Average Error: 0.4 → 0.4
Time: 18.9s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)
double f(double x, double y) {
        double r30629634 = 3.0;
        double r30629635 = x;
        double r30629636 = sqrt(r30629635);
        double r30629637 = r30629634 * r30629636;
        double r30629638 = y;
        double r30629639 = 1.0;
        double r30629640 = 9.0;
        double r30629641 = r30629635 * r30629640;
        double r30629642 = r30629639 / r30629641;
        double r30629643 = r30629638 + r30629642;
        double r30629644 = r30629643 - r30629639;
        double r30629645 = r30629637 * r30629644;
        return r30629645;
}
↓
double f(double x, double y) {
        double r30629646 = 3.0;
        double r30629647 = x;
        double r30629648 = sqrt(r30629647);
        double r30629649 = y;
        double r30629650 = 1.0;
        double r30629651 = r30629650 / r30629647;
        double r30629652 = 9.0;
        double r30629653 = r30629651 / r30629652;
        double r30629654 = r30629649 + r30629653;
        double r30629655 = r30629654 - r30629650;
        double r30629656 = r30629648 * r30629655;
        double r30629657 = r30629646 * r30629656;
        return r30629657;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))