Inf	✓
logpdf	14	1.6e-15	1.8e-15	Inf	✓
cdf	14	6.8e-15	6.8e-15	7.4e-15	✓
logcdf	14	4.4e-16	6.7e-16	Inf	✓
sf	14	3.5e-14	3.5e-14	1.6e-14	✓
logsf	14	4.4e-16	6.7e-16	Inf	✓
quantile	15	3.3e-16	4.3e-10	3.4e-16	✓

✓ f(df1=5, df2=0.5) 7 quantities worst rel. 1.6e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	14	1.6e-13	1.5e-13	Inf	✓
logpdf	14	3.3e-16	1.7e-16	Inf	✓
cdf	14	2.1e-15	4.9e-15	7.0e-16	✓
logcdf	14	4.4e-16	4.4e-16	Inf	✓
sf	14	3.3e-16	3.3e-16	2.3e-16	✓
logsf	14	2.8e-16	3.3e-16	2.2e-16	✓
quantile	15	1.6e-14	1.0e+0	1.3e-15	✓

✓ f(df1=2, df2=2) 7 quantities worst rel. 2.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	14	1.4e-15	1.4e-16	1.4e-15	✓
logpdf	14	1.1e-16	2.8e-17	2.5e-16	✓
cdf	14	2.2e-14	2.2e-14	1.7e-16	✓
logcdf	14	5.6e-17	5.6e-17	5.6e-17	✓
sf	14	7.5e-16	7.5e-16	1.7e-16	✓
logsf	14	5.6e-17	5.6e-17	5.6e-17	✓
quantile	15	1.2e-14	1.0e+0	0	✓

✓ beta(alpha=2, beta=5) 7 quantities worst rel. 6.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	16	6.9e-14	6.9e-14	1.6e-13	✓
logpdf	16	1.1e-15	7.1e-16	7.1e-16	✓
cdf	16	3.3e-14	3.3e-14	6.4e-16	✓
logcdf	16	4.1e-16	3.3e-16	Inf	✓
sf	16	1.2e-15	2.4e-15	5.3e-16	✓
logsf	16	3.3e-16	3.3e-16	5.6e-16	✓
quantile	15	3.8e-14	2.2e-14	1.6e+100	✓

✓ beta(alpha=0.5, beta=0.5) 7 quantities worst rel. 2.7e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	16	2.7e-14	2.7e-14	2.1e-16	✓
logpdf	16	5.7e-16	5.7e-16	3.3e-16	✓
cdf	16	8.9e-16	8.9e-16	2.2e-16	✓
logcdf	16	8.9e-16	1.0e-15	2.2e-16	✓
sf	16	8.9e-16	8.9e-16	2.6e-13	✓
logsf	16	8.9e-16	1.0e-15	2.2e-16	✓
quantile	15	4.5e-15	3.7e-16	1.7e-16	✓

✓ beta(alpha=1, beta=1) 7 quantities worst rel. 2.4e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	16	0	0	1.3e-14	✓
logpdf	16	0	0	0	✓
cdf	16	2.4e-14	2.4e-14	0	✓
logcdf	16	3.5e-18	3.5e-18	0	✓
sf	16	5.2e-16	5.2e-16	1.6e-16	✓
logsf	16	1.4e-17	1.4e-17	0	✓
quantile	15	2.4e-14	0	0	✓

✓ beta(alpha=0.1, beta=10) 7 quantities worst rel. 6.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	16	6.2e-14	6.2e-14	1.7e-15	✓
logpdf	16	4.4e-16	4.4e-16	1.3e-15	✓
cdf	16	5.3e-15	5.3e-15	4.2e-16	✓
logcdf	16	1.6e-16	5.6e-17	2.2e-16	✓
sf	16	7.8e-15	7.8e-15	2.3e-15	✓
logsf	16	2.5e-16	1.7e-16	5.0e-16	✓
quantile	15	1.0e-14	1.1e-14	2.6e-15	✓

