Average Error: 0.4 → 0.4
Time: 15.0s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y - 1\right) + \frac{1}{x \cdot 9}\right)\right)\]
\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 - 1\right) + \frac{1}{x \cdot 9}\right)\right)
double f(double x, double y) {
        double r340804 = 3.0;
        double r340805 = x;
        double r340806 = sqrt(r340805);
        double r340807 = r340804 * r340806;
        double r340808 = y;
        double r340809 = 1.0;
        double r340810 = 9.0;
        double r340811 = r340805 * r340810;
        double r340812 = r340809 / r340811;
        double r340813 = r340808 + r340812;
        double r340814 = r340813 - r340809;
        double r340815 = r340807 * r340814;
        return r340815;
}
↓
double f(double x, double y) {
        double r340816 = 3.0;
        double r340817 = x;
        double r340818 = sqrt(r340817);
        double r340819 = y;
        double r340820 = 1.0;
        double r340821 = r340819 - r340820;
        double r340822 = 9.0;
        double r340823 = r340817 * r340822;
        double r340824 = r340820 / r340823;
        double r340825 = r340821 + r340824;
        double r340826 = r340818 * r340825;
        double r340827 = r340816 * r340826;
        return r340827;
}

Error

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Bits error versus y

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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. Simplified0.4

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

  4. Applied associate-/r*0.4

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

  6. Applied associate-*l*0.4

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019194 
(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)))