Average Error: 1.0 → 0.0
Time: 16.3s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\left(\left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\left(\left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\right)
double f(double g, double h) {
        double r95040 = 2.0;
        double r95041 = atan2(1.0, 0.0);
        double r95042 = r95040 * r95041;
        double r95043 = 3.0;
        double r95044 = r95042 / r95043;
        double r95045 = g;
        double r95046 = -r95045;
        double r95047 = h;
        double r95048 = r95046 / r95047;
        double r95049 = acos(r95048);
        double r95050 = r95049 / r95043;
        double r95051 = r95044 + r95050;
        double r95052 = cos(r95051);
        double r95053 = r95040 * r95052;
        return r95053;
}
↓
double f(double g, double h) {
        double r95054 = 2.0;
        double r95055 = atan2(1.0, 0.0);
        double r95056 = r95054 * r95055;
        double r95057 = 3.0;
        double r95058 = r95056 / r95057;
        double r95059 = cos(r95058);
        double r95060 = cbrt(r95059);
        double r95061 = r95060 * r95060;
        double r95062 = r95061 * r95060;
        double r95063 = g;
        double r95064 = -r95063;
        double r95065 = h;
        double r95066 = r95064 / r95065;
        double r95067 = acos(r95066);
        double r95068 = r95067 / r95057;
        double r95069 = cos(r95068);
        double r95070 = r95062 * r95069;
        double r95071 = sin(r95058);
        double r95072 = sin(r95068);
        double r95073 = r95071 * r95072;
        double r95074 = r95070 - r95073;
        double r95075 = r95054 * r95074;
        return r95075;
}

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 cos-sum1.0

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

  5. Applied add-cube-cbrt0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))