Average Error: 1.0 → 0.1
Time: 15.3s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\cos \left(\frac{\pi}{3} \cdot 2 + \frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) + \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) \cdot \sin \left(\frac{\pi}{3} \cdot 2 + \frac{\pi}{3}\right)\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\cos \left(\frac{\pi}{3} \cdot 2 + \frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) + \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right) \cdot \sin \left(\frac{\pi}{3} \cdot 2 + \frac{\pi}{3}\right)\right)
double f(double g, double h) {
        double r122531 = 2.0;
        double r122532 = atan2(1.0, 0.0);
        double r122533 = r122531 * r122532;
        double r122534 = 3.0;
        double r122535 = r122533 / r122534;
        double r122536 = g;
        double r122537 = -r122536;
        double r122538 = h;
        double r122539 = r122537 / r122538;
        double r122540 = acos(r122539);
        double r122541 = r122540 / r122534;
        double r122542 = r122535 + r122541;
        double r122543 = cos(r122542);
        double r122544 = r122531 * r122543;
        return r122544;
}
↓
double f(double g, double h) {
        double r122545 = 2.0;
        double r122546 = atan2(1.0, 0.0);
        double r122547 = 3.0;
        double r122548 = r122546 / r122547;
        double r122549 = r122548 * r122545;
        double r122550 = r122549 + r122548;
        double r122551 = cos(r122550);
        double r122552 = g;
        double r122553 = h;
        double r122554 = r122552 / r122553;
        double r122555 = acos(r122554);
        double r122556 = r122555 / r122547;
        double r122557 = cos(r122556);
        double r122558 = r122551 * r122557;
        double r122559 = sin(r122556);
        double r122560 = sin(r122550);
        double r122561 = r122559 * r122560;
        double r122562 = r122558 + r122561;
        double r122563 = r122545 * r122562;
        return r122563;
}

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 distribute-frac-neg1.0

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

  4. Applied acos-neg1.0

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

  5. Applied div-sub1.0

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

  6. Applied associate-+r-1.0

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

  7. Applied cos-diff0.1

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

  8. Simplified0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))