Average Error: 0.4 → 0.4
Time: 7.8s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \left(\left(\frac{\frac{1}{x}}{9} + y\right) - 1\right)\right) \cdot \sqrt{x}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \left(\left(\frac{\frac{1}{x}}{9} + y\right) - 1\right)\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r317312 = 3.0;
        double r317313 = x;
        double r317314 = sqrt(r317313);
        double r317315 = r317312 * r317314;
        double r317316 = y;
        double r317317 = 1.0;
        double r317318 = 9.0;
        double r317319 = r317313 * r317318;
        double r317320 = r317317 / r317319;
        double r317321 = r317316 + r317320;
        double r317322 = r317321 - r317317;
        double r317323 = r317315 * r317322;
        return r317323;
}
↓
double f(double x, double y) {
        double r317324 = 3.0;
        double r317325 = 1.0;
        double r317326 = x;
        double r317327 = r317325 / r317326;
        double r317328 = 9.0;
        double r317329 = r317327 / r317328;
        double r317330 = y;
        double r317331 = r317329 + r317330;
        double r317332 = r317331 - r317325;
        double r317333 = r317324 * r317332;
        double r317334 = sqrt(r317326);
        double r317335 = r317333 * r317334;
        return r317335;
}

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 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 associate-/r*0.4

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

  7. Applied div-inv0.4

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

  9. Applied pow10.4

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

  10. Applied pow10.4

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

  11. Applied pow-prod-down0.4

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

  12. Applied pow10.4

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

  13. Applied pow-prod-down0.4

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

  14. Simplified0.4

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

  15. Final simplification0.4

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

Reproduce

herbie shell --seed 2019308 
(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)))