Average Error: 36.6 → 33.0
Time: 8.3s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\]
\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \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{g \cdot g - h \cdot h}} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}
double f(double g, double h, double a) {
        double r190773 = 1.0;
        double r190774 = 2.0;
        double r190775 = a;
        double r190776 = r190774 * r190775;
        double r190777 = r190773 / r190776;
        double r190778 = g;
        double r190779 = -r190778;
        double r190780 = r190778 * r190778;
        double r190781 = h;
        double r190782 = r190781 * r190781;
        double r190783 = r190780 - r190782;
        double r190784 = sqrt(r190783);
        double r190785 = r190779 + r190784;
        double r190786 = r190777 * r190785;
        double r190787 = cbrt(r190786);
        double r190788 = r190779 - r190784;
        double r190789 = r190777 * r190788;
        double r190790 = cbrt(r190789);
        double r190791 = r190787 + r190790;
        return r190791;
}
↓
double f(double g, double h, double a) {
        double r190792 = 1.0;
        double r190793 = 2.0;
        double r190794 = a;
        double r190795 = r190793 * r190794;
        double r190796 = r190792 / r190795;
        double r190797 = cbrt(r190796);
        double r190798 = g;
        double r190799 = -r190798;
        double r190800 = r190798 * r190798;
        double r190801 = h;
        double r190802 = r190801 * r190801;
        double r190803 = r190800 - r190802;
        double r190804 = sqrt(r190803);
        double r190805 = r190799 + r190804;
        double r190806 = cbrt(r190805);
        double r190807 = r190797 * r190806;
        double r190808 = r190799 - r190804;
        double r190809 = cbrt(r190808);
        double r190810 = r190797 * r190809;
        double r190811 = r190807 + r190810;
        return r190811;
}

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 36.6

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

  3. Applied cbrt-prod34.7

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

  5. Applied cbrt-prod33.0

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

  6. Final simplification33.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))