Average Error: 0.1 → 0.1
Time: 4.5s
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 r180059 = 1.0;
        double r180060 = x;
        double r180061 = 0.253;
        double r180062 = 0.12;
        double r180063 = r180060 * r180062;
        double r180064 = r180061 + r180063;
        double r180065 = r180060 * r180064;
        double r180066 = r180059 - r180065;
        return r180066;
}
↓
double f(double x) {
        double r180067 = x;
        double r180068 = -r180067;
        double r180069 = 0.12;
        double r180070 = 0.253;
        double r180071 = fma(r180069, r180067, r180070);
        double r180072 = 1.0;
        double r180073 = fma(r180068, r180071, r180072);
        return r180073;
}

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 2020100 +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)))))