Average Error: 8.8 → 0.0
Time: 1.3s
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 r585411 = x;
        double r585412 = y;
        double r585413 = r585411 * r585412;
        double r585414 = 1.0;
        double r585415 = r585412 + r585414;
        double r585416 = r585413 / r585415;
        return r585416;
}
↓
double f(double x, double y) {
        double r585417 = x;
        double r585418 = y;
        double r585419 = 1.0;
        double r585420 = r585418 + r585419;
        double r585421 = r585418 / r585420;
        double r585422 = r585417 * r585421;
        return r585422;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.8
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 8.8

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

  3. Applied *-un-lft-identity8.8

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

  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 2020002 +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)))