geometric_growth
std.seq.geometric_growth · Level L2The trajectory of the discrete exponential model xₙ₊₁ = r·xₙ for s steps, s the length of steps (only its length is read): row n is x₀·rⁿ⁺¹. A Scan of growth_step.
xₙ = x₀·rⁿ
Signature
geometric_growth(x0: f64[m], rate: f64[m], steps: f64[s]) → f64[s, 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.
- Equal to the reference
x0 * rate**(n + 1) for each step nin exact rational arithmetic, on all 40 test cases. - All 521 float64 results inside the running error bound; the closest uses 84% 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 87% of it.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 85%
- bit-equal to the NumPy formula in float64
- 83%
- largest error, in units in the last place
- 1.81
Identity
sha256:9c21a76fe6c6547d8531cd629f39081c17ee9477dbafc77b35b0a8f46cfc1e01The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.seq.geometric_growth · Ω:geometric_growth
- Pins
sha256:1de66d9f86d6b039959272b2c8231ac561c565e92485d4a10153d9c72063ca5bthis graph and the 1 it reaches through calls- Evidence
sha256:6c24d5a227bdf34552ba13d97271dacf6d33ce67a7076c4637e8fda0d6580780the 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.