Average Error: 8.0 → 0.1
Time: 7.5s
Precision: 64
\[\frac{x \cdot y}{y + 1}\]
↓
\[x \cdot \frac{1}{\frac{y + 1}{y}}\]
\frac{x \cdot y}{y + 1}
↓
x \cdot \frac{1}{\frac{y + 1}{y}}
double f(double x, double y) {
        double r538225 = x;
        double r538226 = y;
        double r538227 = r538225 * r538226;
        double r538228 = 1.0;
        double r538229 = r538226 + r538228;
        double r538230 = r538227 / r538229;
        return r538230;
}
↓
double f(double x, double y) {
        double r538231 = x;
        double r538232 = 1.0;
        double r538233 = y;
        double r538234 = 1.0;
        double r538235 = r538233 + r538234;
        double r538236 = r538235 / r538233;
        double r538237 = r538232 / r538236;
        double r538238 = r538231 * r538237;
        return r538238;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.0
Target0.0
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.848278829724677052581682801246643066:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891002655029296875:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Initial program 8.0

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

  3. Applied *-un-lft-identity8.0

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

  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. Using strategy rm

  7. Applied clear-num0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(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)))