Linear growth benchmarks

53 of 55 cases match Python Prophet. 2 are intentional differences, explained below.

Each case runs the same input through Effect Prophet and Python Prophet 1.4.0, then compares every forecast row, the trend, each component and the fitted noise. A case matches when all of them agree within its tolerances, and only matching cases are timed.

Each case's dot shows its result: matches, matches with internal differences flagged, intentional difference, doesn't match. Hover over a dot for details.

How to read the tables:

• Effect output and Python output are each library's final forecast value. Open a case to see every row side by side.
• Largest difference is the biggest gap between the two forecasts, as a share of the input data's range.
• Effect time and Python time are the median time for the timed step, usually fitting and predicting. Open a case for every step, including first-run and save/load times.
• A timed step marked different work calls public operations that produce different outputs in the two libraries, so its times aren't a speed comparison. The case page explains the difference.
• Flagged cases match, but the two libraries stopped their fitting search at slightly different points. The case page shows the internal numbers.

About this run

• Run 2026-11-07T174133-142Z-3a5a6cec on 2026-11-07, commit 3a5a6ce
• Both libraries ran in linux/arm64 containers on Apple M4 Pro
• effect-prophet 0.0.0
• effect 4.0.6
• prophet 1.4.0
• Full benchmark report

Timings come from one machine and describe this workload only. They are not a general speed ranking. Where Python is faster, it is often because Python runs Stan's optimizer as compiled C++, while Effect Prophet runs the same algorithm as WebAssembly with narrower vector instructions. The gap is widest for Newton's method on short histories with many parameters.

Country holiday calendars

Pinned country calendars, matching explicit-event controls, dynamic future years and portable saved models. Known-gap opt-in is partial provider output, not a completeness guarantee.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
US holidays, additive	96 rows	21.5688	21.5688	< 0.0001%	Fit and predict	4.49 ms	26.6 ms
Explicit US control, additive	96 rows	21.5688	21.5688	< 0.0001%	Fit and predict	3.94 ms	23.1 ms
US holidays, multiplicative	96 rows	21.5778	21.5778	< 0.0001%	Fit and predict	4.76 ms	27.4 ms
Explicit US control, multiplicative	96 rows	21.5778	21.5778	< 0.0001%	Fit and predict	4.48 ms	23.6 ms
Observed spillovers and unseen future names	96 rows	33.9385	33.9385	< 0.0001%	Fit and predict	5.28 ms	27.8 ms
Global prior scales	96 rows	20.8674	20.8674	< 0.0001%	Fit and predict	5.09 ms	33.8 ms
Global prior scales with explicit overrides	96 rows	20.8727	20.8727	< 0.0001%	Fit and predict	5.11 ms	33.9 ms

Default settings

fit(history) against Prophet().fit(df) with no options on either side. Each library decides on its own which seasonal patterns to use. Warm-start cases fit the first rows, then refit the whole history from the parameters of that fit, as when new data arrives.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Defaults, one month of daily data	32 rows	30.7933	30.7933	< 0.0001%	Fit and predict	18.4 ms	64.1 ms
Refit after a month of new data	256 rows	139.9296	139.9272	0.0025%	Refit from an earlier fit	27.3 ms	73.2 ms
Refit after one new day	256 rows	139.9300	139.9288	0.0012%	Refit from an earlier fit	8.14 ms	21.5 ms
Defaults, eight months of daily data	256 rows	139.9296	139.9278	0.0018%	Fit and predict	26.5 ms	89.9 ms
Defaults, irregular dates	192 rows	108.5108	108.4320	0.11%	Fit and predict	6.80 ms	17.1 ms

Trends and changepoints

Straight-line and bending trends with automatic or hand-picked changepoints, plus unsorted rows, repeated timestamps and both target scalings.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Predicting from a known straight line	256 rows	43.7804	43.7804	< 0.0001%	Predict	532 µs	2.64 ms
One hand-picked changepoint	32 rows	28.5156	28.5156	< 0.0001%	Fit and predict	2.11 ms	13.8 ms
Sorted rows, hand-picked changepoint	96 rows	34.4145	34.4145	< 0.0001%	Fit	4.34 ms	20.8 ms
Sorted rows, automatic changepoints	96 rows	34.4258	34.4258	< 0.0001%	Fit	30.9 ms	108 ms
Shuffled rows, hand-picked changepoint	96 rows	34.4145	34.4145	< 0.0001%	Fit	4.31 ms	20.8 ms
Shuffled rows, automatic changepoints	96 rows	34.4258	34.4258	< 0.0001%	Fit	32.0 ms	109 ms
Repeated timestamps, hand-picked changepoint	96 rows	17.8737	17.8737	< 0.0001%	Fit	4.05 ms	19.8 ms
Repeated timestamps, automatic changepoints	96 rows	17.9039	17.9039	0.0013%	Fit	26.4 ms	84.9 ms
Values far from zero, absmax scaling	96 rows	113.0935	113.0935	< 0.0001%	Fit and predict	4.91 ms	26.7 ms
Values far from zero, minmax scaling	96 rows	113.0928	113.0928	< 0.0001%	Fit and predict	5.03 ms	26.9 ms

