Average Error: 35.5 → 31.9
Time: 37.2s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{a \cdot 2}}\]
\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]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{a \cdot 2}}
double f(double g, double h, double a) {
        double r22232266 = 1.0;
        double r22232267 = 2.0;
        double r22232268 = a;
        double r22232269 = r22232267 * r22232268;
        double r22232270 = r22232266 / r22232269;
        double r22232271 = g;
        double r22232272 = -r22232271;
        double r22232273 = r22232271 * r22232271;
        double r22232274 = h;
        double r22232275 = r22232274 * r22232274;
        double r22232276 = r22232273 - r22232275;
        double r22232277 = sqrt(r22232276);
        double r22232278 = r22232272 + r22232277;
        double r22232279 = r22232270 * r22232278;
        double r22232280 = cbrt(r22232279);
        double r22232281 = r22232272 - r22232277;
        double r22232282 = r22232270 * r22232281;
        double r22232283 = cbrt(r22232282);
        double r22232284 = r22232280 + r22232283;
        return r22232284;
}
↓
double f(double g, double h, double a) {
        double r22232285 = g;
        double r22232286 = -r22232285;
        double r22232287 = r22232285 * r22232285;
        double r22232288 = h;
        double r22232289 = r22232288 * r22232288;
        double r22232290 = r22232287 - r22232289;
        double r22232291 = sqrt(r22232290);
        double r22232292 = r22232286 - r22232291;
        double r22232293 = cbrt(r22232292);
        double r22232294 = 1.0;
        double r22232295 = a;
        double r22232296 = 2.0;
        double r22232297 = r22232295 * r22232296;
        double r22232298 = r22232294 / r22232297;
        double r22232299 = cbrt(r22232298);
        double r22232300 = r22232293 * r22232299;
        double r22232301 = r22232291 - r22232285;
        double r22232302 = cbrt(r22232301);
        double r22232303 = cbrt(r22232297);
        double r22232304 = r22232302 / r22232303;
        double r22232305 = r22232300 + r22232304;
        return r22232305;
}

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 35.5

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

  3. Applied associate-*l/35.5

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

  4. Applied cbrt-div33.7

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

  5. Simplified33.7

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

  7. Applied cbrt-prod31.9

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

  8. Final simplification31.9

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

Reproduce

herbie shell --seed 2019104 +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))))))))