Average Error: 36.3 → 32.6
Time: 8.0s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\]
\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \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 \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}
double f(double g, double h, double a) {
        double r148270 = 1.0;
        double r148271 = 2.0;
        double r148272 = a;
        double r148273 = r148271 * r148272;
        double r148274 = r148270 / r148273;
        double r148275 = g;
        double r148276 = -r148275;
        double r148277 = r148275 * r148275;
        double r148278 = h;
        double r148279 = r148278 * r148278;
        double r148280 = r148277 - r148279;
        double r148281 = sqrt(r148280);
        double r148282 = r148276 + r148281;
        double r148283 = r148274 * r148282;
        double r148284 = cbrt(r148283);
        double r148285 = r148276 - r148281;
        double r148286 = r148274 * r148285;
        double r148287 = cbrt(r148286);
        double r148288 = r148284 + r148287;
        return r148288;
}
↓
double f(double g, double h, double a) {
        double r148289 = 1.0;
        double r148290 = 2.0;
        double r148291 = a;
        double r148292 = r148290 * r148291;
        double r148293 = r148289 / r148292;
        double r148294 = cbrt(r148293);
        double r148295 = g;
        double r148296 = -r148295;
        double r148297 = r148295 * r148295;
        double r148298 = h;
        double r148299 = r148298 * r148298;
        double r148300 = r148297 - r148299;
        double r148301 = sqrt(r148300);
        double r148302 = r148296 + r148301;
        double r148303 = cbrt(r148302);
        double r148304 = r148294 * r148303;
        double r148305 = r148296 - r148301;
        double r148306 = cbrt(r148305);
        double r148307 = r148294 * r148306;
        double r148308 = r148304 + r148307;
        return r148308;
}

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 36.3

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

  3. Applied cbrt-prod34.4

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

  5. Applied cbrt-prod32.6

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

  6. Final simplification32.6

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))