Average Error: 0.4 → 0.4
Time: 13.6s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \left(\left(y - 1\right) + \frac{1}{9 \cdot x}\right)\right) \cdot \sqrt{x}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \left(\left(y - 1\right) + \frac{1}{9 \cdot x}\right)\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r335281 = 3.0;
        double r335282 = x;
        double r335283 = sqrt(r335282);
        double r335284 = r335281 * r335283;
        double r335285 = y;
        double r335286 = 1.0;
        double r335287 = 9.0;
        double r335288 = r335282 * r335287;
        double r335289 = r335286 / r335288;
        double r335290 = r335285 + r335289;
        double r335291 = r335290 - r335286;
        double r335292 = r335284 * r335291;
        return r335292;
}
↓
double f(double x, double y) {
        double r335293 = 3.0;
        double r335294 = y;
        double r335295 = 1.0;
        double r335296 = r335294 - r335295;
        double r335297 = 9.0;
        double r335298 = x;
        double r335299 = r335297 * r335298;
        double r335300 = r335295 / r335299;
        double r335301 = r335296 + r335300;
        double r335302 = r335293 * r335301;
        double r335303 = sqrt(r335298);
        double r335304 = r335302 * r335303;
        return r335304;
}

Error

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

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

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\color{blue}{1 \cdot 1}}{x \cdot 9}\right) - 1\right)\]

  4. Applied times-frac0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{1}{x} \cdot \frac{1}{9}}\right) - 1\right)\]

  5. Final simplification0.4

    \[\leadsto \left(3 \cdot \left(\left(y - 1\right) + \frac{1}{9 \cdot x}\right)\right) \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))