Jmat.Real.erf

Average Error: 13.9 → 13.9

Time: 2.6m

Precision: 64

Math

\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

↓

\[\frac{\frac{1 - {\left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{\left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} + \left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)\right) + 1}}{1 - \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}\]

C

double f(double x) {
        double r41183187 = 1.0;
        double r41183188 = 0.3275911;
        double r41183189 = x;
        double r41183190 = fabs(r41183189);
        double r41183191 = r41183188 * r41183190;
        double r41183192 = r41183187 + r41183191;
        double r41183193 = r41183187 / r41183192;
        double r41183194 = 0.254829592;
        double r41183195 = -0.284496736;
        double r41183196 = 1.421413741;
        double r41183197 = -1.453152027;
        double r41183198 = 1.061405429;
        double r41183199 = r41183193 * r41183198;
        double r41183200 = r41183197 + r41183199;
        double r41183201 = r41183193 * r41183200;
        double r41183202 = r41183196 + r41183201;
        double r41183203 = r41183193 * r41183202;
        double r41183204 = r41183195 + r41183203;
        double r41183205 = r41183193 * r41183204;
        double r41183206 = r41183194 + r41183205;
        double r41183207 = r41183193 * r41183206;
        double r41183208 = r41183190 * r41183190;
        double r41183209 = -r41183208;
        double r41183210 = exp(r41183209);
        double r41183211 = r41183207 * r41183210;
        double r41183212 = r41183187 - r41183211;
        return r41183212;
}

↓

double f(double x) {
        double r41183213 = 1.0;
        double r41183214 = -1.0;
        double r41183215 = 0.3275911;
        double r41183216 = x;
        double r41183217 = fabs(r41183216);
        double r41183218 = fma(r41183215, r41183217, r41183213);
        double r41183219 = r41183214 / r41183218;
        double r41183220 = 0.254829592;
        double r41183221 = 1.453152027;
        double r41183222 = r41183218 * r41183218;
        double r41183223 = r41183221 / r41183222;
        double r41183224 = 0.284496736;
        double r41183225 = r41183223 + r41183224;
        double r41183226 = 1.421413741;
        double r41183227 = r41183226 / r41183222;
        double r41183228 = fma(r41183225, r41183219, r41183227);
        double r41183229 = 1.061405429;
        double r41183230 = r41183222 * r41183222;
        double r41183231 = r41183229 / r41183230;
        double r41183232 = r41183228 + r41183231;
        double r41183233 = r41183220 + r41183232;
        double r41183234 = r41183219 * r41183233;
        double r41183235 = r41183217 * r41183217;
        double r41183236 = exp(r41183235);
        double r41183237 = r41183234 / r41183236;
        double r41183238 = r41183237 * r41183237;
        double r41183239 = 3.0;
        double r41183240 = pow(r41183238, r41183239);
        double r41183241 = r41183213 - r41183240;
        double r41183242 = r41183238 * r41183238;
        double r41183243 = r41183238 + r41183242;
        double r41183244 = r41183243 + r41183213;
        double r41183245 = r41183241 / r41183244;
        double r41183246 = r41183213 - r41183237;
        double r41183247 = r41183245 / r41183246;
        return r41183247;
}

Error

Bits error versus x

Derivation

1. Initial program 13.9

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

2. Taylor expanded around inf 14.7

   \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{blue}{\left(\left(1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 0.254829592\right)\right) - \left(0.284496736 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

3. Simplified 13.9

   \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{blue}{\left(0.254829592 + \left(\left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} - \frac{1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
4. Using strategy rm

5. Applied sub-neg 13.9

   \[\leadsto \color{blue}{1 + \left(-\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \left(\left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} - \frac{1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}\]

6. Simplified 13.9

   \[\leadsto 1 + \color{blue}{\frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}}\]
7. Using strategy rm

8. Applied flip-+ 13.9

   \[\leadsto \color{blue}{\frac{1 \cdot 1 - \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}}{1 - \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}}}\]
9. Using strategy rm

10. Applied flip3-- 13.9

    \[\leadsto \frac{\color{blue}{\frac{{\left(1 \cdot 1\right)}^{3} - {\left(\frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{\left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right) + \left(\left(\frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left(\frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}\right) + \left(1 \cdot 1\right) \cdot \left(\frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}\right)\right)}}}{1 - \frac{\left(\left(\frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)} + \mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right)\right) + 0.254829592\right) \cdot \frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}}{e^{\left|x\right| \cdot \left|x\right|}}}\]

11. Final simplification 13.9

    \[\leadsto \frac{\frac{1 - {\left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{\left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} + \left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left(\frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)\right) + 1}}{1 - \frac{\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} \cdot \left(0.254829592 + \left(\mathsf{fma}\left(\left(\frac{1.453152027}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)} + 0.284496736\right), \left(\frac{-1}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right), \left(\frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)}\right)\right) + \frac{1.061405429}{\left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right) \cdot \mathsf{fma}\left(0.3275911, \left(\left|x\right|\right), 1\right)\right)}\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 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)))))))