Average Error: 0.1 → 0.1
Time: 14.9s
Precision: 64
\[\left(1 - x\right) + y \cdot \sqrt{x}\]
↓
\[\mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)\]
\left(1 - x\right) + y \cdot \sqrt{x}
↓
\mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)
double f(double x, double y) {
        double r71925 = 1.0;
        double r71926 = x;
        double r71927 = r71925 - r71926;
        double r71928 = y;
        double r71929 = sqrt(r71926);
        double r71930 = r71928 * r71929;
        double r71931 = r71927 + r71930;
        return r71931;
}
↓
double f(double x, double y) {
        double r71932 = y;
        double r71933 = x;
        double r71934 = sqrt(r71933);
        double r71935 = 1.0;
        double r71936 = r71935 - r71933;
        double r71937 = fma(r71932, r71934, r71936);
        return r71937;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.1

    \[\left(1 - x\right) + y \cdot \sqrt{x}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1 x) (* y (sqrt x))))