weibull_cdf

std.stats.weibull_cdf · Level L5

The Weibull distribution's cumulative probability with shape k and scale λ: 1 − e^(−(x/λ)ᵏ) for x > 0, written with expm1.

F(x) = 1 − e^(−(x/λ)ᵏ)

Signature

weibull_cdf(x: f64[n], k: f64[], lam: f64[]) → f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Agrees with the reference 1 − np.exp(−(x/λ)**k) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 148 float64 results inside the running error bound; the closest uses 10% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 15% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 67%
bit-equal to the NumPy formula in float64: 74%
largest error, in units in the last place: 12

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

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Called by

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sha256:1d9b2118ea7b30e7d6ee6348ac61c9a7ea7fdb622ef5187d97568e5996fc19e3

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.weibull_cdf · Ω:weibull_cdf
Pins: sha256:aadf957c5a46c985e8f4f320db8c37eedf4835b22a1e7e4a4aba3621d6773764this graph alone
Evidence: sha256:4f70832bf5c88bc5ca9ac92edba774d0e7fe908b605cbbf28de63a41cb84c723the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.