Average Error: 8.1 → 0.0
Time: 10.7s
Precision: 64
\[\frac{x \cdot y}{y + 1}\]
↓
\[\frac{y}{y + 1} \cdot x\]
\frac{x \cdot y}{y + 1}
↓
\frac{y}{y + 1} \cdot x
double f(double x, double y) {
        double r32976742 = x;
        double r32976743 = y;
        double r32976744 = r32976742 * r32976743;
        double r32976745 = 1.0;
        double r32976746 = r32976743 + r32976745;
        double r32976747 = r32976744 / r32976746;
        return r32976747;
}
↓
double f(double x, double y) {
        double r32976748 = y;
        double r32976749 = 1.0;
        double r32976750 = r32976748 + r32976749;
        double r32976751 = r32976748 / r32976750;
        double r32976752 = x;
        double r32976753 = r32976751 * r32976752;
        return r32976753;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.1
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 8.1

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

  3. Applied *-un-lft-identity8.1

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

  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

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

Reproduce

herbie shell --seed 2019172 
(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)))