Average Error: 34.7 → 31.1
Time: 24.7s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{a \cdot 2}}\]
\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)}
↓
\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{a \cdot 2}}
double f(double g, double h, double a) {
        double r2711897 = 1.0;
        double r2711898 = 2.0;
        double r2711899 = a;
        double r2711900 = r2711898 * r2711899;
        double r2711901 = r2711897 / r2711900;
        double r2711902 = g;
        double r2711903 = -r2711902;
        double r2711904 = r2711902 * r2711902;
        double r2711905 = h;
        double r2711906 = r2711905 * r2711905;
        double r2711907 = r2711904 - r2711906;
        double r2711908 = sqrt(r2711907);
        double r2711909 = r2711903 + r2711908;
        double r2711910 = r2711901 * r2711909;
        double r2711911 = cbrt(r2711910);
        double r2711912 = r2711903 - r2711908;
        double r2711913 = r2711901 * r2711912;
        double r2711914 = cbrt(r2711913);
        double r2711915 = r2711911 + r2711914;
        return r2711915;
}
↓
double f(double g, double h, double a) {
        double r2711916 = g;
        double r2711917 = -r2711916;
        double r2711918 = r2711916 * r2711916;
        double r2711919 = h;
        double r2711920 = r2711919 * r2711919;
        double r2711921 = r2711918 - r2711920;
        double r2711922 = sqrt(r2711921);
        double r2711923 = r2711917 + r2711922;
        double r2711924 = cbrt(r2711923);
        double r2711925 = 1.0;
        double r2711926 = a;
        double r2711927 = 2.0;
        double r2711928 = r2711926 * r2711927;
        double r2711929 = r2711925 / r2711928;
        double r2711930 = cbrt(r2711929);
        double r2711931 = r2711924 * r2711930;
        double r2711932 = r2711917 - r2711922;
        double r2711933 = cbrt(r2711932);
        double r2711934 = cbrt(r2711928);
        double r2711935 = r2711933 / r2711934;
        double r2711936 = r2711931 + r2711935;
        return r2711936;
}

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 34.7

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

  3. Applied associate-*l/34.7

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

  4. Applied cbrt-div32.9

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

  6. Applied cbrt-prod31.1

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

  7. Final simplification31.1

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

Reproduce

herbie shell --seed 2019153 
(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))))))))