Average Error: 7.6 → 0.1
Time: 6.2s
Precision: 64
\[\frac{x \cdot y}{y + 1.0}\]
↓
\[\frac{x}{\frac{y + 1.0}{y}}\]
\frac{x \cdot y}{y + 1.0}
↓
\frac{x}{\frac{y + 1.0}{y}}
double f(double x, double y) {
        double r18402104 = x;
        double r18402105 = y;
        double r18402106 = r18402104 * r18402105;
        double r18402107 = 1.0;
        double r18402108 = r18402105 + r18402107;
        double r18402109 = r18402106 / r18402108;
        return r18402109;
}
↓
double f(double x, double y) {
        double r18402110 = x;
        double r18402111 = y;
        double r18402112 = 1.0;
        double r18402113 = r18402111 + r18402112;
        double r18402114 = r18402113 / r18402111;
        double r18402115 = r18402110 / r18402114;
        return r18402115;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.6
Target0.0
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.8482788297247:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891:\\ \;\;\;\;\frac{x \cdot y}{y + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Initial program 7.6

    \[\frac{x \cdot y}{y + 1.0}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{y + 1.0}{y}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{x}{\frac{y + 1.0}{y}}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1.0)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1.0)))