Average Error: 35.3 → 31.4
Time: 26.5s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\frac{\sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + g\right) \cdot \frac{-1}{2}}}{\sqrt[3]{a}} + \frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{a \cdot 2}}\]
\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)}
↓
\frac{\sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + g\right) \cdot \frac{-1}{2}}}{\sqrt[3]{a}} + \frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{a \cdot 2}}
double f(double g, double h, double a) {
        double r2180748 = 1.0;
        double r2180749 = 2.0;
        double r2180750 = a;
        double r2180751 = r2180749 * r2180750;
        double r2180752 = r2180748 / r2180751;
        double r2180753 = g;
        double r2180754 = -r2180753;
        double r2180755 = r2180753 * r2180753;
        double r2180756 = h;
        double r2180757 = r2180756 * r2180756;
        double r2180758 = r2180755 - r2180757;
        double r2180759 = sqrt(r2180758);
        double r2180760 = r2180754 + r2180759;
        double r2180761 = r2180752 * r2180760;
        double r2180762 = cbrt(r2180761);
        double r2180763 = r2180754 - r2180759;
        double r2180764 = r2180752 * r2180763;
        double r2180765 = cbrt(r2180764);
        double r2180766 = r2180762 + r2180765;
        return r2180766;
}
↓
double f(double g, double h, double a) {
        double r2180767 = g;
        double r2180768 = r2180767 * r2180767;
        double r2180769 = h;
        double r2180770 = r2180769 * r2180769;
        double r2180771 = r2180768 - r2180770;
        double r2180772 = sqrt(r2180771);
        double r2180773 = r2180772 + r2180767;
        double r2180774 = -0.5;
        double r2180775 = r2180773 * r2180774;
        double r2180776 = cbrt(r2180775);
        double r2180777 = a;
        double r2180778 = cbrt(r2180777);
        double r2180779 = r2180776 / r2180778;
        double r2180780 = r2180772 - r2180767;
        double r2180781 = cbrt(r2180780);
        double r2180782 = 2.0;
        double r2180783 = r2180777 * r2180782;
        double r2180784 = cbrt(r2180783);
        double r2180785 = r2180781 / r2180784;
        double r2180786 = r2180779 + r2180785;
        return r2180786;
}

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. Initial program 35.3

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

  2. Simplified35.2

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

  4. Applied associate-*l/35.2

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

  5. Applied cbrt-div33.2

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

  7. Applied cbrt-div31.4

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

  8. Final simplification31.4

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

Reproduce

herbie shell --seed 2019152 
(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))))))))