compose

std.func.compose · Level L0

Function composition, g ∘ f: x ↦ g(f(x)), for any two functions from a vector to a vector of the same length. A template: bind f and g with an instance id, std.func.compose[f=…,g=…].

(g ∘ f)(x) = g(f(x))

Signature

compose(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.
Equal to the reference witness f = square, g = softsign: x² / (1 + x²) in exact rational arithmetic, on all 40 test cases.
All 141 float64 results inside the running error bound; the closest uses 58% 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 57% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 82%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 1.04

Identity

Calls

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Called by

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sha256:b19f5044a76ff3102fecc6175628752809f4d1c7828f1c5f133bef4f58adc35f

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

Control handle

Symbol: Ω:std.func.compose[f=std.elementwise.square,g=std.elementwise.softsign]
Pins: sha256:0d5d17f5c3406f71046310fd48051b1a9640e8273aeca2422b369a3abfcec474this graph and the 3 it reaches through calls
Evidence: sha256:63b24e2095d5b50a05b973a486b37b3586558ca896fbcafbc86475b1e6deae97the 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.