Accuracy verification

Generated at build time · last updated 2026-11-09

A calculator that looks good but gives a wrong answer is worse than none. So our calculators are checked against independent reference implementations. The table below is not typed in by hand: it is produced when the site is built, by running our calculators on the same inputs and comparing them with values computed by SciPy, NumPy and Python’s exact integer maths.

50calculators checked

76test cases

199values compared

199 / 199match the reference

How the check works

Reference values come from scipy.stats (t-tests, ANOVA, chi-square, regression, distributions, confidence intervals), NumPy (descriptive statistics, error metrics) and Python’s math.comb / math.perm (exact counting).
A value passes when it agrees with the reference to within the precision we display (relative difference at most 0.05 %, and usually far smaller). Very small p-values that we show as “< 0.0001” pass when the true value is below that threshold.
Cases marked closed form are checked against the textbook formula rather than a library, because no library function exists for them. They confirm the arithmetic, not an independent algorithm.
The script that creates the references is verification/generate.py in our repository. The same checks are part of our test suite, and this page is recomputed every time the site is rebuilt, so it always shows the current state.

Verification covers the numerical results for the example inputs shown. It does not replace judgement: check that a test is appropriate for your data, and report any discrepancy through the contact page.

All checks

T-Test Calculator

Welch two-sample t-test · reference: `scipy.stats.ttest_ind(a, b, equal_var=False)`
Quantity	Reference value	Our result	Status
t statistic	-3.92195	-3.9219	✓ matches
p-value	0.001534143	0.0015341	✓ matches
Degrees of freedom	13.99955	14	✓ matches

Pooled two-sample t-test · reference: `scipy.stats.ttest_ind(a, b, equal_var=True)`
Quantity	Reference value	Our result	Status
t statistic	-3.92195	-3.9219	✓ matches
p-value	0.001534056	0.0015341	✓ matches
Degrees of freedom	14	14	✓ matches

Paired t-test (after − before) · reference: `scipy.stats.ttest_rel(after, before)`
Quantity	Reference value	Our result	Status
t statistic	26.93836	26.938	✓ matches
p-value	2.490034e-8	< 0.0001	✓ matches
Degrees of freedom	7	7	✓ matches

One-sample t-test against μ₀ = 24 · reference: `scipy.stats.ttest_1samp(a, 24)`
Quantity	Reference value	Our result	Status
t statistic	1.550492	1.5505	✓ matches
p-value	0.1649589	0.16496	✓ matches
Degrees of freedom	7	7	✓ matches

One-sample t-test, left-tailed · reference: `scipy.stats.ttest_1samp(a, 24, alternative='less')`
Quantity	Reference value	Our result	Status
p-value	0.9175205	0.91752	✓ matches

One-Sample Z-Test Calculator

One-sample z-test, two-tailed · reference: `2 × scipy.stats.norm.sf(|z|)`
Quantity	Reference value	Our result	Status
z-statistic	2	2	✓ matches
p-value	0.04550026	0.0455	✓ matches
Standard error (σ/√n)	2.5	2.5	✓ matches

One-sample z-test, left-tailed · reference: `scipy.stats.norm.cdf(z)`
Quantity	Reference value	Our result	Status
z-statistic	-1.5	-1.5	✓ matches
p-value	0.0668072	0.066807	✓ matches

One-Way ANOVA Calculator

One-way ANOVA, 3 groups · reference: `scipy.stats.f_oneway(g1, g2, g3)`
Quantity	Reference value	Our result	Status
F statistic	12.63636	12.636	✓ matches
p-value	0.0006068783	0.00060688	✓ matches

One-way ANOVA, 4 groups · reference: `scipy.stats.f_oneway(*groups)`
Quantity	Reference value	Our result	Status
F statistic	43.10061	43.101	✓ matches
p-value	6.854293e-8	< 0.0001	✓ matches

Chi-Square Test Calculator

Chi-square test of independence (2 × 3) · reference: `scipy.stats.chi2_contingency(table, correction=False)`
Quantity	Reference value	Our result	Status
Chi-square statistic χ²	9.863636	9.86364	✓ matches
p-value	0.007213376	0.0072134	✓ matches
Degrees of freedom	2	2	✓ matches
Cramér’s V (effect size)	0.2654328	0.2654	✓ matches

