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\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
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|}
double f(double x) {
        double r21796619 = 1.0;
        double r21796620 = 0.3275911;
        double r21796621 = x;
        double r21796622 = fabs(r21796621);
        double r21796623 = r21796620 * r21796622;
        double r21796624 = r21796619 + r21796623;
        double r21796625 = r21796619 / r21796624;
        double r21796626 = 0.254829592;
        double r21796627 = -0.284496736;
        double r21796628 = 1.421413741;
        double r21796629 = -1.453152027;
        double r21796630 = 1.061405429;
        double r21796631 = r21796625 * r21796630;
        double r21796632 = r21796629 + r21796631;
        double r21796633 = r21796625 * r21796632;
        double r21796634 = r21796628 + r21796633;
        double r21796635 = r21796625 * r21796634;
        double r21796636 = r21796627 + r21796635;
        double r21796637 = r21796625 * r21796636;
        double r21796638 = r21796626 + r21796637;
        double r21796639 = r21796625 * r21796638;
        double r21796640 = r21796622 * r21796622;
        double r21796641 = -r21796640;
        double r21796642 = exp(r21796641);
        double r21796643 = r21796639 * r21796642;
        double r21796644 = r21796619 - r21796643;
        return r21796644;
}

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))