Average Error: 0.4 → 0.2
Time: 11.9s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\sqrt{100} \cdot \frac{x}{\frac{x + y}{\sqrt{100}}}\]
\frac{x \cdot 100}{x + y}
↓
\sqrt{100} \cdot \frac{x}{\frac{x + y}{\sqrt{100}}}
double f(double x, double y) {
        double r540254 = x;
        double r540255 = 100.0;
        double r540256 = r540254 * r540255;
        double r540257 = y;
        double r540258 = r540254 + r540257;
        double r540259 = r540256 / r540258;
        return r540259;
}
↓
double f(double x, double y) {
        double r540260 = 100.0;
        double r540261 = sqrt(r540260);
        double r540262 = x;
        double r540263 = y;
        double r540264 = r540262 + r540263;
        double r540265 = r540264 / r540261;
        double r540266 = r540262 / r540265;
        double r540267 = r540261 * r540266;
        return r540267;
}

Error

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Results

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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 add-sqr-sqrt0.2

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

  6. Applied *-un-lft-identity0.2

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

  7. Applied times-frac0.4

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

  8. Applied *-un-lft-identity0.4

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

  9. Applied times-frac0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))