Average Error: 0.3 → 0.2
Time: 2.0s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{x + y} \cdot 100\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{x + y} \cdot 100
double f(double x, double y) {
        double r806740 = x;
        double r806741 = 100.0;
        double r806742 = r806740 * r806741;
        double r806743 = y;
        double r806744 = r806740 + r806743;
        double r806745 = r806742 / r806744;
        return r806745;
}
↓
double f(double x, double y) {
        double r806746 = x;
        double r806747 = y;
        double r806748 = r806746 + r806747;
        double r806749 = r806746 / r806748;
        double r806750 = 100.0;
        double r806751 = r806749 * r806750;
        return r806751;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.3

    \[\frac{x \cdot 100}{x + y}\]
  2. Using strategy rm

  3. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.2

    \[\leadsto \color{blue}{\frac{x}{x + y} \cdot 100}\]

  6. Final simplification0.2

    \[\leadsto \frac{x}{x + y} \cdot 100\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1) (/ 100 (+ x y)))

  (/ (* x 100) (+ x y)))