Average Error: 35.6 → 32.1
Time: 24.7s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\frac{\sqrt[3]{\frac{-1}{2} \cdot \left(\sqrt{g \cdot g - h \cdot h} + g\right)}}{\sqrt[3]{a}} + \sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}\]
\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]{\frac{-1}{2} \cdot \left(\sqrt{g \cdot g - h \cdot h} + g\right)}}{\sqrt[3]{a}} + \sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}
double f(double g, double h, double a) {
        double r7523353 = 1.0;
        double r7523354 = 2.0;
        double r7523355 = a;
        double r7523356 = r7523354 * r7523355;
        double r7523357 = r7523353 / r7523356;
        double r7523358 = g;
        double r7523359 = -r7523358;
        double r7523360 = r7523358 * r7523358;
        double r7523361 = h;
        double r7523362 = r7523361 * r7523361;
        double r7523363 = r7523360 - r7523362;
        double r7523364 = sqrt(r7523363);
        double r7523365 = r7523359 + r7523364;
        double r7523366 = r7523357 * r7523365;
        double r7523367 = cbrt(r7523366);
        double r7523368 = r7523359 - r7523364;
        double r7523369 = r7523357 * r7523368;
        double r7523370 = cbrt(r7523369);
        double r7523371 = r7523367 + r7523370;
        return r7523371;
}
↓
double f(double g, double h, double a) {
        double r7523372 = -0.5;
        double r7523373 = g;
        double r7523374 = r7523373 * r7523373;
        double r7523375 = h;
        double r7523376 = r7523375 * r7523375;
        double r7523377 = r7523374 - r7523376;
        double r7523378 = sqrt(r7523377);
        double r7523379 = r7523378 + r7523373;
        double r7523380 = r7523372 * r7523379;
        double r7523381 = cbrt(r7523380);
        double r7523382 = a;
        double r7523383 = cbrt(r7523382);
        double r7523384 = r7523381 / r7523383;
        double r7523385 = 0.5;
        double r7523386 = r7523385 / r7523382;
        double r7523387 = cbrt(r7523386);
        double r7523388 = r7523378 - r7523373;
        double r7523389 = cbrt(r7523388);
        double r7523390 = r7523387 * r7523389;
        double r7523391 = r7523384 + r7523390;
        return r7523391;
}

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 35.6

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

  2. Simplified35.6

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

  4. Applied div-inv35.6

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

  5. Applied cbrt-prod33.9

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

  6. Simplified33.9

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

  8. Applied associate-*r/33.9

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

  9. Applied cbrt-div32.1

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

  10. Final simplification32.1

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

Reproduce

herbie shell --seed 2019165 
(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))))))))