Average Error: 20.0 → 0.5
Time: 4.4s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}}}{\frac{x + y}{\frac{\sqrt[3]{x}}{\sqrt[3]{x + y}}}} \cdot y}{\left(x + y\right) + 1}\]
\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{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}}}{\frac{x + y}{\frac{\sqrt[3]{x}}{\sqrt[3]{x + y}}}} \cdot y}{\left(x + y\right) + 1}
double f(double x, double y) {
        double r465228 = x;
        double r465229 = y;
        double r465230 = r465228 * r465229;
        double r465231 = r465228 + r465229;
        double r465232 = r465231 * r465231;
        double r465233 = 1.0;
        double r465234 = r465231 + r465233;
        double r465235 = r465232 * r465234;
        double r465236 = r465230 / r465235;
        return r465236;
}
↓
double f(double x, double y) {
        double r465237 = x;
        double r465238 = cbrt(r465237);
        double r465239 = r465238 * r465238;
        double r465240 = y;
        double r465241 = r465237 + r465240;
        double r465242 = cbrt(r465241);
        double r465243 = r465242 * r465242;
        double r465244 = r465239 / r465243;
        double r465245 = r465238 / r465242;
        double r465246 = r465241 / r465245;
        double r465247 = r465244 / r465246;
        double r465248 = r465247 * r465240;
        double r465249 = 1.0;
        double r465250 = r465241 + r465249;
        double r465251 = r465248 / r465250;
        return r465251;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.0
Target0.1
Herbie0.5
\[\frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}}\]

Derivation

  1. Initial program 20.0

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

  9. Applied add-cube-cbrt0.7

    \[\leadsto \frac{\frac{\frac{x}{\color{blue}{\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) \cdot \sqrt[3]{x + y}}}}{x + y} \cdot y}{\left(x + y\right) + 1}\]

  10. Applied add-cube-cbrt0.5

    \[\leadsto \frac{\frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) \cdot \sqrt[3]{x + y}}}{x + y} \cdot y}{\left(x + y\right) + 1}\]

  11. Applied times-frac0.5

    \[\leadsto \frac{\frac{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{x + y}}}}{x + y} \cdot y}{\left(x + y\right) + 1}\]

  12. Applied associate-/l*0.5

    \[\leadsto \frac{\color{blue}{\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}}}{\frac{x + y}{\frac{\sqrt[3]{x}}{\sqrt[3]{x + y}}}}} \cdot y}{\left(x + y\right) + 1}\]

  13. Final simplification0.5

    \[\leadsto \frac{\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}}}{\frac{x + y}{\frac{\sqrt[3]{x}}{\sqrt[3]{x + y}}}} \cdot y}{\left(x + y\right) + 1}\]

Reproduce

herbie shell --seed 2020036 
(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))))