Average Error: 0.1 → 0.1
Time: 4.6s
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 r103453 = 1.0;
        double r103454 = x;
        double r103455 = 0.253;
        double r103456 = 0.12;
        double r103457 = r103454 * r103456;
        double r103458 = r103455 + r103457;
        double r103459 = r103454 * r103458;
        double r103460 = r103453 - r103459;
        return r103460;
}
↓
double f(double x) {
        double r103461 = x;
        double r103462 = -r103461;
        double r103463 = 0.12;
        double r103464 = 0.253;
        double r103465 = fma(r103463, r103461, r103464);
        double r103466 = 1.0;
        double r103467 = fma(r103462, r103465, r103466);
        return r103467;
}

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 2020083 +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)))))