Average Error: 0.4 → 0.2
Time: 2.5s
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 r788542 = x;
        double r788543 = 100.0;
        double r788544 = r788542 * r788543;
        double r788545 = y;
        double r788546 = r788542 + r788545;
        double r788547 = r788544 / r788546;
        return r788547;
}
↓
double f(double x, double y) {
        double r788548 = 100.0;
        double r788549 = sqrt(r788548);
        double r788550 = x;
        double r788551 = y;
        double r788552 = r788550 + r788551;
        double r788553 = r788552 / r788549;
        double r788554 = r788550 / r788553;
        double r788555 = r788549 * r788554;
        return r788555;
}

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 2020064 +o rules:numerics
(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)))