✓ beta(alpha=50, beta=200) 7 quantities worst rel. 3.4e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	16	3.4e-14	3.4e-14	1.3e-14	✓
logpdf	16	4.6e-16	4.6e-16	8.5e-14	✓
cdf	16	9.4e-15	9.4e-15	4.8e-15	✓
logcdf	16	1.7e-15	8.9e-16	Inf	✓
sf	16	1.8e-14	3.8e-14	1.2e-14	✓
logsf	16	1.8e-15	8.9e-16	Inf	✓
quantile	15	6.2e-16	7.6e-16	3.8e-15	✓

✓ beta(alpha=1000, beta=1000) 7 quantities worst rel. 1.5e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	16	1.5e-13	1.5e-13	1.2e-13	✓
logpdf	16	8.3e-16	8.3e-16	5.4e-14	✓
cdf	16	1.2e-13	1.2e-13	1.2e-13	✓
logcdf	16	6.6e-16	2.2e-15	Inf	✓
sf	16	4.1e-14	4.1e-14	3.4e-14	✓
logsf	16	4.2e-16	2.2e-15	Inf	✓
quantile	15	7.8e-16	2.1e-16	8.0e-16	✓

✓ beta(alpha=3, beta=1) 7 quantities worst rel. 8.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	16	2.4e-14	2.4e-14	9.1e-16	✓
logpdf	16	1.3e-16	1.3e-16	1.3e-16	✓
cdf	16	8.9e-14	3.5e-14	0	✓
logcdf	16	2.1e-16	2.2e-16	Inf	✓
sf	16	6.9e-16	6.9e-16	1.7e-16	✓
logsf	16	1.7e-16	1.7e-16	1.7e-16	✓
quantile	15	1.8e-14	8.6e-15	1.3e-14	✓

✓ gamma(shape=2, scale=3) 7 quantities worst rel. 3.0e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	17	3.0e-14	2.8e-16	Inf	✓
logpdf	17	2.0e-16	2.0e-16	Inf	✓
cdf	17	1.1e-14	2.1e-16	1.1e-14	✓
logcdf	17	1.1e-16	1.7e-16	Inf	✓
sf	17	6.7e-16	3.0e-16	1.2e-15	✓
logsf	17	1.1e-16	1.1e-16	Inf	✓
quantile	15	1.5e-14	1.3e-14	1.5e-14	✓

✓ gamma(shape=0.5, scale=1) 7 quantities worst rel. 1.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	17	1.9e-14	1.9e-16	1.9e-14	✓
logpdf	17	2.8e-16	1.6e-16	1.5e-16	✓
cdf	17	6.4e-16	1.3e-15	4.8e-15	✓
logcdf	17	6.7e-16	1.3e-15	4.8e-15	✓
sf	17	2.7e-15	7.2e-15	2.6e-14	✓
logsf	17	6.7e-16	3.8e-15	Inf	✓
quantile	15	1.1e-14	8.7e-15	1.9e-14	✓

✓ gamma(shape=1, scale=1) 7 quantities worst rel. 2.4e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	17	0	0	0	✓
logpdf	17	0	0	0	✓
cdf	17	2.4e-14	2.4e-14	2.4e-14	✓
logcdf	17	1.9e-16	1.9e-16	2.2e-16	✓
sf	17	1.1e-15	1.2e-16	1.1e-15	✓
logsf	17	1.1e-16	1.4e-17	Inf	✓
quantile	15	2.4e-14	3.1e-14	3.9e-15	✓

✓ gamma(shape=0.01, scale=1) 7 quantities worst rel. 4.9e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	17	4.9e-14	6.8e-16	4.9e-14	✓
logpdf	17	6.7e-16	5.6e-16	4.4e-16	✓
cdf	17	4.3e-16	1.3e-16	7.0e-16	✓
logcdf	17	1.9e-16	2.8e-17	5.8e-16	✓
sf	17	1.4e-15	1.6e-15	8.9e-16	✓
logsf	17	4.9e-16	2.9e-16	Inf	✓
quantile	15	4.1e-14	4.2e-14	4.6e-14	✓

✓ gamma(shape=100, scale=0.01) 7 quantities worst rel. 1.5e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	17	1.5e-13	1.9e-14	Inf	✓
logpdf	17	8.4e-16	2.1e-16	Inf	✓
cdf	17	1.1e-13	1.2e-14	2.4e-14	✓
logcdf	17	3.1e-16	2.2e-16	Inf	✓
sf	17	7.4e-14	3.9e-14	4.7e-14	✓
logsf	17	2.2e-16	3.3e-16	Inf	✓
quantile	15	9.2e-16	2.9e-15	3.4e-16	✓