Chi-square goodness of fit (equal expected) · reference: `scipy.stats.chisquare(observed)`
Quantity	Reference value	Our result	Status
Chi-square statistic χ²	12.32	12.32	✓ matches
p-value	0.00636363	0.0063636	✓ matches

Chi-square goodness of fit (given expected) · reference: `scipy.stats.chisquare(observed, f_exp)`
Quantity	Reference value	Our result	Status
Chi-square statistic χ²	2.666667	2.66667	✓ matches
p-value	0.4459217	0.44592	✓ matches

P-Value from Chi-Square Calculator

χ² = 7.81, df = 3 · reference: `scipy.stats.chi2.sf / ppf`
Quantity	Reference value	Our result	Status
p-value (right-tail)	0.05010606	0.0501061	✓ matches
Critical value (right tail, α = 0.05)	7.814728	7.81473	✓ matches

χ² = 18.307, df = 10 · reference: `scipy.stats.chi2.sf / ppf`
Quantity	Reference value	Our result	Status
p-value (right-tail)	0.05000059	0.0500006	✓ matches
Critical value (right tail, α = 0.05)	18.30704	18.307	✓ matches

χ² = 1.2, df = 2 · reference: `scipy.stats.chi2.sf / ppf`
Quantity	Reference value	Our result	Status
p-value (right-tail)	0.5488116	0.548812	✓ matches
Critical value (right tail, α = 0.05)	5.991465	5.99146	✓ matches

Regression Equation Calculator

Simple linear regression · reference: `scipy.stats.linregress(x, y)`
Quantity	Reference value	Our result	Status
Slope b₁	1.978571	1.97857	✓ matches
Intercept b₀	0.1714286	0.171429	✓ matches
Correlation r	0.9976494	0.99765	✓ matches
R² (coefficient of determination)	0.9953043	0.9953	✓ matches
Prediction at x = 10	19.95714	19.9571	✓ matches

Weak relationship (non-significant slope) · reference: `scipy.stats.linregress(x, y)`
Quantity	Reference value	Our result	Status
Slope b₁	0.1826008	0.182601	✓ matches
Intercept b₀	29.72406	29.7241	✓ matches
Correlation r	0.3952696	0.39527	✓ matches
p-value for the slope	0.3324464	0.33245	✓ matches

Confidence Interval Calculator

Confidence interval for a mean (t, raw data) · reference: `scipy.stats.t.interval(0.95, n − 1, mean, sem)`
Quantity	Reference value	Our result	Status
95% confidence interval for the mean	12.15685 to 13.09315	12.1568 to 13.0932	✓ matches
Sample mean	12.625	12.625	✓ matches

Wilson interval for a proportion (45 of 120) · reference: `scipy.stats.binomtest(45, 120).proportion_ci(method='wilson')`
Quantity	Reference value	Our result	Status
95% CI (Wilson, recommended)	29.35243 to 46.42305	29.352 % to 46.423 %	✓ matches

Mean and Standard Deviation Calculator

Sample mean and SD · reference: `numpy.std(ddof=1), numpy.var(ddof=1)`
Quantity	Reference value	Our result	Status
Sample standard deviation (s)	2.13809	2.13809	✓ matches
Mean (x̄)	5	5	✓ matches
Sample variance (s²)	4.571429	4.57143	✓ matches

Population SD · reference: `numpy.std(ddof=0)`
Quantity	Reference value	Our result	Status
Population standard deviation (σ)	2	2	✓ matches
Population variance (σ²)	4	4	✓ matches

Mean Absolute Deviation (MAD) Calculator

Mean absolute deviation · reference: `numpy.mean(|x − mean|), scipy.stats.median_abs_deviation`
Quantity	Reference value	Our result	Status
Mean absolute deviation (MAD)	3.75	3.75	✓ matches
Median absolute deviation	2.5	2.5	✓ matches

RSD Calculator: Relative Standard Deviation

Relative standard deviation · reference: `numpy.std(ddof=1) / numpy.mean × 100`
Quantity	Reference value	Our result	Status
Relative standard deviation (RSD)	2.368519	2.3685 %	✓ matches

Mean, Median, Mode and Range Calculator

Mean, median, range · reference: `numpy.mean, numpy.median`
Quantity	Reference value	Our result	Status
Mean	6.125	6.125	✓ matches
Median	7	7	✓ matches
Range	8	8	✓ matches

