Average Error: 19.5 → 0.1
Time: 48.2s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{\frac{x}{x + y} \cdot y}{\left(x + y\right) + 1}}{x + y}\]
\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{\frac{x}{x + y} \cdot y}{\left(x + y\right) + 1}}{x + y}
double f(double x, double y) {
        double r20567480 = x;
        double r20567481 = y;
        double r20567482 = r20567480 * r20567481;
        double r20567483 = r20567480 + r20567481;
        double r20567484 = r20567483 * r20567483;
        double r20567485 = 1.0;
        double r20567486 = r20567483 + r20567485;
        double r20567487 = r20567484 * r20567486;
        double r20567488 = r20567482 / r20567487;
        return r20567488;
}
↓
double f(double x, double y) {
        double r20567489 = x;
        double r20567490 = y;
        double r20567491 = r20567489 + r20567490;
        double r20567492 = r20567489 / r20567491;
        double r20567493 = r20567492 * r20567490;
        double r20567494 = 1.0;
        double r20567495 = r20567491 + r20567494;
        double r20567496 = r20567493 / r20567495;
        double r20567497 = r20567496 / r20567491;
        return r20567497;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.5
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 19.5

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

  3. Applied times-frac8.1

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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 associate-*r/0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(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))))