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 r84489 = 1.0;
        double r84490 = x;
        double r84491 = 0.253;
        double r84492 = 0.12;
        double r84493 = r84490 * r84492;
        double r84494 = r84491 + r84493;
        double r84495 = r84490 * r84494;
        double r84496 = r84489 - r84495;
        return r84496;
}
↓
double f(double x) {
        double r84497 = x;
        double r84498 = -r84497;
        double r84499 = 0.12;
        double r84500 = 0.253;
        double r84501 = fma(r84499, r84497, r84500);
        double r84502 = 1.0;
        double r84503 = fma(r84498, r84501, r84502);
        return r84503;
}

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 2020036 +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)))))