Skewness Calculator

Skewness (types 1 and 2) · reference: `scipy.stats.skew(bias=False / True)`
Quantity	Reference value	Our result	Status
G₁: adjusted Fisher-Pearson (type 2, Excel SKEW)	1.543273	1.5433	✓ matches
g₁: moment coefficient (type 1)	1.343247	1.3432	✓ matches

Kurtosis Calculator

Excess kurtosis (types 1 and 2) · reference: `scipy.stats.kurtosis(bias=False / True)`
Quantity	Reference value	Our result	Status
G₂: adjusted (type 2, Excel KURT)	1.642372	1.6424	✓ matches
g₂: moment coefficient (type 1)	0.5721223	0.57212	✓ matches

Standard Error of the Mean (SEM) Calculator

Standard error of the mean · reference: `scipy.stats.sem`
Quantity	Reference value	Our result	Status
Standard error of the mean (SEM)	0.9689043	0.968904	✓ matches
Mean (x̄)	14.71429	14.7143	✓ matches

Sample Variance Calculator

Sample and population variance · reference: `numpy.var(ddof=1 / 0)`
Quantity	Reference value	Our result	Status
Sample variance (s²)	6.571429	6.571429	✓ matches
Population variance (σ²)	5.632653	5.632653	✓ matches

Binomial Probability Calculator with Steps

Binomial n = 10, p = 0.4, k = 3 · reference: `scipy.stats.binom.pmf / cdf / sf`
Quantity	Reference value	Our result	Status
P(X = 3)	0.2149908	0.21499085	✓ matches
P(X ≤ 3)	0.3822806	0.3822806	✓ matches
P(X ≥ 3)	0.8327102	0.83271025	✓ matches
P(X > 3)	0.6177194	0.6177194	✓ matches

Binomial n = 50, p = 0.07, k = 5 · reference: `scipy.stats.binom.pmf / cdf`
Quantity	Reference value	Our result	Status
P(X = 5)	0.1359267	0.13592666	✓ matches
P(X ≤ 5)	0.8649536	0.86495357	✓ matches

Geometric Distribution Calculator

Geometric p = 0.2, k = 4 · reference: `scipy.stats.geom.pmf / cdf`
Quantity	Reference value	Our result	Status
P(X = 4)	0.1024	0.1024	✓ matches
P(success within 4 trials)	0.5904	0.5904	✓ matches
Expected number of trials 1/p	5	5	✓ matches

Gamma Distribution Calculator

Gamma shape 3, scale 2, x = 5 · reference: `scipy.stats.gamma.cdf / pdf`
Quantity	Reference value	Our result	Status
P(X ≤ 5)	0.4561869	0.45618688	✓ matches
Density f(5)	0.1282578	0.12825781	✓ matches
Mean kθ	6	6	✓ matches
Variance kθ²	12	12	✓ matches

Z-Table Calculator

Standard normal at z = 1.96 · reference: `scipy.stats.norm.cdf / sf`
Quantity	Reference value	Our result	Status
Area to the left P(Z < z)	0.9750021	0.9750021	✓ matches
Area to the right P(Z > z)	0.0249979	0.0249979	✓ matches

Standard normal at z = -0.5 · reference: `scipy.stats.norm.cdf / sf`
Quantity	Reference value	Our result	Status
Area to the left P(Z < z)	0.3085375	0.3085375	✓ matches
Area to the right P(Z > z)	0.6914625	0.6914625	✓ matches

Standard normal at z = 2.576 · reference: `scipy.stats.norm.cdf / sf`
Quantity	Reference value	Our result	Status
Area to the left P(Z < z)	0.9950025	0.9950025	✓ matches
Area to the right P(Z > z)	0.004997532	0.004997532	✓ matches

Z Test Statistic Calculator

z for a sample mean · reference: `scipy.stats.norm.sf`
Quantity	Reference value	Our result	Status
z for a sample mean	1.725	1.725	✓ matches
Two-tailed p-value	0.08452747	0.084527	✓ matches

nCr Calculator (Combinations)

C(52, 5) · reference: `math.comb(52, 5)`
Quantity	Reference value	Our result	Status
C(52, 5) = 52C5	2598960	2,598,960	✓ matches

C(40, 20) exact integer · reference: `math.comb(40, 20)`
Quantity	Reference value	Our result	Status
C(40, 20) = 40C20	137846528820	137,846,528,820	✓ matches

