Average Error: 0.4 → 0.2
Time: 11.1s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[x \cdot \frac{100}{x + y}\]
\frac{x \cdot 100}{x + y}
↓
x \cdot \frac{100}{x + y}
double f(double x, double y) {
        double r491163 = x;
        double r491164 = 100.0;
        double r491165 = r491163 * r491164;
        double r491166 = y;
        double r491167 = r491163 + r491166;
        double r491168 = r491165 / r491167;
        return r491168;
}
↓
double f(double x, double y) {
        double r491169 = x;
        double r491170 = 100.0;
        double r491171 = y;
        double r491172 = r491169 + r491171;
        double r491173 = r491170 / r491172;
        double r491174 = r491169 * r491173;
        return r491174;
}

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 *-un-lft-identity0.4

    \[\leadsto \frac{x \cdot 100}{\color{blue}{1 \cdot \left(x + y\right)}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{100}{x + y}}\]

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(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)))