Average Error: 0.4 → 0.4
Time: 48.5s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0
double f(double x, double y) {
        double r20930830 = 3.0;
        double r20930831 = x;
        double r20930832 = sqrt(r20930831);
        double r20930833 = r20930830 * r20930832;
        double r20930834 = y;
        double r20930835 = 1.0;
        double r20930836 = 9.0;
        double r20930837 = r20930831 * r20930836;
        double r20930838 = r20930835 / r20930837;
        double r20930839 = r20930834 + r20930838;
        double r20930840 = r20930839 - r20930835;
        double r20930841 = r20930833 * r20930840;
        return r20930841;
}
↓
double f(double x, double y) {
        double r20930842 = x;
        double r20930843 = sqrt(r20930842);
        double r20930844 = y;
        double r20930845 = 0.1111111111111111;
        double r20930846 = r20930845 / r20930842;
        double r20930847 = r20930844 + r20930846;
        double r20930848 = 1.0;
        double r20930849 = r20930847 - r20930848;
        double r20930850 = r20930843 * r20930849;
        double r20930851 = 3.0;
        double r20930852 = r20930850 * r20930851;
        return r20930852;
}

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-/r*0.4

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

  5. Applied associate-*l*0.4

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

  6. Taylor expanded around 0 0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111}{x}}\right) - 1.0\right)\right)\]

  7. Final simplification0.4

    \[\leadsto \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(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)))