C(100, 50) in scientific notation · reference: `math.comb(100, 50)`
Quantity	Reference value	Our result	Status
C(100, 50) = 100C50	1.008913e+29	1.00891 × 10^29 (30 digits)	✓ matches

nPr Calculator (Permutations)

P(10, 4) · reference: `math.perm(10, 4)`
Quantity	Reference value	Our result	Status
P(10, 4) = 10P4	5040	5,040	✓ matches

Combination Calculator (nCr and nPr)

C(49, 6) lottery · reference: `math.comb, math.perm`
Quantity	Reference value	Our result	Status
Combinations C(n, r)	13983816	13,983,816	✓ matches
Permutations P(n, r)	10068347520	10,068,347,520	✓ matches

Birthday Paradox Calculator

Birthday paradox, 23 people · closed form: `exact product 1 − ∏(365 − i)/365`
Quantity	Reference value	Our result	Status
Chance at least two of 23 share a birthday	0.5072972	0.5072972	✓ matches

Mean Squared Error (MSE) Calculator

MSE, RMSE, MAE · reference: `numpy`
Quantity	Reference value	Our result	Status
Mean squared error (MSE)	1.071429	1.071429	✓ matches
Root mean squared error (RMSE)	1.035098	1.0351	✓ matches
Mean absolute error (MAE)	1	1	✓ matches

SSE Calculator (Sum of Squared Errors)

Sum of squared errors · reference: `numpy`
Quantity	Reference value	Our result	Status
Sum of squared errors (SSE)	0.59	0.59	✓ matches
Total sum of squares (SST)	80.83333	80.8333	✓ matches

Cosine Similarity Calculator

Cosine similarity · reference: `numpy.dot, numpy.linalg.norm`
Quantity	Reference value	Our result	Status
Cosine similarity	0.9722843	0.9722843	✓ matches
Dot product A·B	2557	2557	✓ matches
Euclidean distance	16.94107	16.9411	✓ matches

Entropy Calculator (Shannon Entropy)

Shannon entropy of counts 9, 5 (bits) · reference: `scipy.stats.entropy(base=2)`
Quantity	Reference value	Our result	Status
Shannon entropy H (bits)	0.940286	0.940286	✓ matches

F1 Score Calculator

F1 from confusion counts · closed form: `F1 = 2TP / (2TP + FP + FN)`
Quantity	Reference value	Our result	Status
F1 score	0.75	0.75	✓ matches
Precision	80	80 %	✓ matches
Recall	70.58824	70.588 %	✓ matches

Doubling Time Calculator

Doubling time at 3.5% growth · closed form: `ln 2 / ln(1.035)`
Quantity	Reference value	Our result	Status
Doubling time (years)	20.14879	20.1488	✓ matches

Cochran’s Formula Calculator

Cochran sample size (95%, ±5%, p = 0.5, N = 2000) · closed form: `n₀ = z²pq/e², n = n₀ / (1 + (n₀ − 1)/N)`
Quantity	Reference value	Our result	Status
Cochran’s n₀ (infinite population)	385	385	✓ matches
After finite population correction	323	323	✓ matches

Probability of 3 Events Calculator

3 independent events (exact enumeration of all outcomes) · closed form: `enumeration of all 2ⁿ outcomes with independent probabilities`
Quantity	Reference value	Our result	Status
All 3 events occur P(A ∩ B ∩ C)	0.03	0.03	✓ matches
None occur	0.28	0.28	✓ matches
At least one occurs P(A ∪ B ∪ …)	0.72	0.72	✓ matches
Exactly 1 of 3 occur	0.47	0.47	✓ matches
Exactly 2 of 3 occur	0.22	0.22	✓ matches
Expected number of events	1	1	✓ matches
At least 2 occur	0.25	0.25	✓ matches

4 Event Probability Calculator

4 independent events (exact enumeration of all outcomes) · closed form: `enumeration of all 2ⁿ outcomes with independent probabilities`
Quantity	Reference value	Our result	Status
All 4 events occur P(A ∩ B ∩ C ∩ D)	0.009	0.009	✓ matches
None occur	0.126	0.126	✓ matches
At least one occurs P(A ∪ B ∪ …)	0.874	0.874	✓ matches
Exactly 1 of 4 occur	0.383	0.383	✓ matches
Exactly 2 of 4 occur	0.365	0.365	✓ matches
Expected number of events	1.5	1.5	✓ matches
At least 2 occur	0.491	0.491	✓ matches

