Average Error: 0.4 → 0.4
Time: 22.7s
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 r266496 = 3.0;
        double r266497 = x;
        double r266498 = sqrt(r266497);
        double r266499 = r266496 * r266498;
        double r266500 = y;
        double r266501 = 1.0;
        double r266502 = 9.0;
        double r266503 = r266497 * r266502;
        double r266504 = r266501 / r266503;
        double r266505 = r266500 + r266504;
        double r266506 = r266505 - r266501;
        double r266507 = r266499 * r266506;
        return r266507;
}
↓
double f(double x, double y) {
        double r266508 = 3.0;
        double r266509 = x;
        double r266510 = sqrt(r266509);
        double r266511 = y;
        double r266512 = 1.0;
        double r266513 = r266512 / r266509;
        double r266514 = 9.0;
        double r266515 = r266513 / r266514;
        double r266516 = r266511 + r266515;
        double r266517 = r266516 - r266512;
        double r266518 = r266510 * r266517;
        double r266519 = r266508 * r266518;
        return r266519;
}

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 2019325 
(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)))