Average Error: 19.6 → 0.1
Time: 14.8s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{y \cdot \frac{x}{x + y}}{x + y}}{\left(x + y\right) + 1}\]
\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{y \cdot \frac{x}{x + y}}{x + y}}{\left(x + y\right) + 1}
double f(double x, double y) {
        double r26000303 = x;
        double r26000304 = y;
        double r26000305 = r26000303 * r26000304;
        double r26000306 = r26000303 + r26000304;
        double r26000307 = r26000306 * r26000306;
        double r26000308 = 1.0;
        double r26000309 = r26000306 + r26000308;
        double r26000310 = r26000307 * r26000309;
        double r26000311 = r26000305 / r26000310;
        return r26000311;
}
↓
double f(double x, double y) {
        double r26000312 = y;
        double r26000313 = x;
        double r26000314 = r26000313 + r26000312;
        double r26000315 = r26000313 / r26000314;
        double r26000316 = r26000312 * r26000315;
        double r26000317 = r26000316 / r26000314;
        double r26000318 = 1.0;
        double r26000319 = r26000314 + r26000318;
        double r26000320 = r26000317 / r26000319;
        return r26000320;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.6
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 19.6

    \[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
  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 *-un-lft-identity7.8

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

  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. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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))))