Average Error: 19.9 → 0.2
Time: 10.6s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{\frac{x}{y + x}}{y + x} \cdot y}{\left(x + y\right) + 1}\]
\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}{y + x}}{y + x} \cdot y}{\left(x + y\right) + 1}
double f(double x, double y) {
        double r552350 = x;
        double r552351 = y;
        double r552352 = r552350 * r552351;
        double r552353 = r552350 + r552351;
        double r552354 = r552353 * r552353;
        double r552355 = 1.0;
        double r552356 = r552353 + r552355;
        double r552357 = r552354 * r552356;
        double r552358 = r552352 / r552357;
        return r552358;
}
↓
double f(double x, double y) {
        double r552359 = x;
        double r552360 = y;
        double r552361 = r552360 + r552359;
        double r552362 = r552359 / r552361;
        double r552363 = r552362 / r552361;
        double r552364 = r552363 * r552360;
        double r552365 = r552359 + r552360;
        double r552366 = 1.0;
        double r552367 = r552365 + r552366;
        double r552368 = r552364 / r552367;
        return r552368;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.9
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 19.9

    \[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
  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 *-un-lft-identity8.0

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

  6. Applied times-frac0.2

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

  8. Applied associate-*r/0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"
  :precision binary64

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

  (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1))))