Average Error: 8.4 → 0.0
Time: 24.2s
Precision: 64
\[\frac{x \cdot y}{y + 1.0}\]
↓
\[\frac{y}{y + 1.0} \cdot x\]
\frac{x \cdot y}{y + 1.0}
↓
\frac{y}{y + 1.0} \cdot x
double f(double x, double y) {
        double r32383617 = x;
        double r32383618 = y;
        double r32383619 = r32383617 * r32383618;
        double r32383620 = 1.0;
        double r32383621 = r32383618 + r32383620;
        double r32383622 = r32383619 / r32383621;
        return r32383622;
}
↓
double f(double x, double y) {
        double r32383623 = y;
        double r32383624 = 1.0;
        double r32383625 = r32383623 + r32383624;
        double r32383626 = r32383623 / r32383625;
        double r32383627 = x;
        double r32383628 = r32383626 * r32383627;
        return r32383628;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.4
Target0.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.8482788297247:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891:\\ \;\;\;\;\frac{x \cdot y}{y + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Initial program 8.4

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

  3. Applied *-un-lft-identity8.4

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

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{y + 1.0}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{x} \cdot \frac{y}{y + 1.0}\]

  6. Final simplification0.0

    \[\leadsto \frac{y}{y + 1.0} \cdot x\]

Reproduce

herbie shell --seed 2019165 
(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)))