Average Error: 19.7 → 0.5
Time: 6.0s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{\frac{x}{x + y}}{\left(x + y\right) \cdot \frac{\left(x + y\right) + 1}{y}}\]
\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{x}{x + y}}{\left(x + y\right) \cdot \frac{\left(x + y\right) + 1}{y}}
double f(double x, double y) {
        double r297239 = x;
        double r297240 = y;
        double r297241 = r297239 * r297240;
        double r297242 = r297239 + r297240;
        double r297243 = r297242 * r297242;
        double r297244 = 1.0;
        double r297245 = r297242 + r297244;
        double r297246 = r297243 * r297245;
        double r297247 = r297241 / r297246;
        return r297247;
}
↓
double f(double x, double y) {
        double r297248 = x;
        double r297249 = y;
        double r297250 = r297248 + r297249;
        double r297251 = r297248 / r297250;
        double r297252 = 1.0;
        double r297253 = r297250 + r297252;
        double r297254 = r297253 / r297249;
        double r297255 = r297250 * r297254;
        double r297256 = r297251 / r297255;
        return r297256;
}

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

Original19.7
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 19.7

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

  3. Applied times-frac7.6

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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-*l/0.1

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

  9. Applied clear-num0.1

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 1978988140 
(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))))