erfinv

std.elementwise.erfinv · Level L5

The inverse error function: the y with erf(y) = x, for −1 < x < 1. Written as −sign(x)·Φ⁻¹((1 − |x|)/2)/√2, so that near ±1, where erfinv grows without bound, the tail 1 − |x| is computed exactly and keeps its digits; for |x| < ½ one Newton step on erf restores the low bits of x that (1 − |x|)/2 rounds away (in exact arithmetic the step is zero).

erfinv x = −sign(x)·Φ⁻¹((1 − |x|)/2)/√2, then a Newton step on erf for |x| < ½

Signature

erfinv(x: 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 the inverse of math.erf (mpmath.erfinv) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 148 float64 results inside the running error bound; the closest uses 30% 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 14% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 31%
bit-equal to the NumPy formula in float64: 61%
largest error, in units in the last place: 2.55

Identity

Calls

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Called by

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sha256:332d88740253a5d0b9acba1e84dfd109acd7587cc7a1c77c9e7bdac3f21c0ef1

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

Control handle

Symbol: Ω:std.elementwise.erfinv · Ω:erfinv
Pins: sha256:5636771097cade2cea9799b48ed6dc269d0a8fd4b3260e7f4c5d8ed9fbe2931bthis graph alone
Evidence: sha256:49c35092f98b1914d061787a05804712477fad5a3112f6c622f02c5bcdc06e40the 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.