Average Error: 35.3 → 31.9
Time: 38.3s
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 r5398275 = 1.0;
        double r5398276 = 2.0;
        double r5398277 = a;
        double r5398278 = r5398276 * r5398277;
        double r5398279 = r5398275 / r5398278;
        double r5398280 = g;
        double r5398281 = -r5398280;
        double r5398282 = r5398280 * r5398280;
        double r5398283 = h;
        double r5398284 = r5398283 * r5398283;
        double r5398285 = r5398282 - r5398284;
        double r5398286 = sqrt(r5398285);
        double r5398287 = r5398281 + r5398286;
        double r5398288 = r5398279 * r5398287;
        double r5398289 = cbrt(r5398288);
        double r5398290 = r5398281 - r5398286;
        double r5398291 = r5398279 * r5398290;
        double r5398292 = cbrt(r5398291);
        double r5398293 = r5398289 + r5398292;
        return r5398293;
}
↓
double f(double g, double h, double a) {
        double r5398294 = 1.0;
        double r5398295 = a;
        double r5398296 = 2.0;
        double r5398297 = r5398295 * r5398296;
        double r5398298 = r5398294 / r5398297;
        double r5398299 = cbrt(r5398298);
        double r5398300 = g;
        double r5398301 = -r5398300;
        double r5398302 = r5398300 * r5398300;
        double r5398303 = h;
        double r5398304 = r5398303 * r5398303;
        double r5398305 = r5398302 - r5398304;
        double r5398306 = sqrt(r5398305);
        double r5398307 = r5398301 - r5398306;
        double r5398308 = cbrt(r5398307);
        double r5398309 = r5398299 * r5398308;
        double r5398310 = r5398301 + r5398306;
        double r5398311 = cbrt(r5398310);
        double r5398312 = r5398311 * r5398299;
        double r5398313 = r5398309 + r5398312;
        return r5398313;
}

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 35.3

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

  3. Applied cbrt-prod33.4

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

  5. Applied cbrt-prod31.9

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

  6. Final simplification31.9

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

Reproduce

herbie shell --seed 2019142 
(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))))))))