Jmat.Real.erf

Average Error: 13.8 → 13.1

Time: 39.4s

Precision: 64

Math

\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

↓

\[e^{\log \left(\frac{{1}^{3} - \sqrt{{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} + 1\right) + 1 \cdot 1}\right)}\]

C

double f(double x) {
        double r374209 = 1.0;
        double r374210 = 0.3275911;
        double r374211 = x;
        double r374212 = fabs(r374211);
        double r374213 = r374210 * r374212;
        double r374214 = r374209 + r374213;
        double r374215 = r374209 / r374214;
        double r374216 = 0.254829592;
        double r374217 = -0.284496736;
        double r374218 = 1.421413741;
        double r374219 = -1.453152027;
        double r374220 = 1.061405429;
        double r374221 = r374215 * r374220;
        double r374222 = r374219 + r374221;
        double r374223 = r374215 * r374222;
        double r374224 = r374218 + r374223;
        double r374225 = r374215 * r374224;
        double r374226 = r374217 + r374225;
        double r374227 = r374215 * r374226;
        double r374228 = r374216 + r374227;
        double r374229 = r374215 * r374228;
        double r374230 = r374212 * r374212;
        double r374231 = -r374230;
        double r374232 = exp(r374231);
        double r374233 = r374229 * r374232;
        double r374234 = r374209 - r374233;
        return r374234;
}

↓

double f(double x) {
        double r374235 = 1.0;
        double r374236 = 3.0;
        double r374237 = pow(r374235, r374236);
        double r374238 = 0.3275911;
        double r374239 = x;
        double r374240 = fabs(r374239);
        double r374241 = r374238 * r374240;
        double r374242 = r374235 + r374241;
        double r374243 = r374235 / r374242;
        double r374244 = 0.254829592;
        double r374245 = -0.284496736;
        double r374246 = sqrt(r374243);
        double r374247 = 1.421413741;
        double r374248 = -1.453152027;
        double r374249 = 1.061405429;
        double r374250 = r374243 * r374249;
        double r374251 = r374248 + r374250;
        double r374252 = r374243 * r374251;
        double r374253 = r374247 + r374252;
        double r374254 = r374246 * r374253;
        double r374255 = r374246 * r374254;
        double r374256 = r374245 + r374255;
        double r374257 = r374243 * r374256;
        double r374258 = r374244 + r374257;
        double r374259 = r374243 * r374258;
        double r374260 = r374240 * r374240;
        double r374261 = -r374260;
        double r374262 = exp(r374261);
        double r374263 = r374259 * r374262;
        double r374264 = pow(r374263, r374236);
        double r374265 = sqrt(r374264);
        double r374266 = r374265 * r374265;
        double r374267 = r374237 - r374266;
        double r374268 = r374263 + r374235;
        double r374269 = r374263 * r374268;
        double r374270 = r374235 * r374235;
        double r374271 = r374269 + r374270;
        double r374272 = r374267 / r374271;
        double r374273 = log(r374272);
        double r374274 = exp(r374273);
        return r374274;
}

Error

Bits error versus x

Derivation

1. Initial program 13.8

   \[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
2. Using strategy rm

3. Applied add-sqr-sqrt 13.8

   \[\leadsto 1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \color{blue}{\left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}}\right)} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

4. Applied associate-*l* 13.8

   \[\leadsto 1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \color{blue}{\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
5. Using strategy rm

6. Applied add-exp-log 13.8

   \[\leadsto \color{blue}{e^{\log \left(1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}}\]
7. Using strategy rm

8. Applied flip3-- 13.8

   \[\leadsto e^{\log \color{blue}{\left(\frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{1 \cdot 1 + \left(\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1 \cdot \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}\right)}}\]

9. Simplified 13.8

   \[\leadsto e^{\log \left(\frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{\color{blue}{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} + 1\right) + 1 \cdot 1}}\right)}\]
10. Using strategy rm

11. Applied add-sqr-sqrt 13.1

    \[\leadsto e^{\log \left(\frac{{1}^{3} - \color{blue}{\sqrt{{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}}{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} + 1\right) + 1 \cdot 1}\right)}\]

12. Final simplification 13.1

    \[\leadsto e^{\log \left(\frac{{1}^{3} - \sqrt{{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}{\left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(\sqrt{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|}} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} + 1\right) + 1 \cdot 1}\right)}\]

Reproduce

herbie shell --seed 2020021 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))