Average Error: 1.0 → 0.0
Time: 3.9s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \cdot \cos \left(\left(\sqrt[3]{\frac{2 \cdot \pi}{3}} \cdot \sqrt[3]{\frac{2 \cdot \pi}{3}}\right) \cdot \sqrt[3]{\frac{2 \cdot \pi}{3}} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)}\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \cdot \cos \left(\left(\sqrt[3]{\frac{2 \cdot \pi}{3}} \cdot \sqrt[3]{\frac{2 \cdot \pi}{3}}\right) \cdot \sqrt[3]{\frac{2 \cdot \pi}{3}} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)}\right)
double f(double g, double h) {
        double r143594 = 2.0;
        double r143595 = atan2(1.0, 0.0);
        double r143596 = r143594 * r143595;
        double r143597 = 3.0;
        double r143598 = r143596 / r143597;
        double r143599 = g;
        double r143600 = -r143599;
        double r143601 = h;
        double r143602 = r143600 / r143601;
        double r143603 = acos(r143602);
        double r143604 = r143603 / r143597;
        double r143605 = r143598 + r143604;
        double r143606 = cos(r143605);
        double r143607 = r143594 * r143606;
        return r143607;
}
↓
double f(double g, double h) {
        double r143608 = 2.0;
        double r143609 = atan2(1.0, 0.0);
        double r143610 = r143608 * r143609;
        double r143611 = 3.0;
        double r143612 = r143610 / r143611;
        double r143613 = g;
        double r143614 = -r143613;
        double r143615 = h;
        double r143616 = r143614 / r143615;
        double r143617 = acos(r143616);
        double r143618 = r143617 / r143611;
        double r143619 = r143612 + r143618;
        double r143620 = cos(r143619);
        double r143621 = cbrt(r143620);
        double r143622 = cbrt(r143612);
        double r143623 = r143622 * r143622;
        double r143624 = r143623 * r143622;
        double r143625 = r143624 + r143618;
        double r143626 = cos(r143625);
        double r143627 = r143620 * r143626;
        double r143628 = cbrt(r143627);
        double r143629 = r143621 * r143628;
        double r143630 = r143608 * r143629;
        return r143630;
}

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-cbrt-cube1.5

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

  4. Simplified1.0

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

  6. Applied cube-mult1.5

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

  7. Applied cbrt-prod0.1

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

  9. Applied add-cube-cbrt0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))