Average Error: 1.0 → 0.1
Time: 11.3s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \sqrt[3]{{\left(\sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}\right)}^{3}}\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \sqrt[3]{{\left(\sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}\right)}^{3}}
double code(double g, double h) {
	return ((double) (2.0 * ((double) cos(((double) (((double) (((double) (2.0 * ((double) M_PI))) / 3.0)) + ((double) (((double) acos(((double) (((double) -(g)) / h)))) / 3.0))))))));
}
↓
double code(double g, double h) {
	return ((double) (2.0 * ((double) cbrt(((double) pow(((double) (((double) cbrt(((double) (((double) cos(((double) (((double) (((double) (((double) (3.0 / ((double) (2.0 * ((double) M_PI))))) * ((double) (((double) acos(((double) (((double) -(g)) / h)))) / ((double) (((double) cbrt(3.0)) * ((double) cbrt(3.0)))))))) + ((double) cbrt(3.0)))) / ((double) (((double) (3.0 / ((double) (2.0 * ((double) M_PI))))) * ((double) cbrt(3.0)))))))) * ((double) cos(((double) (((double) (((double) (((double) (3.0 / ((double) (2.0 * ((double) M_PI))))) * ((double) (((double) acos(((double) (((double) -(g)) / h)))) / ((double) (((double) cbrt(3.0)) * ((double) cbrt(3.0)))))))) + ((double) cbrt(3.0)))) / ((double) (((double) (3.0 / ((double) (2.0 * ((double) M_PI))))) * ((double) cbrt(3.0)))))))))))) * ((double) cbrt(((double) cos(((double) (((double) (((double) (((double) (3.0 / ((double) (2.0 * ((double) M_PI))))) * ((double) (((double) acos(((double) (((double) -(g)) / h)))) / ((double) (((double) cbrt(3.0)) * ((double) cbrt(3.0)))))))) + ((double) cbrt(3.0)))) / ((double) (((double) (3.0 / ((double) (2.0 * ((double) M_PI))))) * ((double) cbrt(3.0)))))))))))), 3.0))))));
}

Error

Bits error versus g

Bits error versus h

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}}\right)\]

  4. Applied associate-/r*1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \color{blue}{\frac{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}}\right)\]

  5. Applied clear-num1.0

    \[\leadsto 2 \cdot \cos \left(\color{blue}{\frac{1}{\frac{3}{2 \cdot \pi}}} + \frac{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\right)\]

  6. Applied frac-add1.0

    \[\leadsto 2 \cdot \cos \color{blue}{\left(\frac{1 \cdot \sqrt[3]{3} + \frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}\]

  7. Simplified1.0

    \[\leadsto 2 \cdot \cos \left(\frac{\color{blue}{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)\]
  8. Using strategy rm

  9. Applied add-cbrt-cube1.0

    \[\leadsto 2 \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)\right) \cdot \cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}}\]

  10. Simplified1.0

    \[\leadsto 2 \cdot \sqrt[3]{\color{blue}{{\left(\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)\right)}^{3}}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt1.0

    \[\leadsto 2 \cdot \sqrt[3]{{\color{blue}{\left(\left(\sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}\right)}}^{3}}\]

  13. Simplified0.1

    \[\leadsto 2 \cdot \sqrt[3]{{\left(\color{blue}{\sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}} \cdot \sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}\right)}^{3}}\]

  14. Final simplification0.1

    \[\leadsto 2 \cdot \sqrt[3]{{\left(\sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right) \cdot \cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)} \cdot \sqrt[3]{\cos \left(\frac{\frac{3}{2 \cdot \pi} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt[3]{3} \cdot \sqrt[3]{3}} + \sqrt[3]{3}}{\frac{3}{2 \cdot \pi} \cdot \sqrt[3]{3}}\right)}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020114 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))