Average Error: 0.2 → 0.2
Time: 21.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}
double f(double x, double y) {
        double r297492 = 1.0;
        double r297493 = x;
        double r297494 = 9.0;
        double r297495 = r297493 * r297494;
        double r297496 = r297492 / r297495;
        double r297497 = r297492 - r297496;
        double r297498 = y;
        double r297499 = 3.0;
        double r297500 = sqrt(r297493);
        double r297501 = r297499 * r297500;
        double r297502 = r297498 / r297501;
        double r297503 = r297497 - r297502;
        return r297503;
}
↓
double f(double x, double y) {
        double r297504 = 1.0;
        double r297505 = x;
        double r297506 = r297504 / r297505;
        double r297507 = 9.0;
        double r297508 = r297506 / r297507;
        double r297509 = r297504 - r297508;
        double r297510 = 1.0;
        double r297511 = sqrt(r297505);
        double r297512 = y;
        double r297513 = 3.0;
        double r297514 = r297512 / r297513;
        double r297515 = r297511 / r297514;
        double r297516 = r297510 / r297515;
        double r297517 = r297509 - r297516;
        return r297517;
}

Error

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

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

  3. Applied associate-/r*0.2

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

  5. Applied *-un-lft-identity0.2

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

  6. Applied *-un-lft-identity0.2

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

  7. Applied distribute-lft-out--0.2

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

  8. Simplified0.2

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

  10. Applied *-un-lft-identity0.2

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

  11. Applied *-un-lft-identity0.2

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

  12. Applied times-frac0.2

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

  13. Applied associate-/l*0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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