Average Error: 0.4 → 0.5
Time: 5.1s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt{x}\right)\right)\right) \cdot \left(-1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt{x}\right)\right)\right) \cdot \left(-1\right)
double f(double x, double y) {
        double r394822 = 3.0;
        double r394823 = x;
        double r394824 = sqrt(r394823);
        double r394825 = r394822 * r394824;
        double r394826 = y;
        double r394827 = 1.0;
        double r394828 = 9.0;
        double r394829 = r394823 * r394828;
        double r394830 = r394827 / r394829;
        double r394831 = r394826 + r394830;
        double r394832 = r394831 - r394827;
        double r394833 = r394825 * r394832;
        return r394833;
}
↓
double f(double x, double y) {
        double r394834 = 3.0;
        double r394835 = x;
        double r394836 = sqrt(r394835);
        double r394837 = r394834 * r394836;
        double r394838 = y;
        double r394839 = 1.0;
        double r394840 = r394839 / r394835;
        double r394841 = 9.0;
        double r394842 = r394840 / r394841;
        double r394843 = r394838 + r394842;
        double r394844 = r394837 * r394843;
        double r394845 = cbrt(r394834);
        double r394846 = r394845 * r394845;
        double r394847 = cbrt(r394845);
        double r394848 = r394847 * r394847;
        double r394849 = r394847 * r394836;
        double r394850 = r394848 * r394849;
        double r394851 = r394846 * r394850;
        double r394852 = -r394839;
        double r394853 = r394851 * r394852;
        double r394854 = r394844 + r394853;
        return r394854;
}

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
Herbie0.5
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

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-/r*0.4

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

  5. Applied sub-neg0.4

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

  6. Applied distribute-lft-in0.4

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

  8. Applied add-cube-cbrt0.4

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

  9. Applied associate-*l*0.5

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

  11. Applied add-cube-cbrt0.5

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

  12. Applied associate-*l*0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(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)))