Average Error: 7.9 → 0.0
Time: 5.9s
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 r536517 = x;
        double r536518 = y;
        double r536519 = r536517 * r536518;
        double r536520 = 1.0;
        double r536521 = r536518 + r536520;
        double r536522 = r536519 / r536521;
        return r536522;
}
↓
double f(double x, double y) {
        double r536523 = x;
        double r536524 = y;
        double r536525 = 1.0;
        double r536526 = r536524 + r536525;
        double r536527 = r536524 / r536526;
        double r536528 = r536523 * r536527;
        return r536528;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.9
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 7.9

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

  3. Applied *-un-lft-identity7.9

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

  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 2019212 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (if (< y -3693.84827882972468) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891003) (/ (* x y) (+ y 1)) (- (/ x (* y y)) (- (/ x y) x))))

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