Binomial Distribution Table Calculator

Binomial n = 12, p = 0.35 summary · reference: `scipy.stats.binom(12, 0.35).mean / std / var / stats("s") / median`
Quantity	Reference value	Our result	Status
Mean μ = np	4.2	4.2	✓ matches
Standard deviation σ	1.652271	1.65227	✓ matches
Variance	2.73	2.73	✓ matches
Skewness	0.1815683	0.1816	✓ matches
Median	4	4	✓ matches

Combinations with Repetition Calculator

Multisets: 8 items from 5 types · reference: `math.comb(n + r − 1, r), n ** r, math.comb(r − 1, n − 1)`
Quantity	Reference value	Our result	Status
Combinations with repetition, 8 from 5 types	495	495	✓ matches
Ordered with repetition nʳ	390625	390,625	✓ matches
Positive integer solutions (each xᵢ ≥ 1)	35	35	✓ matches

Confusion Matrix Calculator

Confusion matrix metrics · closed form: `standard definitions (scikit-learn conventions)`
Quantity	Reference value	Our result	Status
Accuracy	87.5	87.5 %	✓ matches
Precision (PPV)	89.47368	89.47 %	✓ matches
Recall (sensitivity, TPR)	85	85 %	✓ matches
Specificity (TNR)	90	90 %	✓ matches
F1 score	87.17949	87.18 %	✓ matches
Negative predictive value	85.71429	85.71 %	✓ matches
False positive rate	10	10 %	✓ matches
False negative rate (miss rate)	15	15 %	✓ matches

Hypothesis Testing Calculator

One-sample t-test from summary statistics · reference: `scipy.stats.t.sf`
Quantity	Reference value	Our result	Status
Test statistic t	1.844662	1.8447	✓ matches
p-value	0.07269149	0.072691	✓ matches
Standard error	1.897367	1.89737	✓ matches

One-sample proportion z-test (58 of 100 vs 0.5) · reference: `scipy.stats.norm.sf`
Quantity	Reference value	Our result	Status
Test statistic z	1.6	1.6	✓ matches
p-value	0.1095986	0.1096	✓ matches

One-sample z-test, right-tailed · reference: `scipy.stats.norm.sf`
Quantity	Reference value	Our result	Status
Test statistic z	1.844662	1.8447	✓ matches
p-value	0.03254336	0.032543	✓ matches

Level of Significance Calculator

Critical value and power (α = 0.05, d = 0.5, n = 32) · reference: `scipy.stats.norm.ppf / cdf`
Quantity	Reference value	Our result	Status
Critical values (±)	1.959964	± 1.96	✓ matches
Power (1 − β)	80.74304	80.74 %	✓ matches
Type II error probability β	19.25696	19.26 %	✓ matches

Critical t value (α = 0.01, df = 12, right tail) · reference: `scipy.stats.t.ppf`
Quantity	Reference value	Our result	Status
Critical value	2.680998	2.681	✓ matches

Probability and Chance Calculator

Chance of an event with p = 1/6 · reference: `scipy.stats.binom.pmf, 1 − (1 − p)ⁿ`
Quantity	Reference value	Our result	Status
Probability of the event (single trial)	0.1666667	0.16666667	✓ matches
At least once in 10 trials	0.8384944	0.83849442	✓ matches
Exactly 2 times in 10 trials	0.29071	0.29071005	✓ matches

Raosoft Sample Size Calculator

Raosoft sample size (±5%, 95%, N = 1500) · closed form: `n = N·x / ((N − 1)E² + x), x = z²·r(100 − r)`
Quantity	Reference value	Our result	Status
Recommended sample size	306	306	✓ matches
Without population correction	385	385	✓ matches

Statistical Significance Calculator

A/B test: 250/5000 vs 300/5000 conversions · reference: `scipy.stats.chi2_contingency (z² = χ² for a 2 × 2 table)`
Quantity	Reference value	Our result	Status
p-value	0.02829497	0.028295	✓ matches
z statistic	2.193172	2.193	✓ matches
Relative uplift of B over A	20	20 %	✓ matches

