Average Error: 7.7 → 0.1
Time: 5.8s
Precision: 64
\[\frac{x \cdot y}{y + 1}\]
↓
\[\frac{x}{\frac{y + 1}{y}}\]
\frac{x \cdot y}{y + 1}
↓
\frac{x}{\frac{y + 1}{y}}
double f(double x, double y) {
        double r576441 = x;
        double r576442 = y;
        double r576443 = r576441 * r576442;
        double r576444 = 1.0;
        double r576445 = r576442 + r576444;
        double r576446 = r576443 / r576445;
        return r576446;
}
↓
double f(double x, double y) {
        double r576447 = x;
        double r576448 = y;
        double r576449 = 1.0;
        double r576450 = r576448 + r576449;
        double r576451 = r576450 / r576448;
        double r576452 = r576447 / r576451;
        return r576452;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.7
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 7.7

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

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(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)))