Average Error: 20.2 → 0.1
Time: 17.4s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{x}{y + x} \cdot \frac{y}{\left(y + x\right) + 1}}{y + x}\]
\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 r18523959 = x;
        double r18523960 = y;
        double r18523961 = r18523959 * r18523960;
        double r18523962 = r18523959 + r18523960;
        double r18523963 = r18523962 * r18523962;
        double r18523964 = 1.0;
        double r18523965 = r18523962 + r18523964;
        double r18523966 = r18523963 * r18523965;
        double r18523967 = r18523961 / r18523966;
        return r18523967;
}
↓
double f(double x, double y) {
        double r18523968 = x;
        double r18523969 = y;
        double r18523970 = r18523969 + r18523968;
        double r18523971 = r18523968 / r18523970;
        double r18523972 = 1.0;
        double r18523973 = r18523970 + r18523972;
        double r18523974 = r18523969 / r18523973;
        double r18523975 = r18523971 * r18523974;
        double r18523976 = r18523975 / r18523970;
        return r18523976;
}

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))))