✓ gamma(shape=10000, scale=2) 7 quantities worst rel. 7.5e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	17	1.9e-13	1.6e-16	Inf	✓
logpdf	17	3.5e-16	2.2e-16	Inf	✓
cdf	17	2.5e-14	4.7e-15	1.7e-15	✓
logcdf	17	1.6e-15	2.3e-16	Inf	✓
sf	17	7.5e-13	5.0e-16	1.9e-13	✓
logsf	17	5.5e-15	2.2e-16	Inf	✓
quantile	15	3.1e-15	2.3e-16	1.7e-16	✓

✓ gamma(shape=3, scale=100000) 7 quantities worst rel. 4.4e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	17	2.1e-14	3.9e-15	Inf	✓
logpdf	17	1.9e-16	1.9e-16	Inf	✓
cdf	17	4.4e-14	3.5e-16	4.6e-14	✓
logcdf	17	2.0e-16	1.8e-16	Inf	✓
sf	17	2.7e-15	3.9e-15	4.7e-15	✓
logsf	17	2.2e-16	2.4e-16	Inf	✓
quantile	15	1.7e-14	1.9e-14	1.7e-14	✓

✓ exponential(rate=1) 7 quantities worst rel. 5.6e-17

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	0	0	0	✓
logpdf	13	0	0	0	✓
cdf	13	0	0	0	✓
logcdf	13	5.6e-17	5.6e-17	5.6e-17	✓
sf	13	0	0	0	✓
logsf	13	0	0	0	✓
quantile	15	0	0	0	✓

✓ exponential(rate=0.5) 7 quantities worst rel. 1.1e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	0	0	0	✓
logpdf	13	1.1e-16	1.1e-16	1.1e-16	✓
cdf	13	0	0	0	✓
logcdf	13	5.6e-17	5.6e-17	5.6e-17	✓
sf	13	0	0	0	✓
logsf	13	0	0	0	✓
quantile	15	0	0	0	✓

✓ exponential(rate=1e-05) 7 quantities worst rel. 5.6e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	6.1e-15	6.1e-15	6.1e-15	✓
logpdf	13	1.7e-16	1.7e-16	1.7e-16	✓
cdf	13	1.4e-16	1.7e-16	1.7e-16	✓
logcdf	13	5.6e-17	1.1e-16	1.1e-16	✓
sf	13	5.6e-14	5.6e-14	5.6e-14	✓
logsf	13	0	1.1e-16	1.1e-16	✓
quantile	15	2.0e-16	2.1e-16	2.1e-16	✓

✓ exponential(rate=100000) 7 quantities worst rel. 1.5e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	1.5e-14	1.4e-14	1.4e-14	✓
logpdf	13	4.4e-16	4.4e-16	4.4e-16	✓
cdf	13	0	1.7e-16	1.7e-16	✓
logcdf	13	1.1e-16	1.1e-16	1.1e-16	✓
sf	13	1.5e-14	1.5e-14	1.5e-14	✓
logsf	13	0	1.5e-16	1.5e-16	✓
quantile	15	2.0e-16	2.1e-16	2.1e-16	✓

✓ lognormal(meanlog=0, sdlog=1) 7 quantities worst rel. 1.3e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	1.7e-15	8.2e-16	1.7e-15	✓
logpdf	13	1.8e-16	1.8e-16	1.8e-16	✓
cdf	13	3.9e-16	3.9e-16	7.3e-15	✓
logcdf	13	1.2e-16	1.2e-16	1.9e-16	✓
sf	13	7.7e-16	7.7e-16	6.2e-15	✓
logsf	13	1.2e-16	1.2e-16	1.9e-16	✓
quantile	15	1.3e-14	2.7e-15	2.3e-15	✓

