Average Error: 20.0 → 0.5
Time: 15.0s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{y}{\left(x + y\right) + 1} \cdot \frac{1}{\frac{x + y}{\frac{x}{x + y}}}\]
\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}
↓
\frac{y}{\left(x + y\right) + 1} \cdot \frac{1}{\frac{x + y}{\frac{x}{x + y}}}
double f(double x, double y) {
        double r20177976 = x;
        double r20177977 = y;
        double r20177978 = r20177976 * r20177977;
        double r20177979 = r20177976 + r20177977;
        double r20177980 = r20177979 * r20177979;
        double r20177981 = 1.0;
        double r20177982 = r20177979 + r20177981;
        double r20177983 = r20177980 * r20177982;
        double r20177984 = r20177978 / r20177983;
        return r20177984;
}
↓
double f(double x, double y) {
        double r20177985 = y;
        double r20177986 = x;
        double r20177987 = r20177986 + r20177985;
        double r20177988 = 1.0;
        double r20177989 = r20177987 + r20177988;
        double r20177990 = r20177985 / r20177989;
        double r20177991 = 1.0;
        double r20177992 = r20177986 / r20177987;
        double r20177993 = r20177987 / r20177992;
        double r20177994 = r20177991 / r20177993;
        double r20177995 = r20177990 * r20177994;
        return r20177995;
}

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
Herbie0.5
\[\frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}}\]

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-frac8.0

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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 clear-num0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019179 
(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))))