Average Error: 0.1 → 0.1
Time: 4.3s
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 r72790 = 1.0;
        double r72791 = x;
        double r72792 = 0.253;
        double r72793 = 0.12;
        double r72794 = r72791 * r72793;
        double r72795 = r72792 + r72794;
        double r72796 = r72791 * r72795;
        double r72797 = r72790 - r72796;
        return r72797;
}
↓
double f(double x) {
        double r72798 = x;
        double r72799 = -r72798;
        double r72800 = 0.12;
        double r72801 = 0.253;
        double r72802 = fma(r72800, r72798, r72801);
        double r72803 = 1.0;
        double r72804 = fma(r72799, r72802, r72803);
        return r72804;
}

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 2020060 +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)))))