2-ancestry mixing, positive discriminant

Average Error: 35.1 → 31.4

Time: 1.7m

Precision: 64

Math

\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]

↓

\[\begin{array}{l} \mathbf{if}\;\sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \le -6.169963939162089 \cdot 10^{-80}:\\ \;\;\;\;\left(\sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\frac{\sqrt[3]{\sqrt[3]{a}}}{\sqrt{\frac{1}{2}}}}} \cdot \sqrt[3]{\left(\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{\sqrt[3]{a}}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\left(-g\right) - g}}{\sqrt[3]{\sqrt[3]{a}}}}\right) \cdot \sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} + \sqrt[3]{\frac{1}{\frac{a}{\frac{1}{2}}}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}\\ \mathbf{elif}\;\sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \le 0.0:\\ \;\;\;\;\sqrt[3]{\frac{1}{\frac{a}{\frac{1}{2}}}} \cdot \sqrt[3]{\left(-g\right) - g} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}{\frac{a}{\frac{1}{2}}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\frac{\sqrt[3]{\sqrt[3]{a}}}{\sqrt{\frac{1}{2}}}}} \cdot \sqrt[3]{\left(\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{\sqrt[3]{a}}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\left(-g\right) - g}}{\sqrt[3]{\sqrt[3]{a}}}}\right) \cdot \sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} + \sqrt[3]{\frac{1}{\frac{a}{\frac{1}{2}}}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}\\ \end{array}\]

C

double f(double g, double h, double a) {
        double r14688760 = 1.0;
        double r14688761 = 2.0;
        double r14688762 = a;
        double r14688763 = r14688761 * r14688762;
        double r14688764 = r14688760 / r14688763;
        double r14688765 = g;
        double r14688766 = -r14688765;
        double r14688767 = r14688765 * r14688765;
        double r14688768 = h;
        double r14688769 = r14688768 * r14688768;
        double r14688770 = r14688767 - r14688769;
        double r14688771 = sqrt(r14688770);
        double r14688772 = r14688766 + r14688771;
        double r14688773 = r14688764 * r14688772;
        double r14688774 = cbrt(r14688773);
        double r14688775 = r14688766 - r14688771;
        double r14688776 = r14688764 * r14688775;
        double r14688777 = cbrt(r14688776);
        double r14688778 = r14688774 + r14688777;
        return r14688778;
}

↓

double f(double g, double h, double a) {
        double r14688779 = 1.0;
        double r14688780 = a;
        double r14688781 = 2.0;
        double r14688782 = r14688780 * r14688781;
        double r14688783 = r14688779 / r14688782;
        double r14688784 = g;
        double r14688785 = -r14688784;
        double r14688786 = r14688784 * r14688784;
        double r14688787 = h;
        double r14688788 = r14688787 * r14688787;
        double r14688789 = r14688786 - r14688788;
        double r14688790 = sqrt(r14688789);
        double r14688791 = r14688785 + r14688790;
        double r14688792 = r14688783 * r14688791;
        double r14688793 = cbrt(r14688792);
        double r14688794 = r14688785 - r14688790;
        double r14688795 = r14688783 * r14688794;
        double r14688796 = cbrt(r14688795);
        double r14688797 = r14688793 + r14688796;
        double r14688798 = -6.169963939162089e-80;
        bool r14688799 = r14688797 <= r14688798;
        double r14688800 = cbrt(r14688794);
        double r14688801 = cbrt(r14688780);
        double r14688802 = cbrt(r14688801);
        double r14688803 = 0.5;
        double r14688804 = sqrt(r14688803);
        double r14688805 = r14688802 / r14688804;
        double r14688806 = r14688800 / r14688805;
        double r14688807 = cbrt(r14688806);
        double r14688808 = r14688800 / r14688802;
        double r14688809 = r14688808 * r14688804;
        double r14688810 = r14688785 - r14688784;
        double r14688811 = cbrt(r14688810);
        double r14688812 = r14688811 / r14688802;
        double r14688813 = r14688809 * r14688812;
        double r14688814 = cbrt(r14688813);
        double r14688815 = r14688807 * r14688814;
        double r14688816 = r14688801 * r14688801;
        double r14688817 = r14688779 / r14688816;
        double r14688818 = cbrt(r14688817);
        double r14688819 = r14688815 * r14688818;
        double r14688820 = r14688780 / r14688803;
        double r14688821 = r14688779 / r14688820;
        double r14688822 = cbrt(r14688821);
        double r14688823 = r14688790 - r14688784;
        double r14688824 = cbrt(r14688823);
        double r14688825 = r14688822 * r14688824;
        double r14688826 = r14688819 + r14688825;
        double r14688827 = 0.0;
        bool r14688828 = r14688797 <= r14688827;
        double r14688829 = r14688822 * r14688811;
        double r14688830 = r14688794 / r14688820;
        double r14688831 = cbrt(r14688830);
        double r14688832 = r14688829 + r14688831;
        double r14688833 = r14688828 ? r14688832 : r14688826;
        double r14688834 = r14688799 ? r14688826 : r14688833;
        return r14688834;
}

