Average Error: 29.1 → 0.0
Time: 26.5s
Precision: 64
\[\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \cdot 10^{-4} \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) + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \cdot 10^{-4} \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 1.789971000000000009994005623070734145585 \cdot 10^{-4}\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\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4377789621347.087890625 \lor \neg \left(x \le 3959.752675162330433522583916783332824707\right):\\ \;\;\;\;\frac{0.5}{x} + \left(\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{{x}^{4} \cdot \left(\left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6} + {x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right) + \left(0.007264418199999999985194687468492702464573 \cdot \left(x \cdot x\right) + 0.04240606040000000076517494562722276896238\right)\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)}{\left(1 + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right) + \left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + {x}^{4} \cdot \left(\left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right) + \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot {x}^{4} + {x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)\right)} \cdot x\\ \end{array}\]
\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \cdot 10^{-4} \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) + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \cdot 10^{-4} \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 1.789971000000000009994005623070734145585 \cdot 10^{-4}\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 -4377789621347.087890625 \lor \neg \left(x \le 3959.752675162330433522583916783332824707\right):\\
\;\;\;\;\frac{0.5}{x} + \left(\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{{x}^{4} \cdot \left(\left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6} + {x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right) + \left(0.007264418199999999985194687468492702464573 \cdot \left(x \cdot x\right) + 0.04240606040000000076517494562722276896238\right)\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)}{\left(1 + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right) + \left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + {x}^{4} \cdot \left(\left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right) + \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot {x}^{4} + {x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)\right)} \cdot x\\

\end{array}
double f(double x) {
        double r210242 = 1.0;
        double r210243 = 0.1049934947;
        double r210244 = x;
        double r210245 = r210244 * r210244;
        double r210246 = r210243 * r210245;
        double r210247 = r210242 + r210246;
        double r210248 = 0.0424060604;
        double r210249 = r210245 * r210245;
        double r210250 = r210248 * r210249;
        double r210251 = r210247 + r210250;
        double r210252 = 0.0072644182;
        double r210253 = r210249 * r210245;
        double r210254 = r210252 * r210253;
        double r210255 = r210251 + r210254;
        double r210256 = 0.0005064034;
        double r210257 = r210253 * r210245;
        double r210258 = r210256 * r210257;
        double r210259 = r210255 + r210258;
        double r210260 = 0.0001789971;
        double r210261 = r210257 * r210245;
        double r210262 = r210260 * r210261;
        double r210263 = r210259 + r210262;
        double r210264 = 0.7715471019;
        double r210265 = r210264 * r210245;
        double r210266 = r210242 + r210265;
        double r210267 = 0.2909738639;
        double r210268 = r210267 * r210249;
        double r210269 = r210266 + r210268;
        double r210270 = 0.0694555761;
        double r210271 = r210270 * r210253;
        double r210272 = r210269 + r210271;
        double r210273 = 0.0140005442;
        double r210274 = r210273 * r210257;
        double r210275 = r210272 + r210274;
        double r210276 = 0.0008327945;
        double r210277 = r210276 * r210261;
        double r210278 = r210275 + r210277;
        double r210279 = 2.0;
        double r210280 = r210279 * r210260;
        double r210281 = r210261 * r210245;
        double r210282 = r210280 * r210281;
        double r210283 = r210278 + r210282;
        double r210284 = r210263 / r210283;
        double r210285 = r210284 * r210244;
        return r210285;
}
↓
double f(double x) {
        double r210286 = x;
        double r210287 = -4377789621347.088;
        bool r210288 = r210286 <= r210287;
        double r210289 = 3959.7526751623304;
        bool r210290 = r210286 <= r210289;
        double r210291 = !r210290;
        bool r210292 = r210288 || r210291;
        double r210293 = 0.5;
        double r210294 = r210293 / r210286;
        double r210295 = 0.15298196345929327;
        double r210296 = 5.0;
        double r210297 = pow(r210286, r210296);
        double r210298 = r210295 / r210297;
        double r210299 = 0.2514179000665375;
        double r210300 = 3.0;
        double r210301 = pow(r210286, r210300);
        double r210302 = r210299 / r210301;
        double r210303 = r210298 + r210302;
        double r210304 = r210294 + r210303;
        double r210305 = 4.0;
        double r210306 = pow(r210286, r210305);
        double r210307 = 0.0001789971;
        double r210308 = 6.0;
        double r210309 = pow(r210286, r210308);
        double r210310 = r210307 * r210309;
        double r210311 = 0.0005064034;
        double r210312 = r210306 * r210311;
        double r210313 = r210310 + r210312;
        double r210314 = 0.0072644182;
        double r210315 = r210286 * r210286;
        double r210316 = r210314 * r210315;
        double r210317 = 0.0424060604;
        double r210318 = r210316 + r210317;
        double r210319 = r210313 + r210318;
        double r210320 = r210306 * r210319;
        double r210321 = 1.0;
        double r210322 = 0.1049934947;
        double r210323 = r210322 * r210315;
        double r210324 = r210321 + r210323;
        double r210325 = r210320 + r210324;
        double r210326 = 0.2909738639;
        double r210327 = r210306 * r210326;
        double r210328 = r210321 + r210327;
        double r210329 = 0.7715471019;
        double r210330 = 0.0694555761;
        double r210331 = 0.0140005442;
        double r210332 = r210315 * r210331;
        double r210333 = r210330 + r210332;
        double r210334 = 0.0008327945;
        double r210335 = r210334 * r210306;
        double r210336 = 2.0;
        double r210337 = r210336 * r210307;
        double r210338 = r210309 * r210337;
        double r210339 = r210335 + r210338;
        double r210340 = r210333 + r210339;
        double r210341 = r210306 * r210340;
        double r210342 = r210329 + r210341;
        double r210343 = r210315 * r210342;
        double r210344 = r210328 + r210343;
        double r210345 = r210325 / r210344;
        double r210346 = r210345 * r210286;
        double r210347 = r210292 ? r210304 : r210346;
        return r210347;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -4377789621347.088 or 3959.7526751623304 < x

