z_test_p

std.stats.z_test_p · Level L5

The two-sided p-value of a standard normal statistic z: P(|Z| > |z|) = erfc(|z|/√2). erfc keeps a small p-value's relative accuracy.

p = erfc(|z|/√2)

Signature

z_test_p(z: f64[n]) → 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 Q(½, z²/2), the upper incomplete gamma function to 80 digits (100-digit arithmetic), on all 40 test cases.
All 158 float64 results inside the running error bound; the closest uses 54% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 44%
bit-equal to the NumPy formula in float64: 42%
largest error, in units in the last place: 37

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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sha256:5743f5bceef26d5d452faf268ec3cd583a82cf2d7d05fe29801073ff22a4106f

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.z_test_p · Ω:z_test_p
Pins: sha256:a5291dfff8a461eedb62b03710b31908f8a2c712372d4b451337f45b6f32ed83this graph alone
Evidence: sha256:0873763c6dd1a7d1e9f7aace9407959a40dae774587985e7317514db8847c324the 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.