Average Error: 0.4 → 0.4
Time: 22.0s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(\left(\frac{\frac{1.0}{x}}{9.0} + y\right) - 1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(\left(\frac{\frac{1.0}{x}}{9.0} + y\right) - 1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r22980894 = 3.0;
        double r22980895 = x;
        double r22980896 = sqrt(r22980895);
        double r22980897 = r22980894 * r22980896;
        double r22980898 = y;
        double r22980899 = 1.0;
        double r22980900 = 9.0;
        double r22980901 = r22980895 * r22980900;
        double r22980902 = r22980899 / r22980901;
        double r22980903 = r22980898 + r22980902;
        double r22980904 = r22980903 - r22980899;
        double r22980905 = r22980897 * r22980904;
        return r22980905;
}
↓
double f(double x, double y) {
        double r22980906 = 1.0;
        double r22980907 = x;
        double r22980908 = r22980906 / r22980907;
        double r22980909 = 9.0;
        double r22980910 = r22980908 / r22980909;
        double r22980911 = y;
        double r22980912 = r22980910 + r22980911;
        double r22980913 = r22980912 - r22980906;
        double r22980914 = 3.0;
        double r22980915 = sqrt(r22980907);
        double r22980916 = r22980914 * r22980915;
        double r22980917 = r22980913 * r22980916;
        return r22980917;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019163 +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)))