Average Error: 1.0 → 0.1
Time: 18.0s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\frac{\sqrt{3} \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \left(\sqrt[3]{\frac{\pi}{\frac{3}{2}}} \cdot \sqrt[3]{\frac{\pi}{\frac{3}{2}}}\right) \cdot \sqrt[3]{\frac{\pi}{\frac{3}{2}}}\right)}{2} + \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2}\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\frac{\sqrt{3} \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \left(\sqrt[3]{\frac{\pi}{\frac{3}{2}}} \cdot \sqrt[3]{\frac{\pi}{\frac{3}{2}}}\right) \cdot \sqrt[3]{\frac{\pi}{\frac{3}{2}}}\right)}{2} + \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2}\right) \cdot 2
double f(double g, double h) {
        double r4801535 = 2.0;
        double r4801536 = atan2(1.0, 0.0);
        double r4801537 = r4801535 * r4801536;
        double r4801538 = 3.0;
        double r4801539 = r4801537 / r4801538;
        double r4801540 = g;
        double r4801541 = -r4801540;
        double r4801542 = h;
        double r4801543 = r4801541 / r4801542;
        double r4801544 = acos(r4801543);
        double r4801545 = r4801544 / r4801538;
        double r4801546 = r4801539 + r4801545;
        double r4801547 = cos(r4801546);
        double r4801548 = r4801535 * r4801547;
        return r4801548;
}
↓
double f(double g, double h) {
        double r4801549 = 3.0;
        double r4801550 = sqrt(r4801549);
        double r4801551 = g;
        double r4801552 = h;
        double r4801553 = r4801551 / r4801552;
        double r4801554 = acos(r4801553);
        double r4801555 = r4801554 / r4801549;
        double r4801556 = atan2(1.0, 0.0);
        double r4801557 = 1.5;
        double r4801558 = r4801556 / r4801557;
        double r4801559 = cbrt(r4801558);
        double r4801560 = r4801559 * r4801559;
        double r4801561 = r4801560 * r4801559;
        double r4801562 = r4801555 - r4801561;
        double r4801563 = sin(r4801562);
        double r4801564 = r4801550 * r4801563;
        double r4801565 = 2.0;
        double r4801566 = r4801564 / r4801565;
        double r4801567 = r4801555 - r4801558;
        double r4801568 = cos(r4801567);
        double r4801569 = 0.5;
        double r4801570 = r4801568 * r4801569;
        double r4801571 = r4801566 + r4801570;
        double r4801572 = r4801571 * r4801565;
        return r4801572;
}

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. Simplified0.1

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

  12. Applied add-cube-cbrt0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))