Average Error: 20.2 → 0.2
Time: 4.5s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{x}{x + y}}{x + y} \cdot \frac{\frac{1}{\left(x + y\right) + 1}}{\frac{1}{y}}\]
\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{x}{x + y}}{x + y} \cdot \frac{\frac{1}{\left(x + y\right) + 1}}{\frac{1}{y}}
double f(double x, double y) {
        double r389742 = x;
        double r389743 = y;
        double r389744 = r389742 * r389743;
        double r389745 = r389742 + r389743;
        double r389746 = r389745 * r389745;
        double r389747 = 1.0;
        double r389748 = r389745 + r389747;
        double r389749 = r389746 * r389748;
        double r389750 = r389744 / r389749;
        return r389750;
}
↓
double f(double x, double y) {
        double r389751 = x;
        double r389752 = y;
        double r389753 = r389751 + r389752;
        double r389754 = r389751 / r389753;
        double r389755 = r389754 / r389753;
        double r389756 = 1.0;
        double r389757 = 1.0;
        double r389758 = r389753 + r389757;
        double r389759 = r389756 / r389758;
        double r389760 = r389756 / r389752;
        double r389761 = r389759 / r389760;
        double r389762 = r389755 * r389761;
        return r389762;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.2
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 20.2

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

  3. Applied times-frac8.3

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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-num0.2

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

  9. Applied div-inv0.2

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

  10. Applied associate-/r*0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 
(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))))