Jmat.Real.dawson

Average Error: 4.3 → 3.4

Time: 1.7m

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r5838190 = 1.0;
        double r5838191 = /* ERROR: no posit support in C */;
        double r5838192 = 0.1049934947;
        double r5838193 = /* ERROR: no posit support in C */;
        double r5838194 = x;
        double r5838195 = r5838194 * r5838194;
        double r5838196 = r5838193 * r5838195;
        double r5838197 = r5838191 + r5838196;
        double r5838198 = 0.0424060604;
        double r5838199 = /* ERROR: no posit support in C */;
        double r5838200 = r5838195 * r5838195;
        double r5838201 = r5838199 * r5838200;
        double r5838202 = r5838197 + r5838201;
        double r5838203 = 0.0072644182;
        double r5838204 = /* ERROR: no posit support in C */;
        double r5838205 = r5838200 * r5838195;
        double r5838206 = r5838204 * r5838205;
        double r5838207 = r5838202 + r5838206;
        double r5838208 = 0.0005064034;
        double r5838209 = /* ERROR: no posit support in C */;
        double r5838210 = r5838205 * r5838195;
        double r5838211 = r5838209 * r5838210;
        double r5838212 = r5838207 + r5838211;
        double r5838213 = 0.0001789971;
        double r5838214 = /* ERROR: no posit support in C */;
        double r5838215 = r5838210 * r5838195;
        double r5838216 = r5838214 * r5838215;
        double r5838217 = r5838212 + r5838216;
        double r5838218 = 0.7715471019;
        double r5838219 = /* ERROR: no posit support in C */;
        double r5838220 = r5838219 * r5838195;
        double r5838221 = r5838191 + r5838220;
        double r5838222 = 0.2909738639;
        double r5838223 = /* ERROR: no posit support in C */;
        double r5838224 = r5838223 * r5838200;
        double r5838225 = r5838221 + r5838224;
        double r5838226 = 0.0694555761;
        double r5838227 = /* ERROR: no posit support in C */;
        double r5838228 = r5838227 * r5838205;
        double r5838229 = r5838225 + r5838228;
        double r5838230 = 0.0140005442;
        double r5838231 = /* ERROR: no posit support in C */;
        double r5838232 = r5838231 * r5838210;
        double r5838233 = r5838229 + r5838232;
        double r5838234 = 0.0008327945;
        double r5838235 = /* ERROR: no posit support in C */;
        double r5838236 = r5838235 * r5838215;
        double r5838237 = r5838233 + r5838236;
        double r5838238 = 2.0;
        double r5838239 = /* ERROR: no posit support in C */;
        double r5838240 = r5838239 * r5838214;
        double r5838241 = r5838215 * r5838195;
        double r5838242 = r5838240 * r5838241;
        double r5838243 = r5838237 + r5838242;
        double r5838244 = r5838217 / r5838243;
        double r5838245 = r5838244 * r5838194;
        return r5838245;
}

↓

double f(double x) {
        double r5838246 = x;
        double r5838247 = r5838246 * r5838246;
        double r5838248 = 0.0424060604;
        double r5838249 = 0.0072644182;
        double r5838250 = 0.0001789971;
        double r5838251 = r5838247 * r5838250;
        double r5838252 = 0.0005064034;
        double r5838253 = r5838251 + r5838252;
        double r5838254 = r5838253 * r5838247;
        double r5838255 = r5838249 + r5838254;
        double r5838256 = r5838255 * r5838247;
        double r5838257 = r5838248 + r5838256;
        double r5838258 = r5838257 * r5838247;
        double r5838259 = 0.1049934947;
        double r5838260 = r5838258 + r5838259;
        double r5838261 = r5838247 * r5838260;
        double r5838262 = 1.0;
        double r5838263 = r5838261 + r5838262;
        double r5838264 = r5838263 * r5838246;
        double r5838265 = r5838247 * r5838247;
        double r5838266 = 0.0140005442;
        double r5838267 = r5838265 * r5838266;
        double r5838268 = r5838267 * r5838265;
        double r5838269 = r5838268 + r5838262;
        double r5838270 = 0.0008327945;
        double r5838271 = 2.0;
        double r5838272 = r5838250 * r5838271;
        double r5838273 = r5838272 * r5838247;
        double r5838274 = r5838270 + r5838273;
        double r5838275 = r5838265 * r5838274;
        double r5838276 = 0.0694555761;
        double r5838277 = r5838275 + r5838276;
        double r5838278 = r5838265 * r5838277;
        double r5838279 = 0.7715471019;
        double r5838280 = 0.2909738639;
        double r5838281 = r5838280 * r5838247;
        double r5838282 = r5838279 + r5838281;
        double r5838283 = r5838278 + r5838282;
        double r5838284 = r5838247 * r5838283;
        double r5838285 = r5838269 + r5838284;
        double r5838286 = r5838264 / r5838285;
        return r5838286;
}

