Average Error: 19.4 → 0.2
Time: 11.3s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{\frac{x}{x + y}}{x + y}}{\frac{\left(x + y\right) + 1}{y}}\]
\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}
↓
\frac{\frac{\frac{x}{x + y}}{x + y}}{\frac{\left(x + y\right) + 1}{y}}
double f(double x, double y) {
        double r493858 = x;
        double r493859 = y;
        double r493860 = r493858 * r493859;
        double r493861 = r493858 + r493859;
        double r493862 = r493861 * r493861;
        double r493863 = 1.0;
        double r493864 = r493861 + r493863;
        double r493865 = r493862 * r493864;
        double r493866 = r493860 / r493865;
        return r493866;
}
↓
double f(double x, double y) {
        double r493867 = x;
        double r493868 = y;
        double r493869 = r493867 + r493868;
        double r493870 = r493867 / r493869;
        double r493871 = r493870 / r493869;
        double r493872 = 1.0;
        double r493873 = r493869 + r493872;
        double r493874 = r493873 / r493868;
        double r493875 = r493871 / r493874;
        return r493875;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.4
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 19.4

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

  3. Applied times-frac7.6

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

  9. Applied associate-/l*0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (/ (/ (/ x (+ (+ y 1) x)) (+ y x)) (/ 1 (/ y (+ y x))))

  (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1))))