Average Error: 0.1 → 0.1
Time: 3.3s
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 r83288 = 1.0;
        double r83289 = x;
        double r83290 = 0.253;
        double r83291 = 0.12;
        double r83292 = r83289 * r83291;
        double r83293 = r83290 + r83292;
        double r83294 = r83289 * r83293;
        double r83295 = r83288 - r83294;
        return r83295;
}
↓
double f(double x) {
        double r83296 = x;
        double r83297 = -r83296;
        double r83298 = 0.12;
        double r83299 = 0.253;
        double r83300 = fma(r83298, r83296, r83299);
        double r83301 = 1.0;
        double r83302 = fma(r83297, r83300, r83301);
        return r83302;
}

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 2020034 +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)))))