Average Error: 19.3 → 0.2
Time: 17.3s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1.0\right)}\]
↓
\[\frac{\left(\frac{x}{y + x} \cdot \frac{1}{y + x}\right) \cdot y}{1.0 + \left(y + x\right)}\]
\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1.0\right)}
↓
\frac{\left(\frac{x}{y + x} \cdot \frac{1}{y + x}\right) \cdot y}{1.0 + \left(y + x\right)}
double f(double x, double y) {
        double r24084339 = x;
        double r24084340 = y;
        double r24084341 = r24084339 * r24084340;
        double r24084342 = r24084339 + r24084340;
        double r24084343 = r24084342 * r24084342;
        double r24084344 = 1.0;
        double r24084345 = r24084342 + r24084344;
        double r24084346 = r24084343 * r24084345;
        double r24084347 = r24084341 / r24084346;
        return r24084347;
}
↓
double f(double x, double y) {
        double r24084348 = x;
        double r24084349 = y;
        double r24084350 = r24084349 + r24084348;
        double r24084351 = r24084348 / r24084350;
        double r24084352 = 1.0;
        double r24084353 = r24084352 / r24084350;
        double r24084354 = r24084351 * r24084353;
        double r24084355 = r24084354 * r24084349;
        double r24084356 = 1.0;
        double r24084357 = r24084356 + r24084350;
        double r24084358 = r24084355 / r24084357;
        return r24084358;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.3
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 19.3

    \[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1.0\right)}\]
  2. Using strategy rm

  3. Applied times-frac7.6

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1.0}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{x + y}}{x + y}} \cdot \frac{y}{\left(x + y\right) + 1.0}\]
  6. Using strategy rm

  7. Applied associate-*r/0.1

    \[\leadsto \color{blue}{\frac{\frac{\frac{x}{x + y}}{x + y} \cdot y}{\left(x + y\right) + 1.0}}\]
  8. Using strategy rm

  9. Applied div-inv0.2

    \[\leadsto \frac{\color{blue}{\left(\frac{x}{x + y} \cdot \frac{1}{x + y}\right)} \cdot y}{\left(x + y\right) + 1.0}\]

  10. Final simplification0.2

    \[\leadsto \frac{\left(\frac{x}{y + x} \cdot \frac{1}{y + x}\right) \cdot y}{1.0 + \left(y + x\right)}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"

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

  (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))))