Average Error: 19.5 → 0.2
Time: 19.5s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{x}{y + x}}{y + x} \cdot \frac{1}{\frac{\left(y + x\right) + 1}{y}}\]
\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}{y + x}}{y + x} \cdot \frac{1}{\frac{\left(y + x\right) + 1}{y}}
double f(double x, double y) {
        double r21579994 = x;
        double r21579995 = y;
        double r21579996 = r21579994 * r21579995;
        double r21579997 = r21579994 + r21579995;
        double r21579998 = r21579997 * r21579997;
        double r21579999 = 1.0;
        double r21580000 = r21579997 + r21579999;
        double r21580001 = r21579998 * r21580000;
        double r21580002 = r21579996 / r21580001;
        return r21580002;
}
↓
double f(double x, double y) {
        double r21580003 = x;
        double r21580004 = y;
        double r21580005 = r21580004 + r21580003;
        double r21580006 = r21580003 / r21580005;
        double r21580007 = r21580006 / r21580005;
        double r21580008 = 1.0;
        double r21580009 = 1.0;
        double r21580010 = r21580005 + r21580009;
        double r21580011 = r21580010 / r21580004;
        double r21580012 = r21580008 / r21580011;
        double r21580013 = r21580007 * r21580012;
        return r21580013;
}

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

Original19.5
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 19.5

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

  3. Applied times-frac8.0

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019170 
(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))))