Seasonality, events and regressors

Custom and switchable seasonal patterns, events with windows, extra regressors, and additive and multiplicative effects mixed together.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Weekly pattern on irregular dates	192 rows	108.5119	108.5118	< 0.0001%	Fit and predict	1.99 ms	11.1 ms
Two switchable weekly patterns	256 rows	139.4380	139.4353	0.0028%	Fit and predict	2.77 ms	16.8 ms
Events with windows	96 rows	54.2821	54.2821	< 0.0001%	Fit and predict	6.75 ms	34.0 ms
Four regressors	256 rows	138.7384	138.7426	0.0043%	Fit and predict	2.65 ms	14.1 ms
A regressor forecast by its own model	256 rows	139.2608	139.2648	0.0040%	Fit and predict	28.6 ms	119 ms
Everything at once, small	24 rows	21.2025	21.2025	< 0.0001%	Fit and predict	1.79 ms	16.0 ms
Everything at once, two years	768 rows	54.2716	54.2657	0.038%	Fit and predict	11.8 ms	44.3 ms
Additive and multiplicative together	96 rows	44.5183	44.5183	< 0.0001%	Fit and predict	4.92 ms	29.5 ms
Repeated timestamps with features	96 rows	18.2191	18.2200	0.017%	Fit	31.9 ms	113 ms

Uncertainty ranges

Both libraries simulate possible futures with random draws, so individual simulated values never match. Each range must still match Python's within the variation expected from that many draws. Anomaly cases also check that both libraries flag the outliers in a history.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Ranges with a forecast regressor	256 rows	139.2608	139.2648	0.0040%	Simulate uncertainty (different work)	9.28 ms	246 ms
Defaults, three years of ranges	1095 rows	611.2687	611.3156	0.011%	Simulate uncertainty (different work)	69.7 ms	375 ms
Defaults, ranges on irregular dates	192 rows	108.5108	108.4320	0.15%	Simulate uncertainty (different work)	11.4 ms	158 ms
Samples with repeated timestamps	96 rows	17.9039	17.9039	0.0013%	Simulate uncertainty (different work)	471 µs	16.8 ms
Ranges over past dates	96 rows	110.0950	110.0950	< 0.0001%	Simulate uncertainty (different work)	331 µs	19.8 ms
Samples for one future date	96 rows	110.0819	110.0819	< 0.0001%	Simulate uncertainty (different work)	204 µs	16.8 ms
Ranges with mixed effects	96 rows	45.1353	45.1353	< 0.0001%	Simulate uncertainty (different work)	487 µs	26.4 ms
Samples with mixed effects	96 rows	45.1353	45.1353	< 0.0001%	Simulate uncertainty (different work)	798 µs	68.6 ms
Anomalies in a history	365 rows	149.0161	148.9947	0.11%	Fit and find anomalies	25.2 ms	199 ms

Full Bayesian fitting

fit(history, { mcmc: { samples, seed } }) against Prophet(mcmc_samples=...) and fit(df, seed=...): both run Stan's NUTS sampler with the same settings. Their chains can't match draw for draw, so each forecast, component and coefficient, a posterior mean, must agree within 0.15 of the narrowest 80% range, and each range bound within the variation expected from that many posterior draws. Divergences and R-hat are reported, and flagged when Effect's chains mix clearly worse than Python's.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Mixed features, 600 draws	96 rows	44.5139	44.5194	0.019%	Simulate uncertainty (different work)	2.95 ms	164 ms
25 automatic changepoints	256 rows	139.9330	139.9339	0.00091%	Simulate uncertainty (different work)	7.58 ms	153 ms
A regressor forecast by its own model	256 rows	139.2825	139.2647	0.019%	Simulate uncertainty (different work)	16.1 ms	306 ms
A regressor forecast by its own sampled model	256 rows	139.2723	139.2547	0.019%	Simulate uncertainty (different work)	16.3 ms	500 ms

Cross-validation and choosing settings

Rolling-origin cross-validation, metrics, baselines, settings search and a final holdout check.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Cross-validation with a forecast regressor	256 rows	106.8125	106.8124	0.0025%	Cross-validate (different work)	51.6 ms	185 ms
Cross-validation with a forecast regressor and ranges	256 rows	106.8125	106.8124	0.0025%	Cross-validate with ranges (different work)	51.9 ms	255 ms
Cross-validation and metrics	96 rows	108.5823	108.5823	< 0.0001%	Cross-validate (different work)	10.1 ms	72.0 ms
Cross-validation with ranges	96 rows	108.5823	108.5823	< 0.0001%	Cross-validate with ranges (different work)	10.5 ms	78.2 ms
Choosing settings and a final holdout	96 rows	108.5823	108.5823	< 0.0001%	Search settings (different work)	20.2 ms	151 ms
Search with a failing candidate	96 rows	108.5823	108.5823	< 0.0001%	Search settings (different work)	21.4 ms	153 ms
Choosing settings by a custom metric	96 rows	108.5823	108.5823	< 0.0001%	Search settings (different work)	20.4 ms	143 ms
Twelve folds, three years, sequential and parallel	1095 rows	420.8894	420.8323	0.052%	Cross-validate (different work)	953 ms	2.61 s
Cross-validation with repeated timestamps	96 rows	15.5221	15.5221	< 0.0001%	Cross-validate (different work)	6.85 ms	53.4 ms

Intentional differences

Inputs where we deliberately behave differently from Python Prophet. These cases are expected to fail the comparison.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Every row on the same date, different values	3 rows	FittingError	Optimizer crash	—	—	—	—
Every row on the same date, same value	3 rows	FittingError	NaN forecast	—	—	—	—