Average Error: 19.9 → 0.1
Time: 20.7s
Precision: 64
\[\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}\]
↓
\[\frac{x \cdot \frac{\frac{y}{\left(x + y\right) + 1}}{x + y}}{x + y}\]
\frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)}
↓
\frac{x \cdot \frac{\frac{y}{\left(x + y\right) + 1}}{x + y}}{x + y}
double f(double x, double y) {
        double r371270 = x;
        double r371271 = y;
        double r371272 = r371270 * r371271;
        double r371273 = r371270 + r371271;
        double r371274 = r371273 * r371273;
        double r371275 = 1.0;
        double r371276 = r371273 + r371275;
        double r371277 = r371274 * r371276;
        double r371278 = r371272 / r371277;
        return r371278;
}
↓
double f(double x, double y) {
        double r371279 = x;
        double r371280 = y;
        double r371281 = r371279 + r371280;
        double r371282 = 1.0;
        double r371283 = r371281 + r371282;
        double r371284 = r371280 / r371283;
        double r371285 = r371284 / r371281;
        double r371286 = r371279 * r371285;
        double r371287 = r371286 / r371281;
        return r371287;
}

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

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-frac8.1

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \frac{y}{\left(x + y\right) + 1}}\]
  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 div-inv0.2

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

  10. Applied associate-*l*0.2

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"

  :herbie-target
  (/ (/ (/ x (+ (+ y 1.0) x)) (+ y x)) (/ 1.0 (/ y (+ y x))))

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