Average Error: 1.0 → 0.0
Time: 15.6s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{\sqrt{3}} \cdot \left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right)\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{\sqrt{3}} \cdot \left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right)\right)\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{\sqrt{3}} \cdot \left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right)\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{\sqrt{3}} \cdot \left(\sqrt{\frac{1}{\sqrt{3}}} \cdot \sqrt{\frac{1}{\sqrt{3}}}\right)\right)\right) \cdot 2
double f(double g, double h) {
        double r7429828 = 2.0;
        double r7429829 = atan2(1.0, 0.0);
        double r7429830 = r7429828 * r7429829;
        double r7429831 = 3.0;
        double r7429832 = r7429830 / r7429831;
        double r7429833 = g;
        double r7429834 = -r7429833;
        double r7429835 = h;
        double r7429836 = r7429834 / r7429835;
        double r7429837 = acos(r7429836);
        double r7429838 = r7429837 / r7429831;
        double r7429839 = r7429832 + r7429838;
        double r7429840 = cos(r7429839);
        double r7429841 = r7429828 * r7429840;
        return r7429841;
}
↓
double f(double g, double h) {
        double r7429842 = 2.0;
        double r7429843 = atan2(1.0, 0.0);
        double r7429844 = r7429842 * r7429843;
        double r7429845 = 3.0;
        double r7429846 = r7429844 / r7429845;
        double r7429847 = cos(r7429846);
        double r7429848 = g;
        double r7429849 = h;
        double r7429850 = r7429848 / r7429849;
        double r7429851 = -r7429850;
        double r7429852 = acos(r7429851);
        double r7429853 = sqrt(r7429845);
        double r7429854 = r7429852 / r7429853;
        double r7429855 = 1.0;
        double r7429856 = r7429855 / r7429853;
        double r7429857 = sqrt(r7429856);
        double r7429858 = r7429857 * r7429857;
        double r7429859 = r7429854 * r7429858;
        double r7429860 = cos(r7429859);
        double r7429861 = r7429847 * r7429860;
        double r7429862 = sin(r7429846);
        double r7429863 = sin(r7429859);
        double r7429864 = r7429862 * r7429863;
        double r7429865 = r7429861 - r7429864;
        double r7429866 = r7429865 * r7429842;
        return r7429866;
}

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-sqr-sqrt1.0

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

  4. Applied *-un-lft-identity1.0

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

  5. Applied times-frac1.0

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

  7. Applied add-sqr-sqrt1.0

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

  9. Applied cos-sum0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))