Average Error: 35.7 → 32.0
Time: 1.2m
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{\frac{a}{\frac{1}{2}}}} + \sqrt[3]{\left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\right) \cdot \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\right)} \cdot \sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\frac{\sqrt[3]{a}}{\sqrt[3]{\frac{1}{2}}}}}\]
\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)}
↓
\frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{\frac{a}{\frac{1}{2}}}} + \sqrt[3]{\left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\right) \cdot \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\right)} \cdot \sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\frac{\sqrt[3]{a}}{\sqrt[3]{\frac{1}{2}}}}}
double f(double g, double h, double a) {
        double r34864662 = 1.0;
        double r34864663 = 2.0;
        double r34864664 = a;
        double r34864665 = r34864663 * r34864664;
        double r34864666 = r34864662 / r34864665;
        double r34864667 = g;
        double r34864668 = -r34864667;
        double r34864669 = r34864667 * r34864667;
        double r34864670 = h;
        double r34864671 = r34864670 * r34864670;
        double r34864672 = r34864669 - r34864671;
        double r34864673 = sqrt(r34864672);
        double r34864674 = r34864668 + r34864673;
        double r34864675 = r34864666 * r34864674;
        double r34864676 = cbrt(r34864675);
        double r34864677 = r34864668 - r34864673;
        double r34864678 = r34864666 * r34864677;
        double r34864679 = cbrt(r34864678);
        double r34864680 = r34864676 + r34864679;
        return r34864680;
}
↓
double f(double g, double h, double a) {
        double r34864681 = g;
        double r34864682 = r34864681 * r34864681;
        double r34864683 = h;
        double r34864684 = r34864683 * r34864683;
        double r34864685 = r34864682 - r34864684;
        double r34864686 = sqrt(r34864685);
        double r34864687 = r34864686 - r34864681;
        double r34864688 = cbrt(r34864687);
        double r34864689 = a;
        double r34864690 = 0.5;
        double r34864691 = r34864689 / r34864690;
        double r34864692 = cbrt(r34864691);
        double r34864693 = r34864688 / r34864692;
        double r34864694 = cbrt(r34864690);
        double r34864695 = cbrt(r34864689);
        double r34864696 = r34864694 / r34864695;
        double r34864697 = -r34864681;
        double r34864698 = r34864697 - r34864686;
        double r34864699 = cbrt(r34864698);
        double r34864700 = r34864696 * r34864699;
        double r34864701 = r34864700 * r34864700;
        double r34864702 = cbrt(r34864701);
        double r34864703 = r34864695 / r34864694;
        double r34864704 = r34864699 / r34864703;
        double r34864705 = cbrt(r34864704);
        double r34864706 = r34864702 * r34864705;
        double r34864707 = r34864693 + r34864706;
        return r34864707;
}

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 35.7

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

  2. Simplified35.7

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

  4. Applied cbrt-div33.6

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

  6. Applied add-cube-cbrt33.6

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

  7. Applied add-cube-cbrt33.6

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

  8. Applied times-frac33.6

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

  9. Applied add-cube-cbrt33.7

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

  10. Applied times-frac33.6

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

  11. Applied cbrt-prod32.0

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

  12. Simplified32.0

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

  13. Final simplification32.0

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

Reproduce

herbie shell --seed 2019120 
(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))))))))