Average Error: 0.4 → 0.4
Time: 24.6s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(y + \frac{1}{x \cdot 9}\right) \cdot \sqrt{x}\right) \cdot 3 + \left(\left(-1\right) \cdot \sqrt{x}\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(y + \frac{1}{x \cdot 9}\right) \cdot \sqrt{x}\right) \cdot 3 + \left(\left(-1\right) \cdot \sqrt{x}\right) \cdot 3
double f(double x, double y) {
        double r378870 = 3.0;
        double r378871 = x;
        double r378872 = sqrt(r378871);
        double r378873 = r378870 * r378872;
        double r378874 = y;
        double r378875 = 1.0;
        double r378876 = 9.0;
        double r378877 = r378871 * r378876;
        double r378878 = r378875 / r378877;
        double r378879 = r378874 + r378878;
        double r378880 = r378879 - r378875;
        double r378881 = r378873 * r378880;
        return r378881;
}
↓
double f(double x, double y) {
        double r378882 = y;
        double r378883 = 1.0;
        double r378884 = x;
        double r378885 = 9.0;
        double r378886 = r378884 * r378885;
        double r378887 = r378883 / r378886;
        double r378888 = r378882 + r378887;
        double r378889 = sqrt(r378884);
        double r378890 = r378888 * r378889;
        double r378891 = 3.0;
        double r378892 = r378890 * r378891;
        double r378893 = -r378883;
        double r378894 = r378893 * r378889;
        double r378895 = r378894 * r378891;
        double r378896 = r378892 + r378895;
        return r378896;
}

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 associate-*l*0.4

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

  5. Applied add-cube-cbrt0.4

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

  6. Applied associate-*l*0.6

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

  8. Applied sub-neg0.6

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

  9. Applied distribute-lft-in0.6

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

  10. Applied distribute-lft-in0.6

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

  11. Applied distribute-lft-in0.6

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

  12. Simplified0.5

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

  13. Simplified0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019303 
(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)))