Average Error: 20.1 → 0.4
Time: 16.4s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{x}{y + x}}{y + x} \cdot \frac{\frac{y}{\sqrt[3]{1 + \left(y + x\right)} \cdot \sqrt[3]{1 + \left(y + x\right)}}}{\sqrt[3]{1 + \left(y + x\right)}}\]
\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{x}{y + x}}{y + x} \cdot \frac{\frac{y}{\sqrt[3]{1 + \left(y + x\right)} \cdot \sqrt[3]{1 + \left(y + x\right)}}}{\sqrt[3]{1 + \left(y + x\right)}}
double f(double x, double y) {
        double r25615879 = x;
        double r25615880 = y;
        double r25615881 = r25615879 * r25615880;
        double r25615882 = r25615879 + r25615880;
        double r25615883 = r25615882 * r25615882;
        double r25615884 = 1.0;
        double r25615885 = r25615882 + r25615884;
        double r25615886 = r25615883 * r25615885;
        double r25615887 = r25615881 / r25615886;
        return r25615887;
}
↓
double f(double x, double y) {
        double r25615888 = x;
        double r25615889 = y;
        double r25615890 = r25615889 + r25615888;
        double r25615891 = r25615888 / r25615890;
        double r25615892 = r25615891 / r25615890;
        double r25615893 = 1.0;
        double r25615894 = r25615893 + r25615890;
        double r25615895 = cbrt(r25615894);
        double r25615896 = r25615895 * r25615895;
        double r25615897 = r25615889 / r25615896;
        double r25615898 = r25615897 / r25615895;
        double r25615899 = r25615892 * r25615898;
        return r25615899;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.1
Target0.1
Herbie0.4
\[\frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}}\]

Derivation

  1. Initial program 20.1

    \[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
  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 add-cube-cbrt0.4

    \[\leadsto \frac{\frac{x}{x + y}}{x + y} \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{\left(x + y\right) + 1} \cdot \sqrt[3]{\left(x + y\right) + 1}\right) \cdot \sqrt[3]{\left(x + y\right) + 1}}}\]

  8. Applied associate-/r*0.4

    \[\leadsto \frac{\frac{x}{x + y}}{x + y} \cdot \color{blue}{\frac{\frac{y}{\sqrt[3]{\left(x + y\right) + 1} \cdot \sqrt[3]{\left(x + y\right) + 1}}}{\sqrt[3]{\left(x + y\right) + 1}}}\]

  9. Final simplification0.4

    \[\leadsto \frac{\frac{x}{y + x}}{y + x} \cdot \frac{\frac{y}{\sqrt[3]{1 + \left(y + x\right)} \cdot \sqrt[3]{1 + \left(y + x\right)}}}{\sqrt[3]{1 + \left(y + x\right)}}\]

Reproduce

herbie shell --seed 2019171 
(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))))