Average Error: 0.4 → 0.4
Time: 16.3s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(\left(\frac{\frac{1}{x}}{9} \cdot 1 - 1\right) + y\right) \cdot \sqrt{x}\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(\left(\frac{\frac{1}{x}}{9} \cdot 1 - 1\right) + y\right) \cdot \sqrt{x}\right) \cdot 3
double f(double x, double y) {
        double r315705 = 3.0;
        double r315706 = x;
        double r315707 = sqrt(r315706);
        double r315708 = r315705 * r315707;
        double r315709 = y;
        double r315710 = 1.0;
        double r315711 = 9.0;
        double r315712 = r315706 * r315711;
        double r315713 = r315710 / r315712;
        double r315714 = r315709 + r315713;
        double r315715 = r315714 - r315710;
        double r315716 = r315708 * r315715;
        return r315716;
}
↓
double f(double x, double y) {
        double r315717 = 1.0;
        double r315718 = x;
        double r315719 = r315717 / r315718;
        double r315720 = 9.0;
        double r315721 = r315719 / r315720;
        double r315722 = 1.0;
        double r315723 = r315721 * r315722;
        double r315724 = r315723 - r315722;
        double r315725 = y;
        double r315726 = r315724 + r315725;
        double r315727 = sqrt(r315718);
        double r315728 = r315726 * r315727;
        double r315729 = 3.0;
        double r315730 = r315728 * r315729;
        return r315730;
}

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. Simplified0.4

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

  6. Applied div-inv0.4

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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)))