Average Error: 1.0 → 0.0
Time: 14.4s
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 r6508666 = 2.0;
        double r6508667 = atan2(1.0, 0.0);
        double r6508668 = r6508666 * r6508667;
        double r6508669 = 3.0;
        double r6508670 = r6508668 / r6508669;
        double r6508671 = g;
        double r6508672 = -r6508671;
        double r6508673 = h;
        double r6508674 = r6508672 / r6508673;
        double r6508675 = acos(r6508674);
        double r6508676 = r6508675 / r6508669;
        double r6508677 = r6508670 + r6508676;
        double r6508678 = cos(r6508677);
        double r6508679 = r6508666 * r6508678;
        return r6508679;
}
↓
double f(double g, double h) {
        double r6508680 = 2.0;
        double r6508681 = atan2(1.0, 0.0);
        double r6508682 = 3.0;
        double r6508683 = r6508681 / r6508682;
        double r6508684 = r6508680 * r6508681;
        double r6508685 = r6508684 / r6508682;
        double r6508686 = r6508683 + r6508685;
        double r6508687 = cos(r6508686);
        double r6508688 = g;
        double r6508689 = h;
        double r6508690 = r6508688 / r6508689;
        double r6508691 = acos(r6508690);
        double r6508692 = r6508691 / r6508682;
        double r6508693 = cos(r6508692);
        double r6508694 = r6508687 * r6508693;
        double r6508695 = sin(r6508686);
        double r6508696 = sin(r6508692);
        double r6508697 = r6508695 * r6508696;
        double r6508698 = r6508694 + r6508697;
        double r6508699 = r6508680 * r6508698;
        return r6508699;
}

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 2019192 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))