exponential_logpdf

std.stats.exponential_logpdf · Level L1

The exponential distribution's log density at x ≥ 0: log λ − λx.

log f(x) = log λ − λx

Signature

exponential_logpdf(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.log(rate) − rate·x to 80 digits (100-digit arithmetic), on all 40 test cases.
All 161 float64 results inside the running error bound; the closest uses 57% 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 52% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 76%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 26

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

—

Called by

—

sha256:f05b96acbc477bd79086c69db4c9e810c8f2707a402fa6a8f817475ea3351b59

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.exponential_logpdf · Ω:exponential_logpdf
Pins: sha256:6d1c7fd2bec68ca51ca81ddb8c00357b592e1ae982e2155074c382fc5200b86ethis graph alone
Evidence: sha256:e35a0cf6f82ae7b84fa9662d105352843ac9da1f9b91ccee138b092199531b3cthe 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.