Average Error: 1.0 → 0.0
Time: 16.3s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\cos \left(\frac{\pi}{\frac{3}{2}}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) - \sin \left(\frac{\sqrt{\pi}}{\frac{3}{2}} \cdot \sqrt{\pi}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\cos \left(\frac{\pi}{\frac{3}{2}}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) - \sin \left(\frac{\sqrt{\pi}}{\frac{3}{2}} \cdot \sqrt{\pi}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\right) \cdot 2
double f(double g, double h) {
        double r2882357 = 2.0;
        double r2882358 = atan2(1.0, 0.0);
        double r2882359 = r2882357 * r2882358;
        double r2882360 = 3.0;
        double r2882361 = r2882359 / r2882360;
        double r2882362 = g;
        double r2882363 = -r2882362;
        double r2882364 = h;
        double r2882365 = r2882363 / r2882364;
        double r2882366 = acos(r2882365);
        double r2882367 = r2882366 / r2882360;
        double r2882368 = r2882361 + r2882367;
        double r2882369 = cos(r2882368);
        double r2882370 = r2882357 * r2882369;
        return r2882370;
}
↓
double f(double g, double h) {
        double r2882371 = atan2(1.0, 0.0);
        double r2882372 = 1.5;
        double r2882373 = r2882371 / r2882372;
        double r2882374 = cos(r2882373);
        double r2882375 = g;
        double r2882376 = -r2882375;
        double r2882377 = h;
        double r2882378 = r2882376 / r2882377;
        double r2882379 = acos(r2882378);
        double r2882380 = 3.0;
        double r2882381 = r2882379 / r2882380;
        double r2882382 = cos(r2882381);
        double r2882383 = r2882374 * r2882382;
        double r2882384 = sqrt(r2882371);
        double r2882385 = r2882384 / r2882372;
        double r2882386 = r2882385 * r2882384;
        double r2882387 = sin(r2882386);
        double r2882388 = sin(r2882381);
        double r2882389 = r2882387 * r2882388;
        double r2882390 = r2882383 - r2882389;
        double r2882391 = 2.0;
        double r2882392 = r2882390 * r2882391;
        return r2882392;
}

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. Simplified1.0

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

  4. Applied cos-sum1.0

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

  6. Applied *-un-lft-identity1.0

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

  7. Applied add-sqr-sqrt1.0

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

  8. Applied times-frac0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))