Average Error: 8.1 → 0.1
Time: 10.8s
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 r436390 = x;
        double r436391 = y;
        double r436392 = r436390 * r436391;
        double r436393 = 1.0;
        double r436394 = r436391 + r436393;
        double r436395 = r436392 / r436394;
        return r436395;
}
↓
double f(double x, double y) {
        double r436396 = x;
        double r436397 = y;
        double r436398 = 1.0;
        double r436399 = r436397 + r436398;
        double r436400 = r436399 / r436397;
        double r436401 = r436396 / r436400;
        return r436401;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.1
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 8.1

    \[\frac{x \cdot y}{y + 1}\]
  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 2019322 +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)))