Average Error: 0.4 → 0.4
Time: 22.8s
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 r316571 = 3.0;
        double r316572 = x;
        double r316573 = sqrt(r316572);
        double r316574 = r316571 * r316573;
        double r316575 = y;
        double r316576 = 1.0;
        double r316577 = 9.0;
        double r316578 = r316572 * r316577;
        double r316579 = r316576 / r316578;
        double r316580 = r316575 + r316579;
        double r316581 = r316580 - r316576;
        double r316582 = r316574 * r316581;
        return r316582;
}
↓
double f(double x, double y) {
        double r316583 = 3.0;
        double r316584 = x;
        double r316585 = sqrt(r316584);
        double r316586 = y;
        double r316587 = 1.0;
        double r316588 = r316587 / r316584;
        double r316589 = 9.0;
        double r316590 = r316588 / r316589;
        double r316591 = r316586 + r316590;
        double r316592 = r316591 - r316587;
        double r316593 = r316585 * r316592;
        double r316594 = r316583 * r316593;
        return r316594;
}

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)))