exponential_cdf
std.stats.exponential_cdf · Level L5The exponential distribution's cumulative probability, 1 − e^(−λx) for x ≥ 0 and 0 below, written as −expm1(−λx) so that it keeps its relative accuracy for small λx.
F(x) = 1 − e^(−λx) (x ≥ 0)
Signature
exponential_cdf(x: f64[n], rate: 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
np.where(x < 0, 0, 1 − np.exp(−rate·x))to 80 digits (100-digit arithmetic), on all 40 test cases. - All 142 float64 results inside the running error bound; the closest uses 22% 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 10% of it.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 92%
- bit-equal to the NumPy formula in float64
- 43%
- largest error, in units in the last place
- 1.42
Identity
Calls
—
Called by
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sha256:0649ec54ecabc4f245e8fc99f16a2e436660e5d999e60dbbb7c82188cbdb52baThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.stats.exponential_cdf · Ω:exponential_cdf
- Pins
sha256:e1e8693c3d5adc9b57ecba4c13ded80917624771eb9aae6886135621ce500852this graph alone- Evidence
sha256:52e23c134b6ab41a35bdc2522942ef4d41a6de36081bd89834f4ba5d02e66d0fthe 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.