    1. Initial program 60.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \cdot 10^{-4} \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) + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \cdot 10^{-4} \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 1.789971000000000009994005623070734145585 \cdot 10^{-4}\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. Simplified59.9

      \[\leadsto \color{blue}{\frac{{x}^{4} \cdot \left(\left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6} + {x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right) + \left(0.007264418199999999985194687468492702464573 \cdot \left(x \cdot x\right) + 0.04240606040000000076517494562722276896238\right)\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)}{\left(1 + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right) + \left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + {x}^{4} \cdot \left(\left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right) + \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot {x}^{4} + {x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)\right)} \cdot x}\]

    3. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{0.2514179000665375252054900556686334311962 \cdot \frac{1}{{x}^{3}} + \left(0.1529819634592932686700805788859724998474 \cdot \frac{1}{{x}^{5}} + 0.5 \cdot \frac{1}{x}\right)}\]

    4. Simplified0.0

      \[\leadsto \color{blue}{\frac{0.5}{x} + \left(\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)}\]

    if -4377789621347.088 < x < 3959.7526751623304

    1. Initial program 0.0

      \[\frac{\left(\left(\left(\left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right) + 0.04240606040000000076517494562722276896238 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.007264418199999999985194687468492702464573 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 5.064034000000000243502107366566633572802 \cdot 10^{-4} \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) + 1.789971000000000009994005623070734145585 \cdot 10^{-4} \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 + 0.7715471018999999763821051601553335785866 \cdot \left(x \cdot x\right)\right) + 0.2909738639000000182122107617033179849386 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.06945557609999999937322456844412954524159 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.01400054419999999938406531896362139377743 \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) + 8.327945000000000442749725770852364803432 \cdot 10^{-4} \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 1.789971000000000009994005623070734145585 \cdot 10^{-4}\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

      \[\leadsto \color{blue}{\frac{{x}^{4} \cdot \left(\left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6} + {x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right) + \left(0.007264418199999999985194687468492702464573 \cdot \left(x \cdot x\right) + 0.04240606040000000076517494562722276896238\right)\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)}{\left(1 + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right) + \left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + {x}^{4} \cdot \left(\left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right) + \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot {x}^{4} + {x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)\right)} \cdot x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4377789621347.087890625 \lor \neg \left(x \le 3959.752675162330433522583916783332824707\right):\\ \;\;\;\;\frac{0.5}{x} + \left(\frac{0.1529819634592932686700805788859724998474}{{x}^{5}} + \frac{0.2514179000665375252054900556686334311962}{{x}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{{x}^{4} \cdot \left(\left(1.789971000000000009994005623070734145585 \cdot 10^{-4} \cdot {x}^{6} + {x}^{4} \cdot 5.064034000000000243502107366566633572802 \cdot 10^{-4}\right) + \left(0.007264418199999999985194687468492702464573 \cdot \left(x \cdot x\right) + 0.04240606040000000076517494562722276896238\right)\right) + \left(1 + 0.1049934946999999951788851149103720672429 \cdot \left(x \cdot x\right)\right)}{\left(1 + {x}^{4} \cdot 0.2909738639000000182122107617033179849386\right) + \left(x \cdot x\right) \cdot \left(0.7715471018999999763821051601553335785866 + {x}^{4} \cdot \left(\left(0.06945557609999999937322456844412954524159 + \left(x \cdot x\right) \cdot 0.01400054419999999938406531896362139377743\right) + \left(8.327945000000000442749725770852364803432 \cdot 10^{-4} \cdot {x}^{4} + {x}^{6} \cdot \left(2 \cdot 1.789971000000000009994005623070734145585 \cdot 10^{-4}\right)\right)\right)\right)} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
  (* (/ (+ (+ (+ (+ (+ 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))