Average Error: 8.1 → 0.0
Time: 2.3s
Precision: 64
\[\frac{x \cdot y}{y + 1}\]
↓
\[x \cdot \frac{y}{y + 1}\]
\frac{x \cdot y}{y + 1}
↓
x \cdot \frac{y}{y + 1}
double f(double x, double y) {
        double r770220 = x;
        double r770221 = y;
        double r770222 = r770220 * r770221;
        double r770223 = 1.0;
        double r770224 = r770221 + r770223;
        double r770225 = r770222 / r770224;
        return r770225;
}
↓
double f(double x, double y) {
        double r770226 = x;
        double r770227 = y;
        double r770228 = 1.0;
        double r770229 = r770227 + r770228;
        double r770230 = r770227 / r770229;
        double r770231 = r770226 * r770230;
        return r770231;
}

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

Original8.1
Target0.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.84827882972468:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891003:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

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

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1)))