Average Error: 0.4 → 0.4
Time: 16.1s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(y \cdot \sqrt{x}\right) \cdot 3.0 + \left(3.0 \cdot \left(\frac{1.0}{9.0 \cdot x} - 1.0\right)\right) \cdot \sqrt{x}\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(y \cdot \sqrt{x}\right) \cdot 3.0 + \left(3.0 \cdot \left(\frac{1.0}{9.0 \cdot x} - 1.0\right)\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r23911663 = 3.0;
        double r23911664 = x;
        double r23911665 = sqrt(r23911664);
        double r23911666 = r23911663 * r23911665;
        double r23911667 = y;
        double r23911668 = 1.0;
        double r23911669 = 9.0;
        double r23911670 = r23911664 * r23911669;
        double r23911671 = r23911668 / r23911670;
        double r23911672 = r23911667 + r23911671;
        double r23911673 = r23911672 - r23911668;
        double r23911674 = r23911666 * r23911673;
        return r23911674;
}
↓
double f(double x, double y) {
        double r23911675 = y;
        double r23911676 = x;
        double r23911677 = sqrt(r23911676);
        double r23911678 = r23911675 * r23911677;
        double r23911679 = 3.0;
        double r23911680 = r23911678 * r23911679;
        double r23911681 = 1.0;
        double r23911682 = 9.0;
        double r23911683 = r23911682 * r23911676;
        double r23911684 = r23911681 / r23911683;
        double r23911685 = r23911684 - r23911681;
        double r23911686 = r23911679 * r23911685;
        double r23911687 = r23911686 * r23911677;
        double r23911688 = r23911680 + r23911687;
        return r23911688;
}

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
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]
  4. Using strategy rm

  5. Applied associate--l+0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \color{blue}{\left(y + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right)\right)}\right)\]

  6. Applied distribute-lft-in0.4

    \[\leadsto 3.0 \cdot \color{blue}{\left(\sqrt{x} \cdot y + \sqrt{x} \cdot \left(\frac{1.0}{x \cdot 9.0} - 1.0\right)\right)}\]

  7. Applied distribute-rgt-in0.4

    \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3.0 + \left(\sqrt{x} \cdot \left(\frac{1.0}{x \cdot 9.0} - 1.0\right)\right) \cdot 3.0}\]
  8. Using strategy rm

  9. Applied associate-*l*0.4

    \[\leadsto \left(\sqrt{x} \cdot y\right) \cdot 3.0 + \color{blue}{\sqrt{x} \cdot \left(\left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot 3.0\right)}\]

  10. Final simplification0.4

    \[\leadsto \left(y \cdot \sqrt{x}\right) \cdot 3.0 + \left(3.0 \cdot \left(\frac{1.0}{9.0 \cdot x} - 1.0\right)\right) \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2019164 
(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)))