Average Error: 1.0 → 0.1
Time: 30.6s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\sqrt[3]{\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi \cdot 2}{3}\right)}\right)\]
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 r6059439 = 2.0;
        double r6059440 = atan2(1.0, 0.0);
        double r6059441 = r6059439 * r6059440;
        double r6059442 = 3.0;
        double r6059443 = r6059441 / r6059442;
        double r6059444 = g;
        double r6059445 = -r6059444;
        double r6059446 = h;
        double r6059447 = r6059445 / r6059446;
        double r6059448 = acos(r6059447);
        double r6059449 = r6059448 / r6059442;
        double r6059450 = r6059443 + r6059449;
        double r6059451 = cos(r6059450);
        double r6059452 = r6059439 * r6059451;
        return r6059452;
}
↓
double f(double g, double h) {
        double r6059453 = 2.0;
        double r6059454 = g;
        double r6059455 = -r6059454;
        double r6059456 = h;
        double r6059457 = r6059455 / r6059456;
        double r6059458 = acos(r6059457);
        double r6059459 = 3.0;
        double r6059460 = r6059458 / r6059459;
        double r6059461 = atan2(1.0, 0.0);
        double r6059462 = r6059461 * r6059453;
        double r6059463 = r6059462 / r6059459;
        double r6059464 = r6059460 + r6059463;
        double r6059465 = cos(r6059464);
        double r6059466 = r6059465 * r6059465;
        double r6059467 = cbrt(r6059466);
        double r6059468 = cbrt(r6059465);
        double r6059469 = r6059467 * r6059468;
        double r6059470 = r6059453 * r6059469;
        return r6059470;
}

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)))))