Average Error: 35.0 → 30.9
Time: 30.4s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;g \le 8.856201020375248 \cdot 10^{-207}:\\ \;\;\;\;\sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} + \frac{\sqrt[3]{-\left(g + g\right)}}{\sqrt[3]{a \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(g + \left(-g\right)\right) \cdot \frac{1}{a \cdot 2}} + \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}\\ \end{array}\]
\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 8.856201020375248 \cdot 10^{-207}:\\
\;\;\;\;\sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} + \frac{\sqrt[3]{-\left(g + g\right)}}{\sqrt[3]{a \cdot 2}}\\

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

\end{array}
double f(double g, double h, double a) {
        double r5188508 = 1.0;
        double r5188509 = 2.0;
        double r5188510 = a;
        double r5188511 = r5188509 * r5188510;
        double r5188512 = r5188508 / r5188511;
        double r5188513 = g;
        double r5188514 = -r5188513;
        double r5188515 = r5188513 * r5188513;
        double r5188516 = h;
        double r5188517 = r5188516 * r5188516;
        double r5188518 = r5188515 - r5188517;
        double r5188519 = sqrt(r5188518);
        double r5188520 = r5188514 + r5188519;
        double r5188521 = r5188512 * r5188520;
        double r5188522 = cbrt(r5188521);
        double r5188523 = r5188514 - r5188519;
        double r5188524 = r5188512 * r5188523;
        double r5188525 = cbrt(r5188524);
        double r5188526 = r5188522 + r5188525;
        return r5188526;
}
↓
double f(double g, double h, double a) {
        double r5188527 = g;
        double r5188528 = 8.856201020375248e-207;
        bool r5188529 = r5188527 <= r5188528;
        double r5188530 = 1.0;
        double r5188531 = a;
        double r5188532 = 2.0;
        double r5188533 = r5188531 * r5188532;
        double r5188534 = r5188530 / r5188533;
        double r5188535 = -r5188527;
        double r5188536 = r5188527 * r5188527;
        double r5188537 = h;
        double r5188538 = r5188537 * r5188537;
        double r5188539 = r5188536 - r5188538;
        double r5188540 = sqrt(r5188539);
        double r5188541 = r5188535 - r5188540;
        double r5188542 = r5188534 * r5188541;
        double r5188543 = cbrt(r5188542);
        double r5188544 = r5188527 + r5188527;
        double r5188545 = -r5188544;
        double r5188546 = cbrt(r5188545);
        double r5188547 = cbrt(r5188533);
        double r5188548 = r5188546 / r5188547;
        double r5188549 = r5188543 + r5188548;
        double r5188550 = r5188527 + r5188535;
        double r5188551 = r5188550 * r5188534;
        double r5188552 = cbrt(r5188551);
        double r5188553 = cbrt(r5188541);
        double r5188554 = cbrt(r5188534);
        double r5188555 = r5188553 * r5188554;
        double r5188556 = r5188552 + r5188555;
        double r5188557 = r5188529 ? r5188549 : r5188556;
        return r5188557;
}

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 < 8.856201020375248e-207

    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-div31.8

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

    5. Taylor expanded around -inf 31.2

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

    6. Simplified31.2

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

    if 8.856201020375248e-207 < g

    1. Initial program 34.4

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

    3. Applied cbrt-prod30.8

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

    4. Taylor expanded around inf 30.6

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

  4. Final simplification30.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;g \le 8.856201020375248 \cdot 10^{-207}:\\ \;\;\;\;\sqrt[3]{\frac{1}{a \cdot 2} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} + \frac{\sqrt[3]{-\left(g + g\right)}}{\sqrt[3]{a \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(g + \left(-g\right)\right) \cdot \frac{1}{a \cdot 2}} + \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 
(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))))))))