Average Error: 1.0 → 0.0
Time: 13.5s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\sin \left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}}\right) \cdot \frac{\sqrt{3}}{2} + \frac{1}{2} \cdot \cos \left(\frac{\frac{\pi}{2}}{3} - \left(\frac{\pi}{\frac{3}{2}} + \frac{\sin^{-1} \left(\frac{g}{h}\right)}{3}\right)\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\sin \left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}}\right) \cdot \frac{\sqrt{3}}{2} + \frac{1}{2} \cdot \cos \left(\frac{\frac{\pi}{2}}{3} - \left(\frac{\pi}{\frac{3}{2}} + \frac{\sin^{-1} \left(\frac{g}{h}\right)}{3}\right)\right)\right)
double f(double g, double h) {
        double r2137968 = 2.0;
        double r2137969 = atan2(1.0, 0.0);
        double r2137970 = r2137968 * r2137969;
        double r2137971 = 3.0;
        double r2137972 = r2137970 / r2137971;
        double r2137973 = g;
        double r2137974 = -r2137973;
        double r2137975 = h;
        double r2137976 = r2137974 / r2137975;
        double r2137977 = acos(r2137976);
        double r2137978 = r2137977 / r2137971;
        double r2137979 = r2137972 + r2137978;
        double r2137980 = cos(r2137979);
        double r2137981 = r2137968 * r2137980;
        return r2137981;
}
↓
double f(double g, double h) {
        double r2137982 = 2.0;
        double r2137983 = g;
        double r2137984 = h;
        double r2137985 = r2137983 / r2137984;
        double r2137986 = acos(r2137985);
        double r2137987 = 3.0;
        double r2137988 = r2137986 / r2137987;
        double r2137989 = atan2(1.0, 0.0);
        double r2137990 = 1.5;
        double r2137991 = r2137989 / r2137990;
        double r2137992 = r2137988 - r2137991;
        double r2137993 = cbrt(r2137992);
        double r2137994 = r2137993 * r2137993;
        double r2137995 = r2137994 * r2137993;
        double r2137996 = sin(r2137995);
        double r2137997 = sqrt(r2137987);
        double r2137998 = r2137997 / r2137982;
        double r2137999 = r2137996 * r2137998;
        double r2138000 = 0.5;
        double r2138001 = r2137989 / r2137982;
        double r2138002 = r2138001 / r2137987;
        double r2138003 = asin(r2137985);
        double r2138004 = r2138003 / r2137987;
        double r2138005 = r2137991 + r2138004;
        double r2138006 = r2138002 - r2138005;
        double r2138007 = cos(r2138006);
        double r2138008 = r2138000 * r2138007;
        double r2138009 = r2137999 + r2138008;
        double r2138010 = r2137982 * r2138009;
        return r2138010;
}

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. Simplified1.0

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

  4. Applied distribute-frac-neg1.0

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

  5. Applied acos-neg1.0

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

  6. Applied div-sub1.0

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

  7. Applied associate-+l-1.0

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

  8. Applied cos-diff0.1

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

  9. Simplified0.1

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

  10. Simplified0.1

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

  12. Applied acos-asin0.1

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

  13. Applied div-sub0.1

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

  14. Applied associate--l-0.0

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

  16. Applied add-cube-cbrt0.0

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

  17. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))