Average Error: 19.8 → 0.1
Time: 4.7s
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 r477038 = x;
        double r477039 = y;
        double r477040 = r477038 * r477039;
        double r477041 = r477038 + r477039;
        double r477042 = r477041 * r477041;
        double r477043 = 1.0;
        double r477044 = r477041 + r477043;
        double r477045 = r477042 * r477044;
        double r477046 = r477040 / r477045;
        return r477046;
}
↓
double f(double x, double y) {
        double r477047 = 1.0;
        double r477048 = x;
        double r477049 = y;
        double r477050 = r477048 + r477049;
        double r477051 = r477050 / r477048;
        double r477052 = r477047 / r477051;
        double r477053 = 1.0;
        double r477054 = r477050 + r477053;
        double r477055 = r477049 / r477054;
        double r477056 = r477052 * r477055;
        double r477057 = r477056 / r477050;
        return r477057;
}

Error

Bits error versus x

Bits error versus y

Try it out

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))))