Average Error: 36.3 → 32.6
Time: 51.6s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2}} \cdot \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\right) + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]
\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]{\frac{1}{2}} \cdot \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\right) + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}
double f(double g, double h, double a) {
        double r7695848 = 1.0;
        double r7695849 = 2.0;
        double r7695850 = a;
        double r7695851 = r7695849 * r7695850;
        double r7695852 = r7695848 / r7695851;
        double r7695853 = g;
        double r7695854 = -r7695853;
        double r7695855 = r7695853 * r7695853;
        double r7695856 = h;
        double r7695857 = r7695856 * r7695856;
        double r7695858 = r7695855 - r7695857;
        double r7695859 = sqrt(r7695858);
        double r7695860 = r7695854 + r7695859;
        double r7695861 = r7695852 * r7695860;
        double r7695862 = cbrt(r7695861);
        double r7695863 = r7695854 - r7695859;
        double r7695864 = r7695852 * r7695863;
        double r7695865 = cbrt(r7695864);
        double r7695866 = r7695862 + r7695865;
        return r7695866;
}
↓
double f(double g, double h, double a) {
        double r7695867 = 1.0;
        double r7695868 = 2.0;
        double r7695869 = r7695867 / r7695868;
        double r7695870 = cbrt(r7695869);
        double r7695871 = 1.0;
        double r7695872 = a;
        double r7695873 = r7695871 / r7695872;
        double r7695874 = cbrt(r7695873);
        double r7695875 = g;
        double r7695876 = -r7695875;
        double r7695877 = r7695875 * r7695875;
        double r7695878 = h;
        double r7695879 = r7695878 * r7695878;
        double r7695880 = r7695877 - r7695879;
        double r7695881 = sqrt(r7695880);
        double r7695882 = r7695876 - r7695881;
        double r7695883 = cbrt(r7695882);
        double r7695884 = r7695874 * r7695883;
        double r7695885 = r7695870 * r7695884;
        double r7695886 = r7695876 + r7695881;
        double r7695887 = r7695867 * r7695886;
        double r7695888 = cbrt(r7695887);
        double r7695889 = r7695868 * r7695872;
        double r7695890 = cbrt(r7695889);
        double r7695891 = r7695888 / r7695890;
        double r7695892 = r7695885 + r7695891;
        return r7695892;
}

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 36.3

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

  3. Applied associate-*l/36.3

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

  4. Applied cbrt-div34.6

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

  6. Applied add-cbrt-cube34.6

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

  7. Simplified34.6

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

  9. Applied times-frac34.6

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

  10. Applied cbrt-prod34.6

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

  12. Applied div-inv34.6

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

  13. Applied cbrt-prod32.6

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

  14. Simplified32.6

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

  15. Final simplification32.6

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

Reproduce

herbie shell --seed 2019200 
(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))))))))