Average Error: 0.1 → 0.1
Time: 20.8s
Precision: 64
\[\left(1 - x\right) + y \cdot \sqrt{x}\]
↓
\[\mathsf{fma}\left(y, \sqrt{x}, 1\right) - x\]
\left(1 - x\right) + y \cdot \sqrt{x}
↓
\mathsf{fma}\left(y, \sqrt{x}, 1\right) - x
double f(double x, double y) {
        double r4282528 = 1.0;
        double r4282529 = x;
        double r4282530 = r4282528 - r4282529;
        double r4282531 = y;
        double r4282532 = sqrt(r4282529);
        double r4282533 = r4282531 * r4282532;
        double r4282534 = r4282530 + r4282533;
        return r4282534;
}
↓
double f(double x, double y) {
        double r4282535 = y;
        double r4282536 = x;
        double r4282537 = sqrt(r4282536);
        double r4282538 = 1.0;
        double r4282539 = fma(r4282535, r4282537, r4282538);
        double r4282540 = r4282539 - r4282536;
        return r4282540;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  (+ (- 1.0 x) (* y (sqrt x))))