Average Error: 1.0 → 0.0
Time: 35.6s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{\pi}{3} + \frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) + \sin \left(\frac{\pi}{3} + \frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\cos \left(\frac{\pi}{3} + \frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) + \sin \left(\frac{\pi}{3} + \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 r6984838 = 2.0;
        double r6984839 = atan2(1.0, 0.0);
        double r6984840 = r6984838 * r6984839;
        double r6984841 = 3.0;
        double r6984842 = r6984840 / r6984841;
        double r6984843 = g;
        double r6984844 = -r6984843;
        double r6984845 = h;
        double r6984846 = r6984844 / r6984845;
        double r6984847 = acos(r6984846);
        double r6984848 = r6984847 / r6984841;
        double r6984849 = r6984842 + r6984848;
        double r6984850 = cos(r6984849);
        double r6984851 = r6984838 * r6984850;
        return r6984851;
}
↓
double f(double g, double h) {
        double r6984852 = 2.0;
        double r6984853 = atan2(1.0, 0.0);
        double r6984854 = 3.0;
        double r6984855 = r6984853 / r6984854;
        double r6984856 = r6984852 * r6984853;
        double r6984857 = r6984856 / r6984854;
        double r6984858 = r6984855 + r6984857;
        double r6984859 = cos(r6984858);
        double r6984860 = g;
        double r6984861 = h;
        double r6984862 = r6984860 / r6984861;
        double r6984863 = acos(r6984862);
        double r6984864 = r6984863 / r6984854;
        double r6984865 = cos(r6984864);
        double r6984866 = r6984859 * r6984865;
        double r6984867 = sin(r6984858);
        double r6984868 = sin(r6984864);
        double r6984869 = r6984867 * r6984868;
        double r6984870 = r6984866 + r6984869;
        double r6984871 = r6984852 * r6984870;
        return r6984871;
}

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 distribute-frac-neg1.0

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

  4. Applied acos-neg1.0

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

  5. Applied div-sub1.0

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

  6. Applied associate-+r-1.0

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

  7. Applied cos-diff0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))