Average Error: 0.4 → 0.2
Time: 16.0s
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 r133730119 = x;
        double r133730120 = 100.0;
        double r133730121 = r133730119 * r133730120;
        double r133730122 = y;
        double r133730123 = r133730119 + r133730122;
        double r133730124 = r133730121 / r133730123;
        return r133730124;
}
↓
double f(double x, double y) {
        double r133730125 = x;
        double r133730126 = y;
        double r133730127 = r133730125 + r133730126;
        double r133730128 = r133730125 / r133730127;
        double r133730129 = 100.0;
        double r133730130 = r133730128 * r133730129;
        return r133730130;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
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. 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 2019173 +o rules:numerics
(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)))