Average Error: 0.4 → 0.4
Time: 33.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(-1\right) \cdot \left(\sqrt{x} \cdot 3\right) + \sqrt{x} \cdot \left(3 \cdot \left(\frac{\frac{1}{x}}{9} + y\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(-1\right) \cdot \left(\sqrt{x} \cdot 3\right) + \sqrt{x} \cdot \left(3 \cdot \left(\frac{\frac{1}{x}}{9} + y\right)\right)
double f(double x, double y) {
        double r22605732 = 3.0;
        double r22605733 = x;
        double r22605734 = sqrt(r22605733);
        double r22605735 = r22605732 * r22605734;
        double r22605736 = y;
        double r22605737 = 1.0;
        double r22605738 = 9.0;
        double r22605739 = r22605733 * r22605738;
        double r22605740 = r22605737 / r22605739;
        double r22605741 = r22605736 + r22605740;
        double r22605742 = r22605741 - r22605737;
        double r22605743 = r22605735 * r22605742;
        return r22605743;
}
↓
double f(double x, double y) {
        double r22605744 = 1.0;
        double r22605745 = -r22605744;
        double r22605746 = x;
        double r22605747 = sqrt(r22605746);
        double r22605748 = 3.0;
        double r22605749 = r22605747 * r22605748;
        double r22605750 = r22605745 * r22605749;
        double r22605751 = r22605744 / r22605746;
        double r22605752 = 9.0;
        double r22605753 = r22605751 / r22605752;
        double r22605754 = y;
        double r22605755 = r22605753 + r22605754;
        double r22605756 = r22605748 * r22605755;
        double r22605757 = r22605747 * r22605756;
        double r22605758 = r22605750 + r22605757;
        return r22605758;
}

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 sub-neg0.4

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

  4. Applied distribute-rgt-in0.4

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

  6. Applied associate-*r*0.4

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

  8. Applied associate-/r*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019168 
(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)))