Average Error: 19.8 → 0.1
Time: 4.6s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{1}{\frac{x + y}{x}} \cdot \frac{y}{\left(x + y\right) + 1}}{x + y}\]
\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}
↓
\frac{\frac{1}{\frac{x + y}{x}} \cdot \frac{y}{\left(x + y\right) + 1}}{x + y}
double f(double x, double y) {
        double r682633 = x;
        double r682634 = y;
        double r682635 = r682633 * r682634;
        double r682636 = r682633 + r682634;
        double r682637 = r682636 * r682636;
        double r682638 = 1.0;
        double r682639 = r682636 + r682638;
        double r682640 = r682637 * r682639;
        double r682641 = r682635 / r682640;
        return r682641;
}
↓
double f(double x, double y) {
        double r682642 = 1.0;
        double r682643 = x;
        double r682644 = y;
        double r682645 = r682643 + r682644;
        double r682646 = r682645 / r682643;
        double r682647 = r682642 / r682646;
        double r682648 = 1.0;
        double r682649 = r682645 + r682648;
        double r682650 = r682644 / r682649;
        double r682651 = r682647 * r682650;
        double r682652 = r682651 / r682645;
        return r682652;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.8
Target0.1
Herbie0.1
\[\frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}}\]

Derivation

  1. Initial program 19.8

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

  3. Applied times-frac7.5

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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-*l/0.1

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

  9. Applied clear-num0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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))))