Average Error: 7.8 → 0.0
Time: 24.4s
Precision: 64
\[\frac{x \cdot y}{y + 1}\]
↓
\[\frac{y}{1 + y} \cdot x\]
\frac{x \cdot y}{y + 1}
↓
\frac{y}{1 + y} \cdot x
double f(double x, double y) {
        double r33274680 = x;
        double r33274681 = y;
        double r33274682 = r33274680 * r33274681;
        double r33274683 = 1.0;
        double r33274684 = r33274681 + r33274683;
        double r33274685 = r33274682 / r33274684;
        return r33274685;
}
↓
double f(double x, double y) {
        double r33274686 = y;
        double r33274687 = 1.0;
        double r33274688 = r33274687 + r33274686;
        double r33274689 = r33274686 / r33274688;
        double r33274690 = x;
        double r33274691 = r33274689 * r33274690;
        return r33274691;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.8
Target0.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.848278829724677052581682801246643066:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891002655029296875:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Initial program 7.8

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

  3. Applied *-un-lft-identity7.8

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

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{y + 1}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{x} \cdot \frac{y}{y + 1}\]

  6. Final simplification0.0

    \[\leadsto \frac{y}{1 + y} \cdot x\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1.0)) (- (/ x (* y y)) (- (/ x y) x))))

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