Error

Bits error versus g

Bits error versus h

Bits error versus a

Derivation

1. Split input into 2 regimes

2. if (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))) < -6.169963939162089e-80 or 0.0 < (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

   1. Initial program 34.5

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]

   2. Simplified 34.5

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

   4. Applied div-inv 34.5

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

   5. Applied cbrt-prod 33.3

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

   7. Applied *-un-lft-identity 33.3

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

   8. Applied add-cube-cbrt 33.4

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

   9. Applied times-frac 33.4

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

   10. Applied *-un-lft-identity 33.4

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

   11. Applied times-frac 33.4

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

   12. Applied cbrt-prod 32.2

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

   13. Simplified 32.2

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

   15. Applied add-sqr-sqrt 32.2

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

   16. Applied add-cube-cbrt 32.2

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

   17. Applied times-frac 32.2

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

   18. Applied add-cube-cbrt 32.2

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

   19. Applied times-frac 32.2

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

   20. Applied cbrt-prod 32.3

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

   21. Simplified 32.3

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

   22. Taylor expanded around inf 32.3

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

   if -6.169963939162089e-80 < (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))) < 0.0

   1. Initial program 44.9

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]

   2. Simplified 44.9

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

   4. Applied div-inv 44.9

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

   5. Applied cbrt-prod 32.5

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

   6. Taylor expanded around -inf 17.0

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

   7. Simplified 17.0

      \[\leadsto \sqrt[3]{\color{blue}{\left(-g\right)} - g} \cdot \sqrt[3]{\frac{1}{\frac{a}{\frac{1}{2}}}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}{\frac{a}{\frac{1}{2}}}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 31.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \le -6.169963939162089 \cdot 10^{-80}:\\ \;\;\;\;\left(\sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\frac{\sqrt[3]{\sqrt[3]{a}}}{\sqrt{\frac{1}{2}}}}} \cdot \sqrt[3]{\left(\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{\sqrt[3]{a}}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\left(-g\right) - g}}{\sqrt[3]{\sqrt[3]{a}}}}\right) \cdot \sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} + \sqrt[3]{\frac{1}{\frac{a}{\frac{1}{2}}}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}\\ \mathbf{elif}\;\sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \le 0.0:\\ \;\;\;\;\sqrt[3]{\frac{1}{\frac{a}{\frac{1}{2}}}} \cdot \sqrt[3]{\left(-g\right) - g} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}{\frac{a}{\frac{1}{2}}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\frac{\sqrt[3]{\sqrt[3]{a}}}{\sqrt{\frac{1}{2}}}}} \cdot \sqrt[3]{\left(\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{\sqrt[3]{a}}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\left(-g\right) - g}}{\sqrt[3]{\sqrt[3]{a}}}}\right) \cdot \sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} + \sqrt[3]{\frac{1}{\frac{a}{\frac{1}{2}}}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}\\ \end{array}\]

Reproduce

herbie shell --seed 2019112 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))