Average Error: 1.0 → 0.1
Time: 17.4s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \sin \left(\frac{\pi}{3}\right) + \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2}\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \sin \left(\frac{\pi}{3}\right) + \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2}\right)
double f(double g, double h) {
        double r27259460 = 2.0;
        double r27259461 = atan2(1.0, 0.0);
        double r27259462 = r27259460 * r27259461;
        double r27259463 = 3.0;
        double r27259464 = r27259462 / r27259463;
        double r27259465 = g;
        double r27259466 = -r27259465;
        double r27259467 = h;
        double r27259468 = r27259466 / r27259467;
        double r27259469 = acos(r27259468);
        double r27259470 = r27259469 / r27259463;
        double r27259471 = r27259464 + r27259470;
        double r27259472 = cos(r27259471);
        double r27259473 = r27259460 * r27259472;
        return r27259473;
}
↓
double f(double g, double h) {
        double r27259474 = 2.0;
        double r27259475 = g;
        double r27259476 = h;
        double r27259477 = r27259475 / r27259476;
        double r27259478 = acos(r27259477);
        double r27259479 = 3.0;
        double r27259480 = r27259478 / r27259479;
        double r27259481 = atan2(1.0, 0.0);
        double r27259482 = 1.5;
        double r27259483 = r27259481 / r27259482;
        double r27259484 = r27259480 - r27259483;
        double r27259485 = sin(r27259484);
        double r27259486 = r27259481 / r27259479;
        double r27259487 = sin(r27259486);
        double r27259488 = r27259485 * r27259487;
        double r27259489 = cos(r27259484);
        double r27259490 = 0.5;
        double r27259491 = r27259489 * r27259490;
        double r27259492 = r27259488 + r27259491;
        double r27259493 = r27259474 * r27259492;
        return r27259493;
}

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 distribute-frac-neg1.0

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

  5. Applied acos-neg1.0

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

  6. Applied div-sub1.0

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

  7. Applied associate-+l-1.0

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

  8. Applied cos-diff0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019124 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))