Average Error: 35.2 → 32.3
Time: 25.7s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\frac{\sqrt[3]{\frac{-1}{2} \cdot \left(\sqrt{g \cdot g - h \cdot h} + g\right)}}{\sqrt[3]{a}} + \sqrt[3]{\frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{a}} \cdot \sqrt[3]{\frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{2}}\]
\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]{\frac{-1}{2} \cdot \left(\sqrt{g \cdot g - h \cdot h} + g\right)}}{\sqrt[3]{a}} + \sqrt[3]{\frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{a}} \cdot \sqrt[3]{\frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{2}}
double f(double g, double h, double a) {
        double r2271295 = 1.0;
        double r2271296 = 2.0;
        double r2271297 = a;
        double r2271298 = r2271296 * r2271297;
        double r2271299 = r2271295 / r2271298;
        double r2271300 = g;
        double r2271301 = -r2271300;
        double r2271302 = r2271300 * r2271300;
        double r2271303 = h;
        double r2271304 = r2271303 * r2271303;
        double r2271305 = r2271302 - r2271304;
        double r2271306 = sqrt(r2271305);
        double r2271307 = r2271301 + r2271306;
        double r2271308 = r2271299 * r2271307;
        double r2271309 = cbrt(r2271308);
        double r2271310 = r2271301 - r2271306;
        double r2271311 = r2271299 * r2271310;
        double r2271312 = cbrt(r2271311);
        double r2271313 = r2271309 + r2271312;
        return r2271313;
}
↓
double f(double g, double h, double a) {
        double r2271314 = -0.5;
        double r2271315 = g;
        double r2271316 = r2271315 * r2271315;
        double r2271317 = h;
        double r2271318 = r2271317 * r2271317;
        double r2271319 = r2271316 - r2271318;
        double r2271320 = sqrt(r2271319);
        double r2271321 = r2271320 + r2271315;
        double r2271322 = r2271314 * r2271321;
        double r2271323 = cbrt(r2271322);
        double r2271324 = a;
        double r2271325 = cbrt(r2271324);
        double r2271326 = r2271323 / r2271325;
        double r2271327 = r2271320 - r2271315;
        double r2271328 = cbrt(r2271327);
        double r2271329 = r2271328 / r2271324;
        double r2271330 = cbrt(r2271329);
        double r2271331 = r2271328 * r2271328;
        double r2271332 = 2.0;
        double r2271333 = r2271331 / r2271332;
        double r2271334 = cbrt(r2271333);
        double r2271335 = r2271330 * r2271334;
        double r2271336 = r2271326 + r2271335;
        return r2271336;
}

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 35.2

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

  2. Simplified35.2

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

  4. Applied associate-*l/35.2

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

  5. Applied cbrt-div33.4

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

  7. Applied add-cube-cbrt33.4

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

  8. Applied times-frac33.4

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

  9. Applied cbrt-prod32.3

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

  10. Final simplification32.3

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

Reproduce

herbie shell --seed 2019151 
(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))))))))