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\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
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|}
double f(double x) {
        double r38477557 = 1.0;
        double r38477558 = 0.3275911;
        double r38477559 = x;
        double r38477560 = fabs(r38477559);
        double r38477561 = r38477558 * r38477560;
        double r38477562 = r38477557 + r38477561;
        double r38477563 = r38477557 / r38477562;
        double r38477564 = 0.254829592;
        double r38477565 = -0.284496736;
        double r38477566 = 1.421413741;
        double r38477567 = -1.453152027;
        double r38477568 = 1.061405429;
        double r38477569 = r38477563 * r38477568;
        double r38477570 = r38477567 + r38477569;
        double r38477571 = r38477563 * r38477570;
        double r38477572 = r38477566 + r38477571;
        double r38477573 = r38477563 * r38477572;
        double r38477574 = r38477565 + r38477573;
        double r38477575 = r38477563 * r38477574;
        double r38477576 = r38477564 + r38477575;
        double r38477577 = r38477563 * r38477576;
        double r38477578 = r38477560 * r38477560;
        double r38477579 = -r38477578;
        double r38477580 = exp(r38477579);
        double r38477581 = r38477577 * r38477580;
        double r38477582 = r38477557 - r38477581;
        return r38477582;
}

Reproduce

herbie shell --seed 2019138 +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)))))))