Average Error: 20.1 → 0.2
Time: 21.4s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{\frac{x}{y + x}}{\frac{\left(y + x\right) + 1}{y}}}{y + x}\]
\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}{y + x}}{\frac{\left(y + x\right) + 1}{y}}}{y + x}
double f(double x, double y) {
        double r27045857 = x;
        double r27045858 = y;
        double r27045859 = r27045857 * r27045858;
        double r27045860 = r27045857 + r27045858;
        double r27045861 = r27045860 * r27045860;
        double r27045862 = 1.0;
        double r27045863 = r27045860 + r27045862;
        double r27045864 = r27045861 * r27045863;
        double r27045865 = r27045859 / r27045864;
        return r27045865;
}
↓
double f(double x, double y) {
        double r27045866 = x;
        double r27045867 = y;
        double r27045868 = r27045867 + r27045866;
        double r27045869 = r27045866 / r27045868;
        double r27045870 = 1.0;
        double r27045871 = r27045868 + r27045870;
        double r27045872 = r27045871 / r27045867;
        double r27045873 = r27045869 / r27045872;
        double r27045874 = r27045873 / r27045868;
        return r27045874;
}

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

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 div-inv0.2

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

  8. Applied associate-*l*0.2

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

  9. Simplified0.1

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

  11. Applied associate-*r/0.1

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

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))))