Average Error: 0.4 → 0.4
Time: 5.0s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)\]
\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 r441737 = 3.0;
        double r441738 = x;
        double r441739 = sqrt(r441738);
        double r441740 = r441737 * r441739;
        double r441741 = y;
        double r441742 = 1.0;
        double r441743 = 9.0;
        double r441744 = r441738 * r441743;
        double r441745 = r441742 / r441744;
        double r441746 = r441741 + r441745;
        double r441747 = r441746 - r441742;
        double r441748 = r441740 * r441747;
        return r441748;
}
↓
double f(double x, double y) {
        double r441749 = 3.0;
        double r441750 = x;
        double r441751 = sqrt(r441750);
        double r441752 = y;
        double r441753 = 1.0;
        double r441754 = r441753 / r441750;
        double r441755 = 9.0;
        double r441756 = r441754 / r441755;
        double r441757 = r441752 + r441756;
        double r441758 = r441757 - r441753;
        double r441759 = r441751 * r441758;
        double r441760 = r441749 * r441759;
        return r441760;
}

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 2020100 
(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)))