Logistic growth benchmarks

58 of 58 cases match Python Prophet.

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 2026-11-07T184211-397Z-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	80.5727	80.5727	< 0.0001%	Fit and predict	31.4 ms	60.2 ms
Explicit US control, additive	96 rows	80.5727	80.5727	< 0.0001%	Fit and predict	30.9 ms	57.1 ms
US holidays, multiplicative	96 rows	86.0085	86.0085	< 0.0001%	Fit and predict	43.4 ms	66.5 ms
Explicit US control, multiplicative	96 rows	86.0085	86.0085	< 0.0001%	Fit and predict	43.1 ms	65.5 ms

Default settings

fit(history, { growth: "logistic" }) against Prophet(growth="logistic").fit(df) with nothing else set. Each library decides on its own which seasonal patterns, changepoints and optimizer 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, three months of daily data	96 rows	105.2798	105.2798	< 0.0001%	Fit	102 ms	121 ms
Defaults, eight months of daily data	256 rows	113.0552	113.0552	0.0012%	Fit	39.0 ms	38.7 ms
Defaults, a year with changing growth	365 rows	193.9557	193.9523	0.0086%	Fit	134 ms	112 ms
Refit after a week of new data	365 rows	193.9774	193.9853	0.039%	Refit from an earlier fit	117 ms	94.2 ms

Growth curves and changepoints

An S-shaped curve rising toward a slowly changing ceiling, with no changepoints, one hand-picked changepoint or automatic ones, under both target scalings. Three cases sit either side of 100 rows, where both libraries switch from Newton to L-BFGS.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
No changepoints, absmax scaling	96 rows	105.2742	105.2742	< 0.0001%	Fit	6.87 ms	13.3 ms
One hand-picked changepoint, absmax scaling	96 rows	105.2754	105.2754	< 0.0001%	Fit	7.91 ms	15.4 ms
Three automatic changepoints, absmax scaling	96 rows	105.2760	105.2760	< 0.0001%	Fit	19.1 ms	27.1 ms
No changepoints, minmax scaling	96 rows	106.7569	106.7569	< 0.0001%	Fit	8.53 ms	15.7 ms
One hand-picked changepoint, minmax scaling	96 rows	105.7871	105.7871	< 0.0001%	Fit	17.0 ms	25.5 ms
Three automatic changepoints, minmax scaling	96 rows	105.5809	105.5809	< 0.0001%	Fit	9.31 ms	17.2 ms
No changepoints, loose prior, absmax scaling	96 rows	99.6666	99.6666	< 0.0001%	Fit	118 ms	128 ms
No changepoints, loose prior, minmax scaling	96 rows	93.1168	93.1168	< 0.0001%	Fit	15.0 ms	20.4 ms
99 rows: just under the optimizer switch	99 rows	105.3754	105.3754	< 0.0001%	Fit	17.2 ms	24.3 ms
100 rows: just over the optimizer switch	100 rows	105.4111	105.4111	< 0.0001%	Fit	1.83 ms	5.85 ms
Eight months of daily data	256 rows	113.6759	113.6759	< 0.0001%	Fit	2.95 ms	7.03 ms
Weekly pattern, absmax scaling	96 rows	71.7786	71.7786	< 0.0001%	Fit and predict	18.9 ms	32.0 ms
Weekly pattern, minmax scaling	96 rows	71.9060	71.9060	< 0.0001%	Fit and predict	20.3 ms	35.9 ms
Weekly pattern, automatic changepoints	96 rows	71.9000	71.9000	< 0.0001%	Fit and predict	19.4 ms	32.6 ms
Weekly pattern, eight months	256 rows	98.0804	98.0804	< 0.0001%	Fit and predict	4.70 ms	13.0 ms

Floors and ceilings

Histories with an explicit floor as well as a ceiling, both changing over time. Values are measured from the floor, as in Prophet.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Explicit floor, absmax scaling	96 rows	105.8329	105.8329	< 0.0001%	Fit	6.51 ms	13.5 ms
Explicit floor, minmax scaling	96 rows	105.8329	105.8329	< 0.0001%	Fit	10.1 ms	15.9 ms
Explicit floor with a regressor, absmax scaling	96 rows	72.2190	72.2190	< 0.0001%	Fit and predict	20.9 ms	36.5 ms
Explicit floor with a regressor, minmax scaling	96 rows	72.2190	72.2190	< 0.0001%	Fit and predict	17.4 ms	32.2 ms