Sample Size Calculator

Two-proportion sample size (30% vs 45%, 80% power) · closed form: `n = [z(α/2)√(2p̄q̄) + z(β)√(p₁q₁ + p₂q₂)]² / (p₁ − p₂)²`
Quantity	Reference value	Our result	Status
Sample size per group (two proportions)	163	163	✓ matches

Percentage Error Calculator

Percentage error · closed form: `(approximate − exact) ÷ exact × 100`
Quantity	Reference value	Our result	Status
Percentage error	-2.140673	-2.14067 %	✓ matches
Absolute percentage error	2.140673	2.14067 %	✓ matches
Absolute error	0.21	0.21	✓ matches

Standard Deviation Calculator for Grouped Data

Grouped data SD (class midpoints) · closed form: `numpy with class midpoints`
Quantity	Reference value	Our result	Status
Mean of grouped data	25.88889	25.8889	✓ matches
Sample standard deviation (s)	11.24565	11.2457	✓ matches
Total frequency (N)	45	45	✓ matches
Σ f(x − x̄)²	5564.444	5564.44	✓ matches

Average Deviation Calculator

Average deviation · reference: `numpy`
Quantity	Reference value	Our result	Status
Average deviation about the mean	3.75	3.75	✓ matches
Average deviation about the median	3.5	3.5	✓ matches

Descriptive Statistics Calculator

Descriptive statistics · reference: `numpy`
Quantity	Reference value	Our result	Status
Count (n)	15	15	✓ matches
Mean	16.33333	16.3333	✓ matches
Median	15	15	✓ matches
Sum	245	245	✓ matches
Range	38	38	✓ matches
Sample variance (s²)	111.2381	111.238	✓ matches

Coefficient of Variation Calculator

Coefficient of variation · reference: `numpy.std(ddof=1) / numpy.mean × 100`
Quantity	Reference value	Our result	Status
Coefficient of variation (CV)	9.819304	9.8193 %	✓ matches
Standard deviation	2.160247	2.16025	✓ matches

Histogram Calculator and Maker

Histogram default bin count (Sturges) · closed form: `numpy.histogram_bin_edges(bins='sturges') uses ⌈log₂ n + 1⌉`
Quantity	Reference value	Our result	Status
Number of bins	5	5	✓ matches

Curve Fitting Calculator

Polynomial fit, degree 1 · reference: `numpy.polyfit(x, y, 1)`
Quantity	Reference value	Our result	Status
R²	0.9463986	0.9464	✓ matches
RMSE	7.506343	7.5063	✓ matches
SSE	563.4519	563.452	✓ matches

Polynomial fit, degree 2 · reference: `numpy.polyfit(x, y, 2)`
Quantity	Reference value	Our result	Status
R²	0.999914	0.99991	✓ matches
RMSE	0.3007541	0.30075	✓ matches
SSE	0.9045303	0.90453	✓ matches

Polynomial fit, degree 3 · reference: `numpy.polyfit(x, y, 3)`
Quantity	Reference value	Our result	Status
R²	0.9999443	0.99994	✓ matches
RMSE	0.242019	0.24202	✓ matches
SSE	0.5857319	0.585732	✓ matches

Exponential fit (log-linear least squares) · reference: `numpy.polyfit(x, ln y, 1), error measured on the original y scale`
Quantity	Reference value	Our result	Status
R²	0.9997947	0.99979	✓ matches
SSE	1.454242	1.45424	✓ matches

Nonlinear Regression Calculator

Logistic curve fit · reference: `scipy.optimize.curve_fit (Levenberg-Marquardt)`
Quantity	Reference value	Our result	Status
Parameter L	76.00643	76.00643	✓ matches
Parameter k	0.7350666	0.7350666	✓ matches
Parameter x₀	5.015195	5.015195	✓ matches
SSE	0.3020473	0.302047	✓ matches

Michaelis-Menten fit · reference: `scipy.optimize.curve_fit (Levenberg-Marquardt)`
Quantity	Reference value	Our result	Status
Parameter Vmax	12.71293	12.71293	✓ matches
Parameter K	2.724184	2.724184	✓ matches
SSE	0.04800794	0.0480079	✓ matches

Decay to a baseline fit · reference: `scipy.optimize.curve_fit (Levenberg-Marquardt)`
Quantity	Reference value	Our result	Status
Parameter a	9.428508	9.428508	✓ matches
Parameter b	0.4687657	0.4687657	✓ matches
Parameter c	2.837218	2.837218	✓ matches