Average Error: 1.0 → 0.0
Time: 4.0s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\left(\left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \cos \left(\frac{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}}{\sqrt{3}}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}}{\sqrt{3}}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\left(\left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \cos \left(\frac{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}}{\sqrt{3}}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}}{\sqrt{3}}\right)\right)
double f(double g, double h) {
        double r210387 = 2.0;
        double r210388 = atan2(1.0, 0.0);
        double r210389 = r210387 * r210388;
        double r210390 = 3.0;
        double r210391 = r210389 / r210390;
        double r210392 = g;
        double r210393 = -r210392;
        double r210394 = h;
        double r210395 = r210393 / r210394;
        double r210396 = acos(r210395);
        double r210397 = r210396 / r210390;
        double r210398 = r210391 + r210397;
        double r210399 = cos(r210398);
        double r210400 = r210387 * r210399;
        return r210400;
}
↓
double f(double g, double h) {
        double r210401 = 2.0;
        double r210402 = atan2(1.0, 0.0);
        double r210403 = r210401 * r210402;
        double r210404 = 3.0;
        double r210405 = r210403 / r210404;
        double r210406 = cos(r210405);
        double r210407 = cbrt(r210406);
        double r210408 = r210407 * r210407;
        double r210409 = r210408 * r210407;
        double r210410 = g;
        double r210411 = -r210410;
        double r210412 = h;
        double r210413 = r210411 / r210412;
        double r210414 = acos(r210413);
        double r210415 = sqrt(r210404);
        double r210416 = r210414 / r210415;
        double r210417 = r210416 / r210415;
        double r210418 = cos(r210417);
        double r210419 = r210409 * r210418;
        double r210420 = sin(r210405);
        double r210421 = sin(r210417);
        double r210422 = r210420 * r210421;
        double r210423 = r210419 - r210422;
        double r210424 = r210401 * r210423;
        return r210424;
}

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-sqr-sqrt1.0

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

  4. Applied associate-/r*1.0

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

  6. Applied cos-sum1.0

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

  8. Applied add-cube-cbrt0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))