Average Error: 13.9 → 13.9
Time: 15.8s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}} \cdot \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]
1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}} \cdot \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)
double f(double x) {
        double r173212 = 1.0;
        double r173213 = 0.3275911;
        double r173214 = x;
        double r173215 = fabs(r173214);
        double r173216 = r173213 * r173215;
        double r173217 = r173212 + r173216;
        double r173218 = r173212 / r173217;
        double r173219 = 0.254829592;
        double r173220 = -0.284496736;
        double r173221 = 1.421413741;
        double r173222 = -1.453152027;
        double r173223 = 1.061405429;
        double r173224 = r173218 * r173223;
        double r173225 = r173222 + r173224;
        double r173226 = r173218 * r173225;
        double r173227 = r173221 + r173226;
        double r173228 = r173218 * r173227;
        double r173229 = r173220 + r173228;
        double r173230 = r173218 * r173229;
        double r173231 = r173219 + r173230;
        double r173232 = r173218 * r173231;
        double r173233 = r173215 * r173215;
        double r173234 = -r173233;
        double r173235 = exp(r173234);
        double r173236 = r173232 * r173235;
        double r173237 = r173212 - r173236;
        return r173237;
}
↓
double f(double x) {
        double r173238 = x;
        double r173239 = fabs(r173238);
        double r173240 = 2.0;
        double r173241 = pow(r173239, r173240);
        double r173242 = -r173241;
        double r173243 = exp(r173242);
        double r173244 = 1.453152027;
        double r173245 = sqrt(r173244);
        double r173246 = 0.3275911;
        double r173247 = 1.0;
        double r173248 = fma(r173246, r173239, r173247);
        double r173249 = pow(r173248, r173240);
        double r173250 = r173245 / r173249;
        double r173251 = r173250 * r173250;
        double r173252 = 0.284496736;
        double r173253 = fma(r173239, r173246, r173247);
        double r173254 = pow(r173253, r173240);
        double r173255 = r173252 / r173254;
        double r173256 = r173251 + r173255;
        double r173257 = fma(r173243, r173256, r173247);
        double r173258 = 1.061405429;
        double r173259 = 5.0;
        double r173260 = pow(r173248, r173259);
        double r173261 = r173258 / r173260;
        double r173262 = 0.254829592;
        double r173263 = r173262 / r173253;
        double r173264 = r173261 + r173263;
        double r173265 = 1.421413741;
        double r173266 = 3.0;
        double r173267 = pow(r173253, r173266);
        double r173268 = exp(r173241);
        double r173269 = r173267 * r173268;
        double r173270 = r173265 / r173269;
        double r173271 = fma(r173243, r173264, r173270);
        double r173272 = r173257 - r173271;
        double r173273 = exp(r173272);
        double r173274 = log(r173273);
        return r173274;
}

Error

Bits error versus x

Derivation

  1. Initial program 13.9

    \[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  2. Simplified13.9

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, -\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, 1.061405428999999900341322245367337018251, -1.453152027000000012790792425221297889948\right), 1.421413741000000063863240029604639858007\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, -0.2844967359999999723108032867457950487733\right), 0.2548295919999999936678136691625695675611\right)}{e^{\left|x\right| \cdot \left|x\right|}}, 1\right)}\]
  3. Using strategy rm

  4. Applied add-log-exp13.9

    \[\leadsto \color{blue}{\log \left(e^{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, -\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, 1.061405428999999900341322245367337018251, -1.453152027000000012790792425221297889948\right), 1.421413741000000063863240029604639858007\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, -0.2844967359999999723108032867457950487733\right), 0.2548295919999999936678136691625695675611\right)}{e^{\left|x\right| \cdot \left|x\right|}}, 1\right)}\right)}\]

  5. Simplified13.9

    \[\leadsto \log \color{blue}{\left(e^{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, -\frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, 1.061405428999999900341322245367337018251, -1.453152027000000012790792425221297889948\right), 1.421413741000000063863240029604639858007\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, -0.2844967359999999723108032867457950487733\right), 0.2548295919999999936678136691625695675611\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right)}\right)}\]

  6. Taylor expanded around 0 13.9

    \[\leadsto \log \left(e^{\color{blue}{\left(1 + \left(1.453152027000000012790792425221297889948 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{4}} + 0.2844967359999999723108032867457950487733 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(1.421413741000000063863240029604639858007 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \left(1.061405428999999900341322245367337018251 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{5}} + 0.2548295919999999936678136691625695675611 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}\right)\right)}}\right)\]

  7. Simplified13.9

    \[\leadsto \log \left(e^{\color{blue}{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}}\right)\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt13.9

    \[\leadsto \log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.453152027000000012790792425221297889948}{{\color{blue}{\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} \cdot \sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}}^{4}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]

  10. Applied unpow-prod-down13.9

    \[\leadsto \log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.453152027000000012790792425221297889948}{\color{blue}{{\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{4} \cdot {\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{4}}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]

  11. Applied add-sqr-sqrt13.9

    \[\leadsto \log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{\color{blue}{\sqrt{1.453152027000000012790792425221297889948} \cdot \sqrt{1.453152027000000012790792425221297889948}}}{{\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{4} \cdot {\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{4}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]

  12. Applied times-frac13.9

    \[\leadsto \log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \color{blue}{\frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{4}} \cdot \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{4}}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]

  13. Simplified13.9

    \[\leadsto \log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \color{blue}{\frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}}} \cdot \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\sqrt{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}^{4}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]

  14. Simplified13.9

    \[\leadsto \log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}} \cdot \color{blue}{\frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]

  15. Final simplification13.9

    \[\leadsto \log \left(e^{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}} \cdot \frac{\sqrt{1.453152027000000012790792425221297889948}}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{2}} + \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\right)\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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)))))))