Average Error: 0.1 → 0.1
Time: 4.3s
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 r87546 = 1.0;
        double r87547 = x;
        double r87548 = 0.253;
        double r87549 = 0.12;
        double r87550 = r87547 * r87549;
        double r87551 = r87548 + r87550;
        double r87552 = r87547 * r87551;
        double r87553 = r87546 - r87552;
        return r87553;
}
↓
double f(double x) {
        double r87554 = x;
        double r87555 = -r87554;
        double r87556 = 0.12;
        double r87557 = 0.253;
        double r87558 = fma(r87556, r87554, r87557);
        double r87559 = 1.0;
        double r87560 = fma(r87555, r87558, r87559);
        return r87560;
}

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 2020064 +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)))))