Error

Bits error versus x

Derivation

1. Initial program 4.3

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

2. Simplified 3.6

   \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(0.2909738639\right)\right)}{\left(0.7715471019\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761\right)\right)}\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(2\right)\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}\right)}\right) \cdot x}\]
3. Using strategy rm

4. Applied associate-*l* 3.5

   \[\leadsto \left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(0.2909738639\right)\right)}{\left(0.7715471019\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761\right)\right)}\right)}{\color{blue}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(2\right)\right) \cdot \left(0.0001789971\right)\right)}\right)\right)\right)}}\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}\right)}\right) \cdot x\]
5. Using strategy rm

6. Applied p16-*-un-lft-identity 3.5

   \[\leadsto \left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\color{blue}{\left(\left(1.0\right) \cdot \left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(0.2909738639\right)\right)}{\left(0.7715471019\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(2\right)\right) \cdot \left(0.0001789971\right)\right)}\right)\right)\right)}\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}\right)\right)}}\right) \cdot x\]

7. Applied associate-/r* 3.5

   \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right)\right)}{\left(\frac{\left(0.0424060604\right)}{\left(\left(0.0072644182\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(0.1049934947\right)\right)}\right)}\right)}{\left(1.0\right)}\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\frac{\left(\frac{\left(\left(x \cdot x\right) \cdot \left(0.2909738639\right)\right)}{\left(0.7715471019\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761\right)\right)}\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(x \cdot x\right) \cdot \left(2\right)\right) \cdot \left(0.0001789971\right)\right)}\right)\right)\right)}\right)\right)}\right)}{\left(\left(0.0140005442\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right)}\right)}\right)} \cdot x\]

8. Simplified 3.5

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

9. Simplified 3.3

   \[\leadsto \color{blue}{\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\frac{\left(\left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right) \cdot \left(x \cdot x\right)\right)}{\left(0.0072644182\right)}\right) \cdot \left(x \cdot x\right)\right)}{\left(0.0424060604\right)}\right)\right)}{\left(\left(0.1049934947\right) \cdot \left(x \cdot x\right)\right)}\right)}\right) \cdot x\right)}{\left(\frac{\left(\frac{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0140005442\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}{\left(1\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(0.0001789971\right) \cdot \left(2\right)\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(0.0694555761\right)}\right)\right)}{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}\right)}}\]
10. Using strategy rm

11. Applied p16-*-un-lft-identity 3.3

    \[\leadsto \frac{\left(\left(\frac{\left(1\right)}{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\frac{\left(\left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right) \cdot \left(x \cdot x\right)\right)}{\left(0.0072644182\right)}\right) \cdot \left(x \cdot x\right)\right)}{\left(0.0424060604\right)}\right)\right)}{\left(\left(0.1049934947\right) \cdot \left(x \cdot x\right)\right)}\right)}\right) \cdot x\right)}{\color{blue}{\left(\left(1.0\right) \cdot \left(\frac{\left(\frac{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0140005442\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}{\left(1\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(0.0001789971\right) \cdot \left(2\right)\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(0.0694555761\right)}\right)\right)}{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}\right)\right)}}\]

12. Applied associate-/r* 3.3

    \[\leadsto \color{blue}{\frac{\left(\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\frac{\left(\left(\frac{\left(0.0005064034\right)}{\left(\left(x \cdot x\right) \cdot \left(0.0001789971\right)\right)}\right) \cdot \left(x \cdot x\right)\right)}{\left(0.0072644182\right)}\right) \cdot \left(x \cdot x\right)\right)}{\left(0.0424060604\right)}\right)\right)}{\left(\left(0.1049934947\right) \cdot \left(x \cdot x\right)\right)}\right)}\right) \cdot x\right)}{\left(1.0\right)}\right)}{\left(\frac{\left(\frac{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0140005442\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)}{\left(1\right)}\right)}{\left(\left(x \cdot x\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\frac{\left(0.0008327945\right)}{\left(\left(\left(0.0001789971\right) \cdot \left(2\right)\right) \cdot \left(x \cdot x\right)\right)}\right)\right)}{\left(0.0694555761\right)}\right)\right)}{\left(\frac{\left(0.7715471019\right)}{\left(\left(0.2909738639\right) \cdot \left(x \cdot x\right)\right)}\right)}\right)\right)}\right)}}\]

13. Simplified 3.4

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

14. Final simplification 3.4

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Jmat.Real.dawson"
  (*.p16 (/.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.1049934947) (*.p16 x x))) (*.p16 (real->posit16 0.0424060604) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0072644182) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0005064034) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0001789971) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (+.p16 (real->posit16 1) (*.p16 (real->posit16 0.7715471019) (*.p16 x x))) (*.p16 (real->posit16 0.2909738639) (*.p16 (*.p16 x x) (*.p16 x x)))) (*.p16 (real->posit16 0.0694555761) (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0140005442) (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (real->posit16 0.0008327945) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)))) (*.p16 (*.p16 (real->posit16 2) (real->posit16 0.0001789971)) (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x)) (*.p16 x x))))) x))