✓ lognormal(meanlog=2, sdlog=0.5) 7 quantities worst rel. 6.4e-15

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	1.3e-15	1.6e-15	1.3e-15	✓
logpdf	13	2.0e-16	2.1e-16	1.7e-16	✓
cdf	13	5.8e-16	5.8e-16	7.5e-15	✓
logcdf	13	1.2e-16	1.7e-16	2.3e-16	✓
sf	13	1.7e-15	1.7e-15	8.7e-15	✓
logsf	13	1.9e-16	1.9e-16	1.9e-16	✓
quantile	15	6.4e-15	1.3e-15	1.1e-15	✓

✓ lognormal(meanlog=-5, sdlog=3) 7 quantities worst rel. 9.1e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	9.1e-14	1.0e+0	2.2e-14	✓
logpdf	13	2.9e-16	2.0e-16	1.8e-16	✓
cdf	13	1.9e-16	1.9e-16	6.7e-15	✓
logcdf	13	1.4e-16	1.2e-16	2.8e-16	✓
sf	13	3.9e-16	3.9e-16	6.6e-15	✓
logsf	13	1.2e-16	1.2e-16	1.9e-16	✓
quantile	15	3.5e-14	9.6e-15	6.5e-15	✓

✓ logistic(location=0, scale=1) 7 quantities worst rel. 1.5e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	1.5e-16	1.5e-16	0	✓
logpdf	13	0	0	0	✓
cdf	13	0	0	0	✓
logcdf	13	5.6e-17	5.6e-17	5.6e-17	✓
sf	13	0	0	0	✓
logsf	13	5.6e-17	5.6e-17	5.6e-17	✓
quantile	15	1.5e-16	0	0	✓

✓ logistic(location=5, scale=2) 7 quantities worst rel. 7.3e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	1.5e-16	1.5e-16	0	✓
logpdf	13	0	0	0	✓
cdf	13	0	0	0	✓
logcdf	13	5.6e-17	5.6e-17	5.6e-17	✓
sf	13	0	0	0	✓
logsf	13	5.6e-17	5.6e-17	5.6e-17	✓
quantile	15	7.3e-16	7.3e-16	7.3e-16	✓

✓ logistic(location=0, scale=1e-05) 7 quantities worst rel. 1.5e-15

Quantity	Values	Max rel. error	r	scipy	Pass
pdf	13	1.4e-15	1.4e-15	1.4e-15	✓
logpdf	13	1.4e-16	1.8e-16	1.4e-16	✓
cdf	13	1.5e-15	1.5e-15	1.5e-15	✓
logcdf	13	1.8e-16	1.8e-16	1.8e-16	✓
sf	13	1.5e-15	1.5e-15	1.5e-15	✓
logsf	13	1.8e-16	1.8e-16	1.8e-16	✓
quantile	15	2.0e-16	1.8e-16	1.8e-16	✓

✓ binomial(size=10, prob=0.5) 7 quantities worst rel. 1.2e-15

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	11	1.2e-15	7.1e-16	8.9e-16	✓
logpmf	11	6.2e-16	2.1e-16	6.3e-16	✓
cdf	11	6.5e-16	6.5e-16	0	✓
logcdf	11	2.0e-16	2.0e-16	0	✓
sf	11	5.1e-16	5.1e-16	0	✓
logsf	11	2.2e-16	2.2e-16	0	✓
quantile	15	0	0	1.0e+300	✓

✓ binomial(size=1, prob=0.3) 7 quantities worst rel. 1.6e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	9	0	0	3.2e-16	✓
logpmf	9	1.1e-16	0	1.1e-16	✓
cdf	9	1.6e-16	1.6e-16	1.6e-16	✓
logcdf	9	0	0	1.1e-16	✓
sf	9	0	0	0	✓
logsf	9	0	0	0	✓
quantile	15	0	0	1.0e+300	✓

✓ binomial(size=100, prob=0.01) 7 quantities worst rel. 3.3e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	3.3e-14	2.5e-14	5.5e-15	✓
logpmf	12	1.7e-16	1.7e-16	1.9e-14	✓
cdf	12	1.5e-16	3.0e-16	1.2e-16	✓
logcdf	12	2.2e-16	2.2e-16	1.5e-16	✓
sf	12	2.3e-14	7.0e-14	2.2e-15	✓
logsf	12	3.3e-16	5.3e-16	8.8e-16	✓
quantile	15	0	5.9e-2	1.0e+300	✓

