Average Error: 0.1 → 0.1
Time: 3.1s
Precision: 64
\[\left(1 - x\right) + y \cdot \sqrt{x}\]
↓
\[1 - \left(x - y \cdot \sqrt{x}\right)\]
\left(1 - x\right) + y \cdot \sqrt{x}
↓
1 - \left(x - y \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r89309 = 1.0;
        double r89310 = x;
        double r89311 = r89309 - r89310;
        double r89312 = y;
        double r89313 = sqrt(r89310);
        double r89314 = r89312 * r89313;
        double r89315 = r89311 + r89314;
        return r89315;
}
↓
double f(double x, double y) {
        double r89316 = 1.0;
        double r89317 = x;
        double r89318 = y;
        double r89319 = sqrt(r89317);
        double r89320 = r89318 * r89319;
        double r89321 = r89317 - r89320;
        double r89322 = r89316 - r89321;
        return r89322;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(1 - x\right) + y \cdot \sqrt{x}\]
  2. Using strategy rm

  3. Applied associate-+l-0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020049 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1 x) (* y (sqrt x))))