Average Error: 1.0 → 0.1
Time: 31.3s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\sqrt[3]{\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right)}\right)\]
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{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right)}\right)
double f(double g, double h) {
        double r5988557 = 2.0;
        double r5988558 = atan2(1.0, 0.0);
        double r5988559 = r5988557 * r5988558;
        double r5988560 = 3.0;
        double r5988561 = r5988559 / r5988560;
        double r5988562 = g;
        double r5988563 = -r5988562;
        double r5988564 = h;
        double r5988565 = r5988563 / r5988564;
        double r5988566 = acos(r5988565);
        double r5988567 = r5988566 / r5988560;
        double r5988568 = r5988561 + r5988567;
        double r5988569 = cos(r5988568);
        double r5988570 = r5988557 * r5988569;
        return r5988570;
}
↓
double f(double g, double h) {
        double r5988571 = 2.0;
        double r5988572 = g;
        double r5988573 = -r5988572;
        double r5988574 = h;
        double r5988575 = r5988573 / r5988574;
        double r5988576 = acos(r5988575);
        double r5988577 = 3.0;
        double r5988578 = r5988576 / r5988577;
        double r5988579 = atan2(1.0, 0.0);
        double r5988580 = r5988579 * r5988571;
        double r5988581 = r5988580 / r5988577;
        double r5988582 = r5988578 + r5988581;
        double r5988583 = cos(r5988582);
        double r5988584 = r5988583 * r5988583;
        double r5988585 = cbrt(r5988584);
        double r5988586 = cbrt(r5988583);
        double r5988587 = r5988585 * r5988586;
        double r5988588 = r5988571 * r5988587;
        return r5988588;
}

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-cube-cbrt1.0

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

  5. Applied cbrt-unprod0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))