✓ binomial(size=1000, prob=0.999) 7 quantities worst rel. 2.2e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	1.5e-16	6.0e-16	1.5e-16	✓
logpmf	12	2.2e-16	6.7e-16	9.9e-13	✓
cdf	12	0	0	0	✓
logcdf	12	1.6e-16	1.3e-16	Inf	✓
sf	12	0	0	0	✓
logsf	12	0	0	0	✓
quantile	15	0	0	1.0e+300	✓

✓ binomial(size=1000000, prob=0.3) 7 quantities worst rel. 7.8e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	13	3.7e-16	6.2e-16	8.0e-12	✓
logpmf	13	5.0e-16	3.3e-16	1.3e-11	✓
cdf	13	6.7e-16	2.2e-16	3.6e-12	✓
logcdf	13	7.8e-16	2.2e-15	Inf	✓
sf	13	7.8e-16	2.2e-16	3.6e-12	✓
logsf	13	7.8e-16	2.2e-15	Inf	✓
quantile	15	0	4.2e-4	1.0e+300	✓

✓ binomial(size=50, prob=0) 7 quantities worst rel. 0

Quantity	Values	r	scipy	Pass
pmf	12	0	0	✓
logpmf	12	0	0	✓
cdf	12	0	0	✓
logcdf	12	0	0	✓
sf	12	0	0	✓
logsf	12	0	0	✓
quantile	15	5.0e+301	5.0e+301	✓

✓ binomial(size=50, prob=1) 7 quantities worst rel. 0

Quantity	Values	scipy	Pass
pmf	12	0	✓
logpmf	12	0	✓
cdf	12	0	✓
logcdf	12	0	✓
sf	12	0	✓
logsf	12	0	✓
quantile	15	1.0e+300	✓

✓ binomial(size=0, prob=0.4) 7 quantities worst rel. 0

Quantity	Values	scipy	Pass
pmf	8	0	✓
logpmf	8	0	✓
cdf	8	0	✓
logcdf	8	0	✓
sf	8	0	✓
logsf	8	0	✓
quantile	15	1.0e+300	✓

✓ poisson(lambda=3.2) 7 quantities worst rel. 1.1e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	13	1.1e-14	7.0e-15	4.6e-14	✓
logpmf	13	4.1e-16	1.5e-16	3.5e-16	✓
cdf	13	1.8e-16	1.8e-16	2.9e-16	✓
logcdf	13	2.2e-16	1.3e-16	3.3e-16	✓
sf	13	3.3e-15	6.9e-15	3.6e-14	✓
logsf	13	3.9e-16	1.7e-16	Inf	✓
quantile	15	0	3.8e-2	1.0e+300	✓

✓ poisson(lambda=1e-10) 7 quantities worst rel. 4.6e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	10	4.6e-14	4.8e-16	4.6e-14	✓
logpmf	10	1.7e-16	1.7e-16	1.5e-16	✓
cdf	10	0	1.1e-16	0	✓
logcdf	10	1.3e-25	1.3e-25	8.3e-18	✓
sf	10	1.7e-14	5.6e-16	2.8e-14	✓
logsf	10	1.7e-16	2.0e-16	Inf	✓
quantile	15	0	0	1.0e+300	✓

✓ poisson(lambda=0.5) 7 quantities worst rel. 5.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	1.5e-14	2.3e-16	4.5e-15	✓
logpmf	12	2.0e-16	2.0e-16	2.1e-16	✓
cdf	12	1.1e-16	1.1e-16	0	✓
logcdf	12	1.1e-16	1.4e-17	2.8e-17	✓
sf	12	5.2e-14	3.6e-16	2.7e-15	✓
logsf	12	2.1e-16	2.1e-16	Inf	✓
quantile	15	0	7.1e-2	1.0e+300	✓

✓ poisson(lambda=12) 7 quantities worst rel. 5.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	13	5.2e-14	3.0e-16	1.1e-13	✓
logpmf	13	2.3e-16	2.0e-16	8.1e-16	✓
cdf	13	2.5e-15	1.9e-16	6.2e-16	✓
logcdf	13	2.6e-15	1.9e-16	5.6e-16	✓
sf	13	3.7e-14	4.3e-16	1.1e-13	✓
logsf	13	3.4e-15	4.8e-16	Inf	✓
quantile	15	0	4.0e-2	1.0e+300	✓

