Average Error: 19.8 → 0.2
Time: 8.9s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{\frac{x}{x + y}}{x + y} \cdot y}{\left(x + y\right) + 1}\]
\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}{x + y}}{x + y} \cdot y}{\left(x + y\right) + 1}
double f(double x, double y) {
        double r2294 = x;
        double r2295 = y;
        double r2296 = r2294 * r2295;
        double r2297 = r2294 + r2295;
        double r2298 = r2297 * r2297;
        double r2299 = 1.0;
        double r2300 = r2297 + r2299;
        double r2301 = r2298 * r2300;
        double r2302 = r2296 / r2301;
        return r2302;
}
↓
double f(double x, double y) {
        double r2303 = x;
        double r2304 = y;
        double r2305 = r2303 + r2304;
        double r2306 = r2303 / r2305;
        double r2307 = r2306 / r2305;
        double r2308 = r2307 * r2304;
        double r2309 = 1.0;
        double r2310 = r2305 + r2309;
        double r2311 = r2308 / r2310;
        return r2311;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.8
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 19.8

    \[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
  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 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-*r/0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 
(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))))