Average Error: 0.4 → 0.5
Time: 13.0s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(y + \sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}}\right) \cdot 3\right) \cdot \sqrt{x} + 3 \cdot \left(\sqrt{x} \cdot \left(-1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(y + \sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}}\right) \cdot 3\right) \cdot \sqrt{x} + 3 \cdot \left(\sqrt{x} \cdot \left(-1\right)\right)
double f(double x, double y) {
        double r300292 = 3.0;
        double r300293 = x;
        double r300294 = sqrt(r300293);
        double r300295 = r300292 * r300294;
        double r300296 = y;
        double r300297 = 1.0;
        double r300298 = 9.0;
        double r300299 = r300293 * r300298;
        double r300300 = r300297 / r300299;
        double r300301 = r300296 + r300300;
        double r300302 = r300301 - r300297;
        double r300303 = r300295 * r300302;
        return r300303;
}
↓
double f(double x, double y) {
        double r300304 = y;
        double r300305 = 1.0;
        double r300306 = x;
        double r300307 = 9.0;
        double r300308 = r300306 * r300307;
        double r300309 = r300305 / r300308;
        double r300310 = sqrt(r300309);
        double r300311 = r300310 * r300310;
        double r300312 = r300304 + r300311;
        double r300313 = 3.0;
        double r300314 = r300312 * r300313;
        double r300315 = sqrt(r300306);
        double r300316 = r300314 * r300315;
        double r300317 = -r300305;
        double r300318 = r300315 * r300317;
        double r300319 = r300313 * r300318;
        double r300320 = r300316 + r300319;
        return r300320;
}

Error

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Results

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Target

Original0.4
Target0.4
Herbie0.5
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

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 associate-*l*0.4

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

  5. Applied sub-neg0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  10. Applied add-sqr-sqrt0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019212 
(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)))