✓ poisson(lambda=85) 7 quantities worst rel. 3.7e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	13	1.9e-14	1.9e-16	1.1e-13	✓
logpmf	13	2.0e-16	1.9e-16	1.4e-14	✓
cdf	13	5.5e-15	1.3e-15	5.9e-15	✓
logcdf	13	1.9e-16	1.3e-15	1.9e-16	✓
sf	13	3.7e-14	1.4e-15	9.7e-14	✓
logsf	13	3.4e-16	1.4e-15	Inf	✓
quantile	15	0	1.8e-2	1.0e+300	✓

✓ poisson(lambda=10000) 7 quantities worst rel. 5.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	14	3.5e-15	1.6e-16	1.1e-11	✓
logpmf	14	2.2e-15	1.9e-16	2.0e-13	✓
cdf	14	5.2e-14	1.0e-14	1.4e-14	✓
logcdf	14	1.2e-15	2.6e-16	Inf	✓
sf	14	3.2e-14	0	8.3e-16	✓
logsf	14	3.2e-14	2.1e-16	Inf	✓
quantile	15	0	2.6e-3	1.0e+300	✓

✓ poisson(lambda=1000000) 7 quantities worst rel. 3.7e-13

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	14	2.8e-15	5.3e-16	2.4e-9	✓
logpmf	14	2.0e-16	1.2e-16	8.7e-11	✓
cdf	14	8.8e-14	2.2e-14	1.9e-15	✓
logcdf	14	4.0e-14	4.0e-16	Inf	✓
sf	14	3.1e-13	7.9e-15	2.6e-10	✓
logsf	14	3.7e-13	4.3e-16	Inf	✓
quantile	15	0	2.7e-4	1.0e+300	✓

✓ poisson(lambda=0) 7 quantities worst rel. 0

Quantity	Values	scipy	Pass
pmf	10	0	✓
logpmf	10	0	✓
cdf	10	0	✓
logcdf	10	0	✓
sf	10	0	✓
logsf	10	0	✓
quantile	15	Inf	✓

✓ nbinom(size=3, prob=0.4) 7 quantities worst rel. 6.8e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	6.8e-14	4.3e-14	2.3e-14	✓
logpmf	12	2.3e-16	2.8e-16	4.6e-15	✓
cdf	12	3.5e-16	1.7e-16	0	✓
logcdf	12	3.9e-16	1.9e-16	1.9e-16	✓
sf	12	2.5e-14	2.5e-14	1.8e-16	✓
logsf	12	2.2e-16	1.6e-16	Inf	✓
quantile	15	0	6.0e-2	1.0e+300	✓

✓ nbinom(size=0.5, prob=0.1) 7 quantities worst rel. 2.4e-15

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	1.7e-15	2.2e-15	1.3e-15	✓
logpmf	12	2.1e-16	2.1e-16	1.1e-14	✓
cdf	12	2.0e-16	3.2e-16	2.0e-16	✓
logcdf	12	1.9e-16	1.7e-16	2.2e-16	✓
sf	12	2.4e-15	1.3e-14	1.6e-15	✓
logsf	12	3.9e-16	3.9e-16	Inf	✓
quantile	15	0	6.6e-2	1.0e+300	✓

✓ nbinom(size=100, prob=0.99) 7 quantities worst rel. 2.1e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	5.6e-15	9.8e-15	1.4e-14	✓
logpmf	12	2.1e-16	4.4e-16	2.0e-14	✓
cdf	12	4.5e-16	4.5e-16	1.5e-16	✓
logcdf	12	5.6e-16	6.1e-16	5.6e-17	✓
sf	12	2.1e-14	2.1e-14	1.4e-14	✓
logsf	12	1.2e-15	1.3e-15	Inf	✓
quantile	15	0	5.6e-2	1.0e+300	✓

