Average Error: 0.4 → 0.2
Time: 32.6s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{\frac{y + x}{\sqrt{100}}} \cdot \sqrt{100}\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{\frac{y + x}{\sqrt{100}}} \cdot \sqrt{100}
double f(double x, double y) {
        double r40766367 = x;
        double r40766368 = 100.0;
        double r40766369 = r40766367 * r40766368;
        double r40766370 = y;
        double r40766371 = r40766367 + r40766370;
        double r40766372 = r40766369 / r40766371;
        return r40766372;
}
↓
double f(double x, double y) {
        double r40766373 = x;
        double r40766374 = y;
        double r40766375 = r40766374 + r40766373;
        double r40766376 = 100.0;
        double r40766377 = sqrt(r40766376);
        double r40766378 = r40766375 / r40766377;
        double r40766379 = r40766373 / r40766378;
        double r40766380 = r40766379 * r40766377;
        return r40766380;
}

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

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

Reproduce

herbie shell --seed 2019168 
(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)))