Average Error: 28.7 → 0.0
Time: 47.3s
Precision: 64
\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -108576937514.12856:\\ \;\;\;\;\frac{0.15298196345929327}{{x}^{5}} + \left(\frac{0.2514179000665375}{x \cdot \left(x \cdot x\right)} + \frac{0.5}{x}\right)\\ \mathbf{elif}\;x \le 672.3709112650113:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\left(x \cdot x\right) \cdot 0.0001789971\right), \left(\mathsf{fma}\left(0.0005064034, \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot 0.0072644182\right), \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), 0.0424060604, \left(\mathsf{fma}\left(0.1049934947, \left(x \cdot x\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(\left(0.0001789971 \cdot 2\right), \left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), \left(\left(0.0140005442 + \left(x \cdot x\right) \cdot 0.0008327945\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), 0.0694555761, \left(\mathsf{fma}\left(0.2909738639, \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), 0.7715471019, 1\right)\right)\right)\right)\right)\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.15298196345929327}{{x}^{5}} + \left(\frac{0.2514179000665375}{x \cdot \left(x \cdot x\right)} + \frac{0.5}{x}\right)\\ \end{array}\]
\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x
↓
\begin{array}{l}
\mathbf{if}\;x \le -108576937514.12856:\\
\;\;\;\;\frac{0.15298196345929327}{{x}^{5}} + \left(\frac{0.2514179000665375}{x \cdot \left(x \cdot x\right)} + \frac{0.5}{x}\right)\\

\mathbf{elif}\;x \le 672.3709112650113:\\
\;\;\;\;\frac{\mathsf{fma}\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\left(x \cdot x\right) \cdot 0.0001789971\right), \left(\mathsf{fma}\left(0.0005064034, \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot 0.0072644182\right), \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), 0.0424060604, \left(\mathsf{fma}\left(0.1049934947, \left(x \cdot x\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(\left(0.0001789971 \cdot 2\right), \left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), \left(\left(0.0140005442 + \left(x \cdot x\right) \cdot 0.0008327945\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), 0.0694555761, \left(\mathsf{fma}\left(0.2909738639, \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), 0.7715471019, 1\right)\right)\right)\right)\right)\right)\right)\right)\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{0.15298196345929327}{{x}^{5}} + \left(\frac{0.2514179000665375}{x \cdot \left(x \cdot x\right)} + \frac{0.5}{x}\right)\\

\end{array}
double f(double x) {
        double r2125252 = 1.0;
        double r2125253 = 0.1049934947;
        double r2125254 = x;
        double r2125255 = r2125254 * r2125254;
        double r2125256 = r2125253 * r2125255;
        double r2125257 = r2125252 + r2125256;
        double r2125258 = 0.0424060604;
        double r2125259 = r2125255 * r2125255;
        double r2125260 = r2125258 * r2125259;
        double r2125261 = r2125257 + r2125260;
        double r2125262 = 0.0072644182;
        double r2125263 = r2125259 * r2125255;
        double r2125264 = r2125262 * r2125263;
        double r2125265 = r2125261 + r2125264;
        double r2125266 = 0.0005064034;
        double r2125267 = r2125263 * r2125255;
        double r2125268 = r2125266 * r2125267;
        double r2125269 = r2125265 + r2125268;
        double r2125270 = 0.0001789971;
        double r2125271 = r2125267 * r2125255;
        double r2125272 = r2125270 * r2125271;
        double r2125273 = r2125269 + r2125272;
        double r2125274 = 0.7715471019;
        double r2125275 = r2125274 * r2125255;
        double r2125276 = r2125252 + r2125275;
        double r2125277 = 0.2909738639;
        double r2125278 = r2125277 * r2125259;
        double r2125279 = r2125276 + r2125278;
        double r2125280 = 0.0694555761;
        double r2125281 = r2125280 * r2125263;
        double r2125282 = r2125279 + r2125281;
        double r2125283 = 0.0140005442;
        double r2125284 = r2125283 * r2125267;
        double r2125285 = r2125282 + r2125284;
        double r2125286 = 0.0008327945;
        double r2125287 = r2125286 * r2125271;
        double r2125288 = r2125285 + r2125287;
        double r2125289 = 2.0;
        double r2125290 = r2125289 * r2125270;
        double r2125291 = r2125271 * r2125255;
        double r2125292 = r2125290 * r2125291;
        double r2125293 = r2125288 + r2125292;
        double r2125294 = r2125273 / r2125293;
        double r2125295 = r2125294 * r2125254;
        return r2125295;
}
↓
double f(double x) {
        double r2125296 = x;
        double r2125297 = -108576937514.12856;
        bool r2125298 = r2125296 <= r2125297;
        double r2125299 = 0.15298196345929327;
        double r2125300 = 5.0;
        double r2125301 = pow(r2125296, r2125300);
        double r2125302 = r2125299 / r2125301;
        double r2125303 = 0.2514179000665375;
        double r2125304 = r2125296 * r2125296;
        double r2125305 = r2125296 * r2125304;
        double r2125306 = r2125303 / r2125305;
        double r2125307 = 0.5;
        double r2125308 = r2125307 / r2125296;
        double r2125309 = r2125306 + r2125308;
        double r2125310 = r2125302 + r2125309;
        double r2125311 = 672.3709112650113;
        bool r2125312 = r2125296 <= r2125311;
        double r2125313 = r2125304 * r2125304;
        double r2125314 = r2125313 * r2125313;
        double r2125315 = 0.0001789971;
        double r2125316 = r2125304 * r2125315;
        double r2125317 = 0.0005064034;
        double r2125318 = 0.0072644182;
        double r2125319 = r2125304 * r2125318;
        double r2125320 = 0.0424060604;
        double r2125321 = 0.1049934947;
        double r2125322 = 1.0;
        double r2125323 = fma(r2125321, r2125304, r2125322);
        double r2125324 = fma(r2125313, r2125320, r2125323);
        double r2125325 = fma(r2125319, r2125313, r2125324);
        double r2125326 = fma(r2125317, r2125314, r2125325);
        double r2125327 = fma(r2125314, r2125316, r2125326);
        double r2125328 = r2125327 * r2125296;
        double r2125329 = 2.0;
        double r2125330 = r2125315 * r2125329;
        double r2125331 = r2125304 * r2125313;
        double r2125332 = r2125331 * r2125331;
        double r2125333 = 0.0140005442;
        double r2125334 = 0.0008327945;
        double r2125335 = r2125304 * r2125334;
        double r2125336 = r2125333 + r2125335;
        double r2125337 = r2125336 * r2125331;
        double r2125338 = 0.0694555761;
        double r2125339 = 0.2909738639;
        double r2125340 = 0.7715471019;
        double r2125341 = fma(r2125304, r2125340, r2125322);
        double r2125342 = fma(r2125339, r2125313, r2125341);
        double r2125343 = fma(r2125331, r2125338, r2125342);
        double r2125344 = fma(r2125304, r2125337, r2125343);
        double r2125345 = fma(r2125330, r2125332, r2125344);
        double r2125346 = r2125328 / r2125345;
        double r2125347 = r2125312 ? r2125346 : r2125310;
        double r2125348 = r2125298 ? r2125310 : r2125347;
        return r2125348;
}

