Average Error: 1.0 → 0.1
Time: 17.4s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[2 \cdot \left(\frac{\sqrt{3}}{2} \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \sqrt[3]{\frac{\pi}{\frac{3}{2}}} \cdot \left(\sqrt[3]{\frac{\pi}{\frac{3}{2}}} \cdot \sqrt[3]{\frac{\pi}{\frac{3}{2}}}\right)\right) + \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2}\right)\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
2 \cdot \left(\frac{\sqrt{3}}{2} \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \sqrt[3]{\frac{\pi}{\frac{3}{2}}} \cdot \left(\sqrt[3]{\frac{\pi}{\frac{3}{2}}} \cdot \sqrt[3]{\frac{\pi}{\frac{3}{2}}}\right)\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 r2693734 = 2.0;
        double r2693735 = atan2(1.0, 0.0);
        double r2693736 = r2693734 * r2693735;
        double r2693737 = 3.0;
        double r2693738 = r2693736 / r2693737;
        double r2693739 = g;
        double r2693740 = -r2693739;
        double r2693741 = h;
        double r2693742 = r2693740 / r2693741;
        double r2693743 = acos(r2693742);
        double r2693744 = r2693743 / r2693737;
        double r2693745 = r2693738 + r2693744;
        double r2693746 = cos(r2693745);
        double r2693747 = r2693734 * r2693746;
        return r2693747;
}
↓
double f(double g, double h) {
        double r2693748 = 2.0;
        double r2693749 = 3.0;
        double r2693750 = sqrt(r2693749);
        double r2693751 = r2693750 / r2693748;
        double r2693752 = g;
        double r2693753 = h;
        double r2693754 = r2693752 / r2693753;
        double r2693755 = acos(r2693754);
        double r2693756 = r2693755 / r2693749;
        double r2693757 = atan2(1.0, 0.0);
        double r2693758 = 1.5;
        double r2693759 = r2693757 / r2693758;
        double r2693760 = cbrt(r2693759);
        double r2693761 = r2693760 * r2693760;
        double r2693762 = r2693760 * r2693761;
        double r2693763 = r2693756 - r2693762;
        double r2693764 = sin(r2693763);
        double r2693765 = r2693751 * r2693764;
        double r2693766 = r2693756 - r2693759;
        double r2693767 = cos(r2693766);
        double r2693768 = 0.5;
        double r2693769 = r2693767 * r2693768;
        double r2693770 = r2693765 + r2693769;
        double r2693771 = r2693748 * r2693770;
        return r2693771;
}

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

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

  12. Applied add-cube-cbrt0.1

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

  13. Final simplification0.1

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

Reproduce

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