Average Error: 0.1 → 0.1
Time: 18.0s
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 r70375 = 1.0;
        double r70376 = x;
        double r70377 = r70375 - r70376;
        double r70378 = y;
        double r70379 = sqrt(r70376);
        double r70380 = r70378 * r70379;
        double r70381 = r70377 + r70380;
        return r70381;
}
↓
double f(double x, double y) {
        double r70382 = y;
        double r70383 = x;
        double r70384 = sqrt(r70383);
        double r70385 = 1.0;
        double r70386 = r70385 - r70383;
        double r70387 = fma(r70382, r70384, r70386);
        return r70387;
}

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 2019326 +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))))