compound_balance

std.elementwise.compound_balance · Level L5

The balance after n periods of compound interest at rate i per period, with no deposits, withdrawals or fees: B₀(1 + i)ⁿ, computed as B₀·exp(n·log1p(i)) so that a small rate keeps its digits. n may be fractional.

Bₙ = B₀(1 + i)ⁿ

Signature

compound_balance(B0: f64[m], i: f64[m], n: f64[m]) → f64[m]

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 B0 * (1 + i)**n to 80 digits (100-digit arithmetic), on all 40 test cases.
All 172 float64 results inside the running error bound; the closest uses 16% 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 23% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 63%
bit-equal to the NumPy formula in float64: 65%
largest error, in units in the last place: 2.78

Identity

Calls

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Called by

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sha256:bba300d0cf538cdf958589c68128f4af330279b08cf419ae36d1c31267edea58

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.compound_balance · Ω:compound_balance
Pins: sha256:37443a38bfa169220174468b2a8ce322e55e5c08a45c9c06c32cb8ab143d4035this graph alone
Evidence: sha256:4f67953cccb2fe6eba9734c86426c8548748ed15b28e6b920db84722f1aa9a2bthe 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.