Average Error: 35.4 → 31.1
Time: 28.7s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;g \le 1.243127623547842309864200055971413705955 \cdot 10^{-220}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{-\left(g + g\right)} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right) \cdot \frac{1}{2 \cdot a}} + \sqrt[3]{\left(-g\right) - \sqrt{\sqrt[3]{g \cdot g - h \cdot h} \cdot \left(\sqrt[3]{g \cdot g - h \cdot h} \cdot \sqrt[3]{g \cdot g - h \cdot h}\right)}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\\ \end{array}\]
\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 1.243127623547842309864200055971413705955 \cdot 10^{-220}:\\
\;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{-\left(g + g\right)} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\\

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

\end{array}
double f(double g, double h, double a) {
        double r3935130 = 1.0;
        double r3935131 = 2.0;
        double r3935132 = a;
        double r3935133 = r3935131 * r3935132;
        double r3935134 = r3935130 / r3935133;
        double r3935135 = g;
        double r3935136 = -r3935135;
        double r3935137 = r3935135 * r3935135;
        double r3935138 = h;
        double r3935139 = r3935138 * r3935138;
        double r3935140 = r3935137 - r3935139;
        double r3935141 = sqrt(r3935140);
        double r3935142 = r3935136 + r3935141;
        double r3935143 = r3935134 * r3935142;
        double r3935144 = cbrt(r3935143);
        double r3935145 = r3935136 - r3935141;
        double r3935146 = r3935134 * r3935145;
        double r3935147 = cbrt(r3935146);
        double r3935148 = r3935144 + r3935147;
        return r3935148;
}
↓
double f(double g, double h, double a) {
        double r3935149 = g;
        double r3935150 = 1.2431276235478423e-220;
        bool r3935151 = r3935149 <= r3935150;
        double r3935152 = 1.0;
        double r3935153 = 2.0;
        double r3935154 = a;
        double r3935155 = r3935153 * r3935154;
        double r3935156 = r3935152 / r3935155;
        double r3935157 = -r3935149;
        double r3935158 = r3935149 * r3935149;
        double r3935159 = h;
        double r3935160 = r3935159 * r3935159;
        double r3935161 = r3935158 - r3935160;
        double r3935162 = sqrt(r3935161);
        double r3935163 = r3935157 - r3935162;
        double r3935164 = r3935156 * r3935163;
        double r3935165 = cbrt(r3935164);
        double r3935166 = r3935149 + r3935149;
        double r3935167 = -r3935166;
        double r3935168 = cbrt(r3935167);
        double r3935169 = cbrt(r3935156);
        double r3935170 = r3935168 * r3935169;
        double r3935171 = r3935165 + r3935170;
        double r3935172 = r3935162 + r3935157;
        double r3935173 = r3935172 * r3935156;
        double r3935174 = cbrt(r3935173);
        double r3935175 = cbrt(r3935161);
        double r3935176 = r3935175 * r3935175;
        double r3935177 = r3935175 * r3935176;
        double r3935178 = sqrt(r3935177);
        double r3935179 = r3935157 - r3935178;
        double r3935180 = cbrt(r3935179);
        double r3935181 = r3935180 * r3935169;
        double r3935182 = r3935174 + r3935181;
        double r3935183 = r3935151 ? r3935171 : r3935182;
        return r3935183;
}

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 < 1.2431276235478423e-220

    1. Initial program 36.0

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

    3. Applied cbrt-prod32.3

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

    4. Taylor expanded around -inf 31.6

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

    5. Simplified31.6

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

    if 1.2431276235478423e-220 < g

    1. Initial program 34.9

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

    3. Applied cbrt-prod30.6

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

    5. Applied add-cube-cbrt30.6

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

  4. Final simplification31.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;g \le 1.243127623547842309864200055971413705955 \cdot 10^{-220}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{-\left(g + g\right)} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right) \cdot \frac{1}{2 \cdot a}} + \sqrt[3]{\left(-g\right) - \sqrt{\sqrt[3]{g \cdot g - h \cdot h} \cdot \left(\sqrt[3]{g \cdot g - h \cdot h} \cdot \sqrt[3]{g \cdot g - h \cdot h}\right)}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))