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\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
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|}
double f(double x) {
        double r380570 = 1.0;
        double r380571 = 0.3275911;
        double r380572 = x;
        double r380573 = fabs(r380572);
        double r380574 = r380571 * r380573;
        double r380575 = r380570 + r380574;
        double r380576 = r380570 / r380575;
        double r380577 = 0.254829592;
        double r380578 = -0.284496736;
        double r380579 = 1.421413741;
        double r380580 = -1.453152027;
        double r380581 = 1.061405429;
        double r380582 = r380576 * r380581;
        double r380583 = r380580 + r380582;
        double r380584 = r380576 * r380583;
        double r380585 = r380579 + r380584;
        double r380586 = r380576 * r380585;
        double r380587 = r380578 + r380586;
        double r380588 = r380576 * r380587;
        double r380589 = r380577 + r380588;
        double r380590 = r380576 * r380589;
        double r380591 = r380573 * r380573;
        double r380592 = -r380591;
        double r380593 = exp(r380592);
        double r380594 = r380590 * r380593;
        double r380595 = r380570 - r380594;
        return r380595;
}

Reproduce

herbie shell --seed 2020060 +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)))))))