Average Error: 1.0 → 0.0
Time: 19.6s
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 r6720647 = 2.0;
        double r6720648 = atan2(1.0, 0.0);
        double r6720649 = r6720647 * r6720648;
        double r6720650 = 3.0;
        double r6720651 = r6720649 / r6720650;
        double r6720652 = g;
        double r6720653 = -r6720652;
        double r6720654 = h;
        double r6720655 = r6720653 / r6720654;
        double r6720656 = acos(r6720655);
        double r6720657 = r6720656 / r6720650;
        double r6720658 = r6720651 + r6720657;
        double r6720659 = cos(r6720658);
        double r6720660 = r6720647 * r6720659;
        return r6720660;
}
↓
double f(double g, double h) {
        double r6720661 = 2.0;
        double r6720662 = atan2(1.0, 0.0);
        double r6720663 = 3.0;
        double r6720664 = r6720662 / r6720663;
        double r6720665 = r6720661 * r6720662;
        double r6720666 = r6720665 / r6720663;
        double r6720667 = r6720664 + r6720666;
        double r6720668 = cos(r6720667);
        double r6720669 = g;
        double r6720670 = h;
        double r6720671 = r6720669 / r6720670;
        double r6720672 = acos(r6720671);
        double r6720673 = r6720672 / r6720663;
        double r6720674 = cos(r6720673);
        double r6720675 = r6720668 * r6720674;
        double r6720676 = sin(r6720667);
        double r6720677 = sin(r6720673);
        double r6720678 = r6720676 * r6720677;
        double r6720679 = r6720675 + r6720678;
        double r6720680 = r6720661 * r6720679;
        return r6720680;
}

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 2019169 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))