Error

Bits error versus x

Derivation

  1. Split input into 2 regimes

  2. if x < -108576937514.12856 or 672.3709112650113 < x

    1. Initial program 59.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

    2. Simplified59.0

      \[\leadsto \color{blue}{\frac{x \cdot \mathsf{fma}\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\left(x \cdot x\right) \cdot 0.0001789971\right), \left(\mathsf{fma}\left(0.0005064034, \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\mathsf{fma}\left(\left(0.0072644182 \cdot \left(x \cdot x\right)\right), \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), 0.0424060604, \left(\mathsf{fma}\left(0.1049934947, \left(x \cdot x\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right)}{\mathsf{fma}\left(\left(2 \cdot 0.0001789971\right), \left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), \left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.0140005442 + 0.0008327945 \cdot \left(x \cdot x\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), 0.0694555761, \left(\mathsf{fma}\left(0.2909738639, \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), 0.7715471019, 1\right)\right)\right)\right)\right)\right)\right)\right)\right)}}\]

    3. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{0.15298196345929327 \cdot \frac{1}{{x}^{5}} + \left(0.2514179000665375 \cdot \frac{1}{{x}^{3}} + 0.5 \cdot \frac{1}{x}\right)}\]

    4. Simplified0.0

      \[\leadsto \color{blue}{\frac{0.15298196345929327}{{x}^{5}} + \left(\frac{0.5}{x} + \frac{0.2514179000665375}{x \cdot \left(x \cdot x\right)}\right)}\]

    if -108576937514.12856 < x < 672.3709112650113

    1. Initial program 0.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]

    2. Simplified0.0

      \[\leadsto \color{blue}{\frac{x \cdot \mathsf{fma}\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\left(x \cdot x\right) \cdot 0.0001789971\right), \left(\mathsf{fma}\left(0.0005064034, \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\mathsf{fma}\left(\left(0.0072644182 \cdot \left(x \cdot x\right)\right), \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), 0.0424060604, \left(\mathsf{fma}\left(0.1049934947, \left(x \cdot x\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right)}{\mathsf{fma}\left(\left(2 \cdot 0.0001789971\right), \left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), \left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(0.0140005442 + 0.0008327945 \cdot \left(x \cdot x\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), 0.0694555761, \left(\mathsf{fma}\left(0.2909738639, \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), 0.7715471019, 1\right)\right)\right)\right)\right)\right)\right)\right)\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -108576937514.12856:\\ \;\;\;\;\frac{0.15298196345929327}{{x}^{5}} + \left(\frac{0.2514179000665375}{x \cdot \left(x \cdot x\right)} + \frac{0.5}{x}\right)\\ \mathbf{elif}\;x \le 672.3709112650113:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\left(x \cdot x\right) \cdot 0.0001789971\right), \left(\mathsf{fma}\left(0.0005064034, \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot 0.0072644182\right), \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), 0.0424060604, \left(\mathsf{fma}\left(0.1049934947, \left(x \cdot x\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(\left(0.0001789971 \cdot 2\right), \left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), \left(\left(0.0140005442 + \left(x \cdot x\right) \cdot 0.0008327945\right) \cdot \left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right), \left(\mathsf{fma}\left(\left(\left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right), 0.0694555761, \left(\mathsf{fma}\left(0.2909738639, \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right), \left(\mathsf{fma}\left(\left(x \cdot x\right), 0.7715471019, 1\right)\right)\right)\right)\right)\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.15298196345929327}{{x}^{5}} + \left(\frac{0.2514179000665375}{x \cdot \left(x \cdot x\right)} + \frac{0.5}{x}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.dawson"
  (* (/ (+ (+ (+ (+ (+ 1 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))