Average Error: 34.7 → 31.1
Time: 27.2s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{a \cdot 2}}\]
\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]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{a \cdot 2}}
double f(double g, double h, double a) {
        double r2252429 = 1.0;
        double r2252430 = 2.0;
        double r2252431 = a;
        double r2252432 = r2252430 * r2252431;
        double r2252433 = r2252429 / r2252432;
        double r2252434 = g;
        double r2252435 = -r2252434;
        double r2252436 = r2252434 * r2252434;
        double r2252437 = h;
        double r2252438 = r2252437 * r2252437;
        double r2252439 = r2252436 - r2252438;
        double r2252440 = sqrt(r2252439);
        double r2252441 = r2252435 + r2252440;
        double r2252442 = r2252433 * r2252441;
        double r2252443 = cbrt(r2252442);
        double r2252444 = r2252435 - r2252440;
        double r2252445 = r2252433 * r2252444;
        double r2252446 = cbrt(r2252445);
        double r2252447 = r2252443 + r2252446;
        return r2252447;
}
↓
double f(double g, double h, double a) {
        double r2252448 = g;
        double r2252449 = -r2252448;
        double r2252450 = r2252448 * r2252448;
        double r2252451 = h;
        double r2252452 = r2252451 * r2252451;
        double r2252453 = r2252450 - r2252452;
        double r2252454 = sqrt(r2252453);
        double r2252455 = r2252449 + r2252454;
        double r2252456 = cbrt(r2252455);
        double r2252457 = 1.0;
        double r2252458 = a;
        double r2252459 = 2.0;
        double r2252460 = r2252458 * r2252459;
        double r2252461 = r2252457 / r2252460;
        double r2252462 = cbrt(r2252461);
        double r2252463 = r2252456 * r2252462;
        double r2252464 = r2252449 - r2252454;
        double r2252465 = cbrt(r2252464);
        double r2252466 = cbrt(r2252460);
        double r2252467 = r2252465 / r2252466;
        double r2252468 = r2252463 + r2252467;
        return r2252468;
}

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 34.7

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

  3. Applied associate-*l/34.7

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

  4. Applied cbrt-div32.9

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

  6. Applied cbrt-prod31.1

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

  7. Final simplification31.1

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(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))))))))