Average Error: 19.2 → 0.2
Time: 16.0s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1.0\right)}\]
↓
\[\frac{1}{\frac{1.0 + \left(y + x\right)}{y}} \cdot \left(\frac{x}{y + x} \cdot \frac{1}{y + x}\right)\]
\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1.0\right)}
↓
\frac{1}{\frac{1.0 + \left(y + x\right)}{y}} \cdot \left(\frac{x}{y + x} \cdot \frac{1}{y + x}\right)
double f(double x, double y) {
        double r22826300 = x;
        double r22826301 = y;
        double r22826302 = r22826300 * r22826301;
        double r22826303 = r22826300 + r22826301;
        double r22826304 = r22826303 * r22826303;
        double r22826305 = 1.0;
        double r22826306 = r22826303 + r22826305;
        double r22826307 = r22826304 * r22826306;
        double r22826308 = r22826302 / r22826307;
        return r22826308;
}
↓
double f(double x, double y) {
        double r22826309 = 1.0;
        double r22826310 = 1.0;
        double r22826311 = y;
        double r22826312 = x;
        double r22826313 = r22826311 + r22826312;
        double r22826314 = r22826310 + r22826313;
        double r22826315 = r22826314 / r22826311;
        double r22826316 = r22826309 / r22826315;
        double r22826317 = r22826312 / r22826313;
        double r22826318 = r22826309 / r22826313;
        double r22826319 = r22826317 * r22826318;
        double r22826320 = r22826316 * r22826319;
        return r22826320;
}

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

Original19.2
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 19.2

    \[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1.0\right)}\]
  2. Using strategy rm

  3. Applied times-frac7.7

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1.0}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{x + y}}{x + y}} \cdot \frac{y}{\left(x + y\right) + 1.0}\]
  6. Using strategy rm

  7. Applied clear-num0.2

    \[\leadsto \frac{\frac{x}{x + y}}{x + y} \cdot \color{blue}{\frac{1}{\frac{\left(x + y\right) + 1.0}{y}}}\]
  8. Using strategy rm

  9. Applied div-inv0.2

    \[\leadsto \color{blue}{\left(\frac{x}{x + y} \cdot \frac{1}{x + y}\right)} \cdot \frac{1}{\frac{\left(x + y\right) + 1.0}{y}}\]

  10. Final simplification0.2

    \[\leadsto \frac{1}{\frac{1.0 + \left(y + x\right)}{y}} \cdot \left(\frac{x}{y + x} \cdot \frac{1}{y + x}\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"

  :herbie-target
  (/ (/ (/ x (+ (+ y 1) x)) (+ y x)) (/ 1 (/ y (+ y x))))

  (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))))