Average Error: 36.5 → 32.6
Time: 11.0s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]
\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 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}}
double f(double g, double h, double a) {
        double r191728 = 1.0;
        double r191729 = 2.0;
        double r191730 = a;
        double r191731 = r191729 * r191730;
        double r191732 = r191728 / r191731;
        double r191733 = g;
        double r191734 = -r191733;
        double r191735 = r191733 * r191733;
        double r191736 = h;
        double r191737 = r191736 * r191736;
        double r191738 = r191735 - r191737;
        double r191739 = sqrt(r191738);
        double r191740 = r191734 + r191739;
        double r191741 = r191732 * r191740;
        double r191742 = cbrt(r191741);
        double r191743 = r191734 - r191739;
        double r191744 = r191732 * r191743;
        double r191745 = cbrt(r191744);
        double r191746 = r191742 + r191745;
        return r191746;
}
↓
double f(double g, double h, double a) {
        double r191747 = 1.0;
        double r191748 = 2.0;
        double r191749 = a;
        double r191750 = r191748 * r191749;
        double r191751 = r191747 / r191750;
        double r191752 = cbrt(r191751);
        double r191753 = g;
        double r191754 = -r191753;
        double r191755 = r191753 * r191753;
        double r191756 = h;
        double r191757 = r191756 * r191756;
        double r191758 = r191755 - r191757;
        double r191759 = sqrt(r191758);
        double r191760 = r191754 + r191759;
        double r191761 = cbrt(r191760);
        double r191762 = r191752 * r191761;
        double r191763 = r191754 - r191759;
        double r191764 = r191747 * r191763;
        double r191765 = cbrt(r191764);
        double r191766 = cbrt(r191750);
        double r191767 = r191765 / r191766;
        double r191768 = r191762 + r191767;
        return r191768;
}

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 36.5

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

  3. Applied cbrt-prod34.4

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

  5. Applied associate-*l/34.4

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

  6. Applied cbrt-div32.6

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

  7. Final simplification32.6

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

Reproduce

herbie shell --seed 2019322 
(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))))))))