Average Error: 0.1 → 0.1
Time: 4.1s
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 r73818 = 1.0;
        double r73819 = x;
        double r73820 = 0.253;
        double r73821 = 0.12;
        double r73822 = r73819 * r73821;
        double r73823 = r73820 + r73822;
        double r73824 = r73819 * r73823;
        double r73825 = r73818 - r73824;
        return r73825;
}
↓
double f(double x) {
        double r73826 = x;
        double r73827 = -r73826;
        double r73828 = 0.12;
        double r73829 = 0.253;
        double r73830 = fma(r73828, r73826, r73829);
        double r73831 = 1.0;
        double r73832 = fma(r73827, r73830, r73831);
        return r73832;
}

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 2020024 +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)))))