Average Error: 36.0 → 32.1
Time: 26.8s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{a \cdot 2}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}\]
\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]{\frac{1}{a \cdot 2}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}
double f(double g, double h, double a) {
        double r5300729 = 1.0;
        double r5300730 = 2.0;
        double r5300731 = a;
        double r5300732 = r5300730 * r5300731;
        double r5300733 = r5300729 / r5300732;
        double r5300734 = g;
        double r5300735 = -r5300734;
        double r5300736 = r5300734 * r5300734;
        double r5300737 = h;
        double r5300738 = r5300737 * r5300737;
        double r5300739 = r5300736 - r5300738;
        double r5300740 = sqrt(r5300739);
        double r5300741 = r5300735 + r5300740;
        double r5300742 = r5300733 * r5300741;
        double r5300743 = cbrt(r5300742);
        double r5300744 = r5300735 - r5300740;
        double r5300745 = r5300733 * r5300744;
        double r5300746 = cbrt(r5300745);
        double r5300747 = r5300743 + r5300746;
        return r5300747;
}
↓
double f(double g, double h, double a) {
        double r5300748 = 1.0;
        double r5300749 = a;
        double r5300750 = 2.0;
        double r5300751 = r5300749 * r5300750;
        double r5300752 = r5300748 / r5300751;
        double r5300753 = cbrt(r5300752);
        double r5300754 = g;
        double r5300755 = -r5300754;
        double r5300756 = r5300754 * r5300754;
        double r5300757 = h;
        double r5300758 = r5300757 * r5300757;
        double r5300759 = r5300756 - r5300758;
        double r5300760 = sqrt(r5300759);
        double r5300761 = r5300755 - r5300760;
        double r5300762 = cbrt(r5300761);
        double r5300763 = r5300753 * r5300762;
        double r5300764 = r5300755 + r5300760;
        double r5300765 = cbrt(r5300764);
        double r5300766 = r5300765 * r5300753;
        double r5300767 = r5300763 + r5300766;
        return r5300767;
}

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 36.0

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

  3. Applied cbrt-prod34.0

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

  5. Applied cbrt-prod32.1

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

  6. Final simplification32.1

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

Reproduce

herbie shell --seed 2019174 
(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))))))))