Average Error: 19.9 → 0.2
Time: 8.9s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{\frac{x}{y + x}}{x + y} \cdot y}{\left(x + y\right) + 1}\]
\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}{y + x}}{x + y} \cdot y}{\left(x + y\right) + 1}
double f(double x, double y) {
        double r1091323 = x;
        double r1091324 = y;
        double r1091325 = r1091323 * r1091324;
        double r1091326 = r1091323 + r1091324;
        double r1091327 = r1091326 * r1091326;
        double r1091328 = 1.0;
        double r1091329 = r1091326 + r1091328;
        double r1091330 = r1091327 * r1091329;
        double r1091331 = r1091325 / r1091330;
        return r1091331;
}
↓
double f(double x, double y) {
        double r1091332 = x;
        double r1091333 = y;
        double r1091334 = r1091333 + r1091332;
        double r1091335 = r1091332 / r1091334;
        double r1091336 = r1091332 + r1091333;
        double r1091337 = r1091335 / r1091336;
        double r1091338 = r1091337 * r1091333;
        double r1091339 = 1.0;
        double r1091340 = r1091336 + r1091339;
        double r1091341 = r1091338 / r1091340;
        return r1091341;
}

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-*l*0.2

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

  9. Simplified0.2

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

  11. Applied associate-*r/0.2

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

  12. Applied associate-*r/0.2

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

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))))