Average Error: 7.6 → 0.1
Time: 7.1s
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 r30360634 = x;
        double r30360635 = y;
        double r30360636 = r30360634 * r30360635;
        double r30360637 = 1.0;
        double r30360638 = r30360635 + r30360637;
        double r30360639 = r30360636 / r30360638;
        return r30360639;
}
↓
double f(double x, double y) {
        double r30360640 = x;
        double r30360641 = y;
        double r30360642 = 1.0;
        double r30360643 = r30360641 + r30360642;
        double r30360644 = r30360643 / r30360641;
        double r30360645 = r30360640 / r30360644;
        return r30360645;
}

Error

Bits error versus x

Bits error versus y

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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)))