Average Error: 8.2 → 0.0
Time: 2.0s
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 r532246 = x;
        double r532247 = y;
        double r532248 = r532246 * r532247;
        double r532249 = 1.0;
        double r532250 = r532247 + r532249;
        double r532251 = r532248 / r532250;
        return r532251;
}
↓
double f(double x, double y) {
        double r532252 = x;
        double r532253 = y;
        double r532254 = 1.0;
        double r532255 = r532253 + r532254;
        double r532256 = r532253 / r532255;
        double r532257 = r532252 * r532256;
        return r532257;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.2
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. Final simplification0.0

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

Reproduce

herbie shell --seed 1978988140 
(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)))