Average Error: 0.4 → 0.4
Time: 3.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot 3\right) \cdot \sqrt{x}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot 3\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r374608 = 3.0;
        double r374609 = x;
        double r374610 = sqrt(r374609);
        double r374611 = r374608 * r374610;
        double r374612 = y;
        double r374613 = 1.0;
        double r374614 = 9.0;
        double r374615 = r374609 * r374614;
        double r374616 = r374613 / r374615;
        double r374617 = r374612 + r374616;
        double r374618 = r374617 - r374613;
        double r374619 = r374611 * r374618;
        return r374619;
}
↓
double f(double x, double y) {
        double r374620 = y;
        double r374621 = 1.0;
        double r374622 = x;
        double r374623 = 9.0;
        double r374624 = r374622 * r374623;
        double r374625 = r374621 / r374624;
        double r374626 = r374620 + r374625;
        double r374627 = r374626 - r374621;
        double r374628 = 3.0;
        double r374629 = r374627 * r374628;
        double r374630 = sqrt(r374622);
        double r374631 = r374629 * r374630;
        return r374631;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 *-commutative0.4

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

  5. Applied associate-*r*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020064 
(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)))