Average Error: 1.0 → 0.0
Time: 14.2s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right) \cdot \cos \left(\frac{2 \cdot \pi}{3}\right) - \left(\sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right)\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right) \cdot \cos \left(\frac{2 \cdot \pi}{3}\right) - \left(\sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right)\right) \cdot 2
double f(double g, double h) {
        double r6738791 = 2.0;
        double r6738792 = atan2(1.0, 0.0);
        double r6738793 = r6738791 * r6738792;
        double r6738794 = 3.0;
        double r6738795 = r6738793 / r6738794;
        double r6738796 = g;
        double r6738797 = -r6738796;
        double r6738798 = h;
        double r6738799 = r6738797 / r6738798;
        double r6738800 = acos(r6738799);
        double r6738801 = r6738800 / r6738794;
        double r6738802 = r6738795 + r6738801;
        double r6738803 = cos(r6738802);
        double r6738804 = r6738791 * r6738803;
        return r6738804;
}
↓
double f(double g, double h) {
        double r6738805 = g;
        double r6738806 = -r6738805;
        double r6738807 = h;
        double r6738808 = r6738806 / r6738807;
        double r6738809 = acos(r6738808);
        double r6738810 = 3.0;
        double r6738811 = sqrt(r6738810);
        double r6738812 = r6738809 / r6738811;
        double r6738813 = 1.0;
        double r6738814 = r6738813 / r6738811;
        double r6738815 = r6738812 * r6738814;
        double r6738816 = cos(r6738815);
        double r6738817 = 2.0;
        double r6738818 = atan2(1.0, 0.0);
        double r6738819 = r6738817 * r6738818;
        double r6738820 = r6738819 / r6738810;
        double r6738821 = cos(r6738820);
        double r6738822 = r6738816 * r6738821;
        double r6738823 = sin(r6738820);
        double r6738824 = sqrt(r6738823);
        double r6738825 = r6738824 * r6738824;
        double r6738826 = sin(r6738815);
        double r6738827 = r6738825 * r6738826;
        double r6738828 = r6738822 - r6738827;
        double r6738829 = r6738828 * r6738817;
        return r6738829;
}

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 cos-sum1.0

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

  9. Applied add-sqr-sqrt0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))