taylor_pass
std.seq.taylor_pass · Level L2Pass t of the Taylor shift by repeated synthetic division: coefficients 1 … n − 1 − t each add a times the coefficient just before them, as already updated. The body poly_taylor_at scans.
cⱼ ← cⱼ + a·cⱼ₋₁, j = 1 … n − 1 − t
Signature
taylor_pass(c: f64[n], t: f64[], a: f64[]) → 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
for j in 1 … n−1−t: c[j] += a·c[j−1]in exact rational arithmetic, on all 40 test cases. - All 137 float64 results inside the running error bound; the closest uses 68% 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 64% of it.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 91%
- bit-equal to the NumPy formula in float64
- 100%
- largest error, in units in the last place
- 2.76
Identity
sha256:2daf0d33b09f6b7579e72e270aefc4fa052647ad726f995808b0caba6c3720a3The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.seq.taylor_pass · Ω:taylor_pass
- Pins
sha256:b277dc0bbb340d3f0f12f425e8cd08c95ca5d48fd1fc7e7713a0c364696d6f3athis graph and the 1 it reaches through calls- Evidence
sha256:9f4cfb95cc9bb0d5aed5f29312712f36c1a9ed94cd41e039c7f304305a3c4c13the 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.