Average Error: 20.2 → 0.1
Time: 18.8s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{x}{y + x} \cdot \frac{y}{\left(y + x\right) + 1}}{y + x}\]
\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{x}{y + x} \cdot \frac{y}{\left(y + x\right) + 1}}{y + x}
double f(double x, double y) {
        double r20775960 = x;
        double r20775961 = y;
        double r20775962 = r20775960 * r20775961;
        double r20775963 = r20775960 + r20775961;
        double r20775964 = r20775963 * r20775963;
        double r20775965 = 1.0;
        double r20775966 = r20775963 + r20775965;
        double r20775967 = r20775964 * r20775966;
        double r20775968 = r20775962 / r20775967;
        return r20775968;
}
↓
double f(double x, double y) {
        double r20775969 = x;
        double r20775970 = y;
        double r20775971 = r20775970 + r20775969;
        double r20775972 = r20775969 / r20775971;
        double r20775973 = 1.0;
        double r20775974 = r20775971 + r20775973;
        double r20775975 = r20775970 / r20775974;
        double r20775976 = r20775972 * r20775975;
        double r20775977 = r20775976 / r20775971;
        return r20775977;
}

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
Target0.2
Herbie0.1
\[\frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}}\]

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-frac7.8

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(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))))