Average Error: 8.2 → 0.0
Time: 9.0s
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 r454215 = x;
        double r454216 = y;
        double r454217 = r454215 * r454216;
        double r454218 = 1.0;
        double r454219 = r454216 + r454218;
        double r454220 = r454217 / r454219;
        return r454220;
}
↓
double f(double x, double y) {
        double r454221 = y;
        double r454222 = 1.0;
        double r454223 = r454221 + r454222;
        double r454224 = r454221 / r454223;
        double r454225 = x;
        double r454226 = r454224 * r454225;
        return r454226;
}

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

Original8.2
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 8.2

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

  3. Applied *-un-lft-identity8.2

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

  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. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(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)))