Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)
double f(double x) {
        double r94509 = 1.0;
        double r94510 = x;
        double r94511 = 0.253;
        double r94512 = 0.12;
        double r94513 = r94510 * r94512;
        double r94514 = r94511 + r94513;
        double r94515 = r94510 * r94514;
        double r94516 = r94509 - r94515;
        return r94516;
}
↓
double f(double x) {
        double r94517 = x;
        double r94518 = -r94517;
        double r94519 = 0.12;
        double r94520 = 0.253;
        double r94521 = fma(r94519, r94517, r94520);
        double r94522 = 1.0;
        double r94523 = fma(r94518, r94521, r94522);
        return r94523;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))