rk4

std.func.rk4 · Level L3

Integrate y′ = f(y) by classical Runge–Kutta from y₀, one step per entry of h (the step sizes): a Scan of rk4_step, returning the final state. A template over the vector field f, verified through f = silu; a test integrates y′ = −y and checks e^(−t) to the method's fourth order.

yₖ₊₁ = rk4_step(yₖ, hₖ), k = 0 … s − 1

Signature

rk4(y0: f64[n], h: f64[s]) → 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 witness f = silu: s RK4 steps written out to 80 digits (100-digit arithmetic), on all 40 test cases.
All 176 float64 results inside the running error bound; the closest uses 45% 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 65% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 67%
bit-equal to the NumPy formula in float64: 81%
largest error, in units in the last place: 3.10

Identity

Calls

rk4_step

Called by

—

sha256:3644b1f4e9268c9b2ebb0d93f3edab32eaaa44d5c59435704de7530c42cf7e02

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.rk4[f=std.elementwise.silu]
Pins: sha256:68a521a183319627f01a6acbfd5d639bd656bef1da5e6c4d8525427af2333260this graph and the 2 it reaches through calls
Evidence: sha256:670e77872d0c7cc0b3a108f3455fdf1c75e8e4479e9ac69b6fcd34c1803b97cethe 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.