Average Error: 0.1 → 0.1
Time: 4.2s
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 r100394 = 1.0;
        double r100395 = x;
        double r100396 = 0.253;
        double r100397 = 0.12;
        double r100398 = r100395 * r100397;
        double r100399 = r100396 + r100398;
        double r100400 = r100395 * r100399;
        double r100401 = r100394 - r100400;
        return r100401;
}
↓
double f(double x) {
        double r100402 = x;
        double r100403 = -r100402;
        double r100404 = 0.12;
        double r100405 = 0.253;
        double r100406 = fma(r100404, r100402, r100405);
        double r100407 = 1.0;
        double r100408 = fma(r100403, r100406, r100407);
        return r100408;
}

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 2020062 +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)))))