Average Error: 34.9 → 30.9
Time: 32.4s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;g \le -1.477469400954285 \cdot 10^{-196}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} + \left(-g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \left(-g\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - g} + \sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right) \cdot \frac{1}{2 \cdot a}}\\ \end{array}\]
\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}\;g \le -1.477469400954285 \cdot 10^{-196}:\\
\;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} + \left(-g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \left(-g\right)\right)}\\

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

\end{array}
double f(double g, double h, double a) {
        double r5944772 = 1.0;
        double r5944773 = 2.0;
        double r5944774 = a;
        double r5944775 = r5944773 * r5944774;
        double r5944776 = r5944772 / r5944775;
        double r5944777 = g;
        double r5944778 = -r5944777;
        double r5944779 = r5944777 * r5944777;
        double r5944780 = h;
        double r5944781 = r5944780 * r5944780;
        double r5944782 = r5944779 - r5944781;
        double r5944783 = sqrt(r5944782);
        double r5944784 = r5944778 + r5944783;
        double r5944785 = r5944776 * r5944784;
        double r5944786 = cbrt(r5944785);
        double r5944787 = r5944778 - r5944783;
        double r5944788 = r5944776 * r5944787;
        double r5944789 = cbrt(r5944788);
        double r5944790 = r5944786 + r5944789;
        return r5944790;
}
↓
double f(double g, double h, double a) {
        double r5944791 = g;
        double r5944792 = -1.477469400954285e-196;
        bool r5944793 = r5944791 <= r5944792;
        double r5944794 = 1.0;
        double r5944795 = 2.0;
        double r5944796 = a;
        double r5944797 = r5944795 * r5944796;
        double r5944798 = r5944794 / r5944797;
        double r5944799 = cbrt(r5944798);
        double r5944800 = r5944791 * r5944791;
        double r5944801 = h;
        double r5944802 = r5944801 * r5944801;
        double r5944803 = r5944800 - r5944802;
        double r5944804 = sqrt(r5944803);
        double r5944805 = -r5944791;
        double r5944806 = r5944804 + r5944805;
        double r5944807 = cbrt(r5944806);
        double r5944808 = r5944799 * r5944807;
        double r5944809 = r5944805 - r5944805;
        double r5944810 = r5944798 * r5944809;
        double r5944811 = cbrt(r5944810);
        double r5944812 = r5944808 + r5944811;
        double r5944813 = r5944805 - r5944791;
        double r5944814 = cbrt(r5944813);
        double r5944815 = r5944799 * r5944814;
        double r5944816 = r5944806 * r5944798;
        double r5944817 = cbrt(r5944816);
        double r5944818 = r5944815 + r5944817;
        double r5944819 = r5944793 ? r5944812 : r5944818;
        return r5944819;
}

Error

Bits error versus g

Bits error versus h

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if g < -1.477469400954285e-196

    1. Initial program 33.5

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

    3. Applied cbrt-prod30.0

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

    4. Taylor expanded around -inf 29.9

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

    5. Simplified29.9

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

    if -1.477469400954285e-196 < g

    1. Initial program 36.1

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

    3. Applied cbrt-prod32.8

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

    4. Taylor expanded around inf 31.9

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

  4. Final simplification30.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;g \le -1.477469400954285 \cdot 10^{-196}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} + \left(-g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \left(-g\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - g} + \sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right) \cdot \frac{1}{2 \cdot a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019141 
(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))))))))