Average Error: 0.4 → 0.4
Time: 30.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(y + \left(\frac{\frac{1}{x}}{9} - 1\right)\right) \cdot 3\right) \cdot \sqrt{x}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(y + \left(\frac{\frac{1}{x}}{9} - 1\right)\right) \cdot 3\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r463546 = 3.0;
        double r463547 = x;
        double r463548 = sqrt(r463547);
        double r463549 = r463546 * r463548;
        double r463550 = y;
        double r463551 = 1.0;
        double r463552 = 9.0;
        double r463553 = r463547 * r463552;
        double r463554 = r463551 / r463553;
        double r463555 = r463550 + r463554;
        double r463556 = r463555 - r463551;
        double r463557 = r463549 * r463556;
        return r463557;
}
↓
double f(double x, double y) {
        double r463558 = y;
        double r463559 = 1.0;
        double r463560 = x;
        double r463561 = r463559 / r463560;
        double r463562 = 9.0;
        double r463563 = r463561 / r463562;
        double r463564 = r463563 - r463559;
        double r463565 = r463558 + r463564;
        double r463566 = 3.0;
        double r463567 = r463565 * r463566;
        double r463568 = sqrt(r463560);
        double r463569 = r463567 * r463568;
        return r463569;
}

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-/r*0.4

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

  5. Applied associate-*l*0.4

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

  7. Applied pow10.4

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

  8. Applied pow10.4

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

  9. Applied pow-prod-down0.4

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

  10. Applied pow10.4

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

  11. Applied pow-prod-down0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(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)))