✓ nbinom(size=100000, prob=0.5) 7 quantities worst rel. 9.7e-16

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	9.7e-16	8.5e-16	1.2e-16	✓
logpmf	12	2.1e-16	2.2e-16	1.0e-10	✓
cdf	12	2.2e-16	2.2e-16	2.2e-16	✓
logcdf	12	2.1e-16	2.0e-15	Inf	✓
sf	12	0	0	0	✓
logsf	12	1.7e-16	2.1e-15	Inf	✓
quantile	15	0	1.2e-3	1.0e+300	✓

✓ nbinom(size=2, prob=1) 7 quantities worst rel. 0

Quantity	Values	scipy	Pass
pmf	12	0	✓
logpmf	12	0	✓
cdf	12	0	✓
logcdf	12	0	✓
sf	12	0	✓
logsf	12	0	✓
quantile	15	Inf	✓

✓ nbinom_mu(mu=4.5, size=2) 7 quantities worst rel. 4.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	6.4e-15	8.6e-15	9.1e-15	✓
logpmf	12	4.0e-16	3.2e-16	1.9e-15	✓
cdf	12	2.5e-16	2.5e-16	1.5e-16	✓
logcdf	12	2.2e-16	2.2e-16	1.6e-22	✓
sf	12	4.2e-14	4.2e-14	1.2e-14	✓
logsf	12	4.0e-16	3.5e-16	Inf	✓
quantile	15	0	5.6e-2	1.0e+300	✓

✓ nbinom_mu(mu=10, size=0.5) 7 quantities worst rel. 5.1e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	1.1e-14	3.2e-14	2.6e-14	✓
logpmf	12	3.0e-16	3.0e-16	2.3e-14	✓
cdf	12	2.2e-16	2.2e-16	1.7e-16	✓
logcdf	12	1.1e-16	1.1e-16	4.4e-16	✓
sf	12	5.1e-14	2.4e-14	3.2e-14	✓
logsf	12	2.7e-16	1.9e-16	Inf	✓
quantile	15	0	6.5e-2	1.0e+300	✓

✓ nbinom_mu(mu=3, size=1000000) 7 quantities worst rel. 2.0e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	1.2e-14	2.5e-11	5.7e-10	✓
logpmf	12	2.5e-16	1.3e-11	7.2e-11	✓
cdf	12	4.5e-15	1.4e-15	3.6e-11	✓
logcdf	12	4.5e-15	1.4e-15	1.9e-11	✓
sf	12	2.0e-14	6.3e-15	5.8e-10	✓
logsf	12	1.2e-14	3.7e-15	Inf	✓
quantile	15	0	3.8e-2	1.0e+300	✓

✓ nbinom_mu(mu=0.001, size=10) 7 quantities worst rel. 2.2e-14

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	1.5e-14	5.3e-14	4.7e-11	✓
logpmf	12	2.5e-16	2.5e-16	1.4e-13	✓
cdf	12	0	0	1.0e-15	✓
logcdf	12	8.7e-19	1.1e-18	9.4e-16	✓
sf	12	2.2e-14	6.8e-14	4.8e-11	✓
logsf	12	3.2e-16	2.0e-16	Inf	✓
quantile	15	0	0	1.0e+300	✓

✓ nbinom_mu(mu=100000, size=1) 7 quantities worst rel. 2.4e-15

Quantity	Values	Max rel. error	r	scipy	Pass
pmf	12	2.4e-15	1.9e-15	6.8e-16	✓
logpmf	12	1.8e-16	1.8e-16	1.8e-16	✓
cdf	12	1.1e-15	1.1e-15	2.5e-16	✓
logcdf	12	1.9e-16	1.9e-16	3.2e-12	✓
sf	12	1.2e-15	1.6e-15	1.0e-15	✓
logsf	12	5.5e-16	2.2e-16	Inf	✓
quantile	15	0	6.2e-2	1.0e+300	✓

✓ nbinom_mu(mu=0, size=3) 7 quantities worst rel. 0

Quantity	Values	scipy	Pass
pmf	12	0	✓
logpmf	12	0	✓
cdf	12	0	✓
logcdf	12	0	✓
sf	12	0	✓
logsf	12	0	✓
quantile	15	Inf	✓

Peer columns give the same error measure for r and scipy against the reference.