Average Error: 0.4 → 0.4
Time: 3.5s
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 r461843 = 3.0;
        double r461844 = x;
        double r461845 = sqrt(r461844);
        double r461846 = r461843 * r461845;
        double r461847 = y;
        double r461848 = 1.0;
        double r461849 = 9.0;
        double r461850 = r461844 * r461849;
        double r461851 = r461848 / r461850;
        double r461852 = r461847 + r461851;
        double r461853 = r461852 - r461848;
        double r461854 = r461846 * r461853;
        return r461854;
}
↓
double f(double x, double y) {
        double r461855 = 3.0;
        double r461856 = x;
        double r461857 = sqrt(r461856);
        double r461858 = y;
        double r461859 = 1.0;
        double r461860 = r461859 / r461856;
        double r461861 = 9.0;
        double r461862 = r461860 / r461861;
        double r461863 = r461858 + r461862;
        double r461864 = r461863 - r461859;
        double r461865 = r461857 * r461864;
        double r461866 = r461855 * r461865;
        return r461866;
}

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. 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 2020060 
(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)))