Average Error: 20.0 → 0.2
Time: 18.5s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{y \cdot \frac{\frac{x}{y + x}}{y + x}}{\left(y + x\right) + 1}\]
\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}
↓
\frac{y \cdot \frac{\frac{x}{y + x}}{y + x}}{\left(y + x\right) + 1}
double f(double x, double y) {
        double r26473683 = x;
        double r26473684 = y;
        double r26473685 = r26473683 * r26473684;
        double r26473686 = r26473683 + r26473684;
        double r26473687 = r26473686 * r26473686;
        double r26473688 = 1.0;
        double r26473689 = r26473686 + r26473688;
        double r26473690 = r26473687 * r26473689;
        double r26473691 = r26473685 / r26473690;
        return r26473691;
}
↓
double f(double x, double y) {
        double r26473692 = y;
        double r26473693 = x;
        double r26473694 = r26473692 + r26473693;
        double r26473695 = r26473693 / r26473694;
        double r26473696 = r26473695 / r26473694;
        double r26473697 = r26473692 * r26473696;
        double r26473698 = 1.0;
        double r26473699 = r26473694 + r26473698;
        double r26473700 = r26473697 / r26473699;
        return r26473700;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.0
Target0.1
Herbie0.2
\[\frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}}\]

Derivation

  1. Initial program 20.0

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

  3. Applied times-frac8.1

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{x + y}}{x + y}} \cdot \frac{y}{\left(x + y\right) + 1}\]
  6. Using strategy rm

  7. Applied associate-*r/0.2

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

  8. Final simplification0.2

    \[\leadsto \frac{y \cdot \frac{\frac{x}{y + x}}{y + x}}{\left(y + x\right) + 1}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"

  :herbie-target
  (/ (/ (/ x (+ (+ y 1.0) x)) (+ y x)) (/ 1.0 (/ y (+ y x))))

  (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))))