Average Error: 1.0 → 0.0
Time: 20.0s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\cos \left(\frac{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{\sqrt{3}}}{\sqrt{3}} - \frac{\pi}{\frac{3}{2}}\right) \cdot \cos \left(\frac{\frac{\pi}{\sqrt{3}}}{\sqrt{3}}\right) + \sin \left(\frac{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{\sqrt{3}}}{\sqrt{3}} - \frac{\pi}{\frac{3}{2}}\right) \cdot \sin \left(\frac{\frac{\pi}{\sqrt{3}}}{\sqrt{3}}\right)\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\cos \left(\frac{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{\sqrt{3}}}{\sqrt{3}} - \frac{\pi}{\frac{3}{2}}\right) \cdot \cos \left(\frac{\frac{\pi}{\sqrt{3}}}{\sqrt{3}}\right) + \sin \left(\frac{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{\sqrt{3}}}{\sqrt{3}} - \frac{\pi}{\frac{3}{2}}\right) \cdot \sin \left(\frac{\frac{\pi}{\sqrt{3}}}{\sqrt{3}}\right)\right) \cdot 2
double f(double g, double h) {
        double r5018403 = 2.0;
        double r5018404 = atan2(1.0, 0.0);
        double r5018405 = r5018403 * r5018404;
        double r5018406 = 3.0;
        double r5018407 = r5018405 / r5018406;
        double r5018408 = g;
        double r5018409 = -r5018408;
        double r5018410 = h;
        double r5018411 = r5018409 / r5018410;
        double r5018412 = acos(r5018411);
        double r5018413 = r5018412 / r5018406;
        double r5018414 = r5018407 + r5018413;
        double r5018415 = cos(r5018414);
        double r5018416 = r5018403 * r5018415;
        return r5018416;
}
↓
double f(double g, double h) {
        double r5018417 = g;
        double r5018418 = h;
        double r5018419 = r5018417 / r5018418;
        double r5018420 = acos(r5018419);
        double r5018421 = 3.0;
        double r5018422 = sqrt(r5018421);
        double r5018423 = r5018420 / r5018422;
        double r5018424 = r5018423 / r5018422;
        double r5018425 = atan2(1.0, 0.0);
        double r5018426 = 1.5;
        double r5018427 = r5018425 / r5018426;
        double r5018428 = r5018424 - r5018427;
        double r5018429 = cos(r5018428);
        double r5018430 = r5018425 / r5018422;
        double r5018431 = r5018430 / r5018422;
        double r5018432 = cos(r5018431);
        double r5018433 = r5018429 * r5018432;
        double r5018434 = sin(r5018428);
        double r5018435 = sin(r5018431);
        double r5018436 = r5018434 * r5018435;
        double r5018437 = r5018433 + r5018436;
        double r5018438 = 2.0;
        double r5018439 = r5018437 * r5018438;
        return r5018439;
}

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 add-sqr-sqrt1.0

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

  5. Applied associate-/r*1.0

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

  7. Applied distribute-frac-neg1.0

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

  8. Applied acos-neg1.0

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

  9. Applied div-sub1.0

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

  10. Applied div-sub1.0

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

  11. Applied associate-+l-1.0

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

  12. Applied cos-diff0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2019142 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))