Average Error: 35.6 → 31.3
Time: 25.9s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;g \le -5.401023155583567976051803909194293242719 \cdot 10^{-158}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} + \left(-g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - g} + \sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right) \cdot \frac{1}{2 \cdot a}}\\ \end{array}\]
\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)}
↓
\begin{array}{l}
\mathbf{if}\;g \le -5.401023155583567976051803909194293242719 \cdot 10^{-158}:\\
\;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} + \left(-g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\\

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

\end{array}
double f(double g, double h, double a) {
        double r4420256 = 1.0;
        double r4420257 = 2.0;
        double r4420258 = a;
        double r4420259 = r4420257 * r4420258;
        double r4420260 = r4420256 / r4420259;
        double r4420261 = g;
        double r4420262 = -r4420261;
        double r4420263 = r4420261 * r4420261;
        double r4420264 = h;
        double r4420265 = r4420264 * r4420264;
        double r4420266 = r4420263 - r4420265;
        double r4420267 = sqrt(r4420266);
        double r4420268 = r4420262 + r4420267;
        double r4420269 = r4420260 * r4420268;
        double r4420270 = cbrt(r4420269);
        double r4420271 = r4420262 - r4420267;
        double r4420272 = r4420260 * r4420271;
        double r4420273 = cbrt(r4420272);
        double r4420274 = r4420270 + r4420273;
        return r4420274;
}
↓
double f(double g, double h, double a) {
        double r4420275 = g;
        double r4420276 = -5.401023155583568e-158;
        bool r4420277 = r4420275 <= r4420276;
        double r4420278 = 1.0;
        double r4420279 = 2.0;
        double r4420280 = a;
        double r4420281 = r4420279 * r4420280;
        double r4420282 = r4420278 / r4420281;
        double r4420283 = cbrt(r4420282);
        double r4420284 = r4420275 * r4420275;
        double r4420285 = h;
        double r4420286 = r4420285 * r4420285;
        double r4420287 = r4420284 - r4420286;
        double r4420288 = sqrt(r4420287);
        double r4420289 = -r4420275;
        double r4420290 = r4420288 + r4420289;
        double r4420291 = cbrt(r4420290);
        double r4420292 = r4420283 * r4420291;
        double r4420293 = r4420289 - r4420288;
        double r4420294 = r4420282 * r4420293;
        double r4420295 = cbrt(r4420294);
        double r4420296 = r4420292 + r4420295;
        double r4420297 = r4420289 - r4420275;
        double r4420298 = cbrt(r4420297);
        double r4420299 = r4420283 * r4420298;
        double r4420300 = r4420290 * r4420282;
        double r4420301 = cbrt(r4420300);
        double r4420302 = r4420299 + r4420301;
        double r4420303 = r4420277 ? r4420296 : r4420302;
        return r4420303;
}

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. Split input into 2 regimes

  2. if g < -5.401023155583568e-158

    1. Initial program 34.7

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

    3. Applied cbrt-prod31.2

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

    if -5.401023155583568e-158 < g

    1. Initial program 36.4

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

    3. Applied cbrt-prod32.8

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

    4. Taylor expanded around inf 31.5

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \color{blue}{g}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification31.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;g \le -5.401023155583567976051803909194293242719 \cdot 10^{-158}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} + \left(-g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - g} + \sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right) \cdot \frac{1}{2 \cdot a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))