Average Error: 0.3 → 0.2
Time: 10.0s
Precision: 64
\[\frac{x \cdot 100.0}{x + y}\]
↓
\[\frac{x}{y + x} \cdot 100.0\]
\frac{x \cdot 100.0}{x + y}
↓
\frac{x}{y + x} \cdot 100.0
double f(double x, double y) {
        double r35738936 = x;
        double r35738937 = 100.0;
        double r35738938 = r35738936 * r35738937;
        double r35738939 = y;
        double r35738940 = r35738936 + r35738939;
        double r35738941 = r35738938 / r35738940;
        return r35738941;
}
↓
double f(double x, double y) {
        double r35738942 = x;
        double r35738943 = y;
        double r35738944 = r35738943 + r35738942;
        double r35738945 = r35738942 / r35738944;
        double r35738946 = 100.0;
        double r35738947 = r35738945 * r35738946;
        return r35738947;
}

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
\[\frac{x}{1} \cdot \frac{100.0}{x + y}\]

Derivation

  1. Initial program 0.3

    \[\frac{x \cdot 100.0}{x + y}\]
  2. Using strategy rm

  3. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100.0}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.2

    \[\leadsto \color{blue}{\frac{x}{x + y} \cdot 100.0}\]

  6. Final simplification0.2

    \[\leadsto \frac{x}{y + x} \cdot 100.0\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1) (/ 100.0 (+ x y)))

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