Average Error: 35.3 → 31.9
Time: 40.3s
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 r4870300 = 1.0;
        double r4870301 = 2.0;
        double r4870302 = a;
        double r4870303 = r4870301 * r4870302;
        double r4870304 = r4870300 / r4870303;
        double r4870305 = g;
        double r4870306 = -r4870305;
        double r4870307 = r4870305 * r4870305;
        double r4870308 = h;
        double r4870309 = r4870308 * r4870308;
        double r4870310 = r4870307 - r4870309;
        double r4870311 = sqrt(r4870310);
        double r4870312 = r4870306 + r4870311;
        double r4870313 = r4870304 * r4870312;
        double r4870314 = cbrt(r4870313);
        double r4870315 = r4870306 - r4870311;
        double r4870316 = r4870304 * r4870315;
        double r4870317 = cbrt(r4870316);
        double r4870318 = r4870314 + r4870317;
        return r4870318;
}
↓
double f(double g, double h, double a) {
        double r4870319 = 1.0;
        double r4870320 = a;
        double r4870321 = 2.0;
        double r4870322 = r4870320 * r4870321;
        double r4870323 = r4870319 / r4870322;
        double r4870324 = cbrt(r4870323);
        double r4870325 = g;
        double r4870326 = -r4870325;
        double r4870327 = r4870325 * r4870325;
        double r4870328 = h;
        double r4870329 = r4870328 * r4870328;
        double r4870330 = r4870327 - r4870329;
        double r4870331 = sqrt(r4870330);
        double r4870332 = r4870326 - r4870331;
        double r4870333 = cbrt(r4870332);
        double r4870334 = r4870324 * r4870333;
        double r4870335 = r4870326 + r4870331;
        double r4870336 = cbrt(r4870335);
        double r4870337 = r4870336 * r4870324;
        double r4870338 = r4870334 + r4870337;
        return r4870338;
}

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 +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))))))))