Seasonality, events and regressors

Each supported effect on its own, then all of them together: a weekly pattern, a switchable weekly pattern, an event with a window, and additive and multiplicative regressors.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Weekly pattern	96 rows	105.2764	105.2764	< 0.0001%	Fit	15.0 ms	25.0 ms
Switchable weekly pattern	96 rows	105.2763	105.2763	< 0.0001%	Fit	17.1 ms	27.1 ms
Event with a window	96 rows	105.2751	105.2751	< 0.0001%	Fit	9.53 ms	18.5 ms
Additive regressor	96 rows	105.2753	105.2753	< 0.0001%	Fit	8.10 ms	14.5 ms
Multiplicative regressor	96 rows	105.2751	105.2751	< 0.0001%	Fit	10.1 ms	16.7 ms
Everything at once, absmax scaling	96 rows	105.8453	105.8453	< 0.0001%	Fit	28.2 ms	42.9 ms
Everything at once, minmax scaling	96 rows	105.8453	105.8453	< 0.0001%	Fit	26.2 ms	39.3 ms

Unusual data

Shuffled rows, repeated dates, a falling curve, a curve pinned at its ceiling, a perfectly constant series and values outside the bounds.

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Shuffled rows	96 rows	105.2754	105.2754	< 0.0001%	Fit	7.71 ms	14.6 ms
Repeated dates	96 rows	103.2373	103.2373	< 0.0001%	Fit	5.85 ms	13.0 ms
Falling curve	96 rows	4.2479	4.2479	< 0.0001%	Fit	6.38 ms	13.1 ms
Pinned at the ceiling	96 rows	109.5200	109.5200	< 0.0001%	Fit	10.5 ms	18.3 ms
Perfectly constant	96 rows	49.9301	49.9301	7.9e-12	Fit	16.4 ms	24.9 ms
Values outside the bounds	96 rows	106.0168	106.0168	< 0.0001%	Fit	8.97 ms	16.2 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
Anomalies in a history	365 rows	157.6301	157.6272	0.073%	Fit and find anomalies	71.6 ms	298 ms
Defaults, ranges with changing growth	365 rows	193.9557	193.9523	0.0086%	Simulate uncertainty (different work)	23.3 ms	293 ms
Defaults, ranges with changing growth, second seed	365 rows	193.9557	193.9523	0.0086%	Simulate uncertainty (different work)	23.5 ms	298 ms
Samples, weekly pattern	96 rows	71.9060	71.9060	< 0.0001%	Simulate uncertainty (different work)	1.22 ms	80.4 ms
Ranges, eight months	256 rows	98.0804	98.0804	< 0.0001%	Simulate uncertainty (different work)	1.55 ms	25.9 ms
Ranges with an explicit floor	96 rows	72.2190	72.2190	< 0.0001%	Simulate uncertainty (different work)	1.01 ms	92.3 ms
Samples with an explicit floor	96 rows	72.2190	72.2190	< 0.0001%	Simulate uncertainty (different work)	733 µs	24.1 ms
Ranges with mixed effects	96 rows	72.2270	72.2270	< 0.0001%	Simulate uncertainty (different work)	760 µs	30.3 ms
Samples with mixed effects	96 rows	72.2270	72.2270	< 0.0001%	Simulate uncertainty (different work)	759 µs	25.1 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
Capacity, floor and a multiplicative regressor	96 rows	72.2189	72.2188	0.0091%	Simulate uncertainty (different work)	2.91 ms	210 ms
A year of changing growth rates	365 rows	193.9262	193.9405	0.027%	Simulate uncertainty (different work)	38.4 ms	356 ms

Cross-validation and choosing settings

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

Case	Input	Effect output	Python output	Largest difference	Timed step	Effect time	Python time
Cross-validation and metrics	96 rows	59.1345	59.1345	< 0.0001%	Cross-validate (different work)	17.1 ms	59.5 ms
Cross-validation with ranges	96 rows	59.1345	59.1345	< 0.0001%	Cross-validate with ranges (different work)	18.1 ms	64.1 ms
Choosing settings and a final holdout	96 rows	59.1345	59.1345	< 0.0001%	Search settings (different work)	35.5 ms	115 ms
Cross-validation, eight months	256 rows	88.5367	88.5214	0.034%	Cross-validate (different work)	14.1 ms	41.5 ms
Cross-validation with ranges, eight months	256 rows	88.5367	88.5214	0.034%	Cross-validate with ranges (different work)	15.1 ms	56.4 ms
Twelve folds and a search, sequential and parallel	256 rows	90.7830	90.7874	0.079%	Cross-validate (different work)	61.3 ms	170 ms
Monthly, custom and scaled metrics	256 rows	90.9241	90.9228	0.20%	—	—	—