Average Error: 0.4 → 0.2
Time: 8.8s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{\frac{x + y}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{\frac{x + y}{100}}
double f(double x, double y) {
        double r530889 = x;
        double r530890 = 100.0;
        double r530891 = r530889 * r530890;
        double r530892 = y;
        double r530893 = r530889 + r530892;
        double r530894 = r530891 / r530893;
        return r530894;
}
↓
double f(double x, double y) {
        double r530895 = x;
        double r530896 = y;
        double r530897 = r530895 + r530896;
        double r530898 = 100.0;
        double r530899 = r530897 / r530898;
        double r530900 = r530895 / r530899;
        return r530900;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.4

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

  3. Applied associate-/l*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))