Average Error: 0.1 → 0.1
Time: 3.2s
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 r74766 = 1.0;
        double r74767 = x;
        double r74768 = 0.253;
        double r74769 = 0.12;
        double r74770 = r74767 * r74769;
        double r74771 = r74768 + r74770;
        double r74772 = r74767 * r74771;
        double r74773 = r74766 - r74772;
        return r74773;
}
↓
double f(double x) {
        double r74774 = x;
        double r74775 = -r74774;
        double r74776 = 0.12;
        double r74777 = 0.253;
        double r74778 = fma(r74776, r74774, r74777);
        double r74779 = 1.0;
        double r74780 = fma(r74775, r74778, r74779);
        return r74780;
}

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 2020018 +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)))))