Average Error: 13.8 → 13.0
Time: 22.2s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\mathsf{fma}\left(\sqrt{{1}^{3}}, \sqrt{{1}^{3}}, -\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right) + \mathsf{fma}\left(-\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}, \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}, \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right)}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\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|}
↓
\frac{\mathsf{fma}\left(\sqrt{{1}^{3}}, \sqrt{{1}^{3}}, -\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right) + \mathsf{fma}\left(-\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}, \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}, \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right)}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}
double f(double x) {
        double r251233 = 1.0;
        double r251234 = 0.3275911;
        double r251235 = x;
        double r251236 = fabs(r251235);
        double r251237 = r251234 * r251236;
        double r251238 = r251233 + r251237;
        double r251239 = r251233 / r251238;
        double r251240 = 0.254829592;
        double r251241 = -0.284496736;
        double r251242 = 1.421413741;
        double r251243 = -1.453152027;
        double r251244 = 1.061405429;
        double r251245 = r251239 * r251244;
        double r251246 = r251243 + r251245;
        double r251247 = r251239 * r251246;
        double r251248 = r251242 + r251247;
        double r251249 = r251239 * r251248;
        double r251250 = r251241 + r251249;
        double r251251 = r251239 * r251250;
        double r251252 = r251240 + r251251;
        double r251253 = r251239 * r251252;
        double r251254 = r251236 * r251236;
        double r251255 = -r251254;
        double r251256 = exp(r251255);
        double r251257 = r251253 * r251256;
        double r251258 = r251233 - r251257;
        return r251258;
}
↓
double f(double x) {
        double r251259 = 1.0;
        double r251260 = 3.0;
        double r251261 = pow(r251259, r251260);
        double r251262 = sqrt(r251261);
        double r251263 = x;
        double r251264 = fabs(r251263);
        double r251265 = 0.3275911;
        double r251266 = fma(r251264, r251265, r251259);
        double r251267 = r251259 / r251266;
        double r251268 = 1.061405429;
        double r251269 = -1.453152027;
        double r251270 = fma(r251267, r251268, r251269);
        double r251271 = 1.421413741;
        double r251272 = fma(r251267, r251270, r251271);
        double r251273 = -0.284496736;
        double r251274 = fma(r251272, r251267, r251273);
        double r251275 = 0.254829592;
        double r251276 = fma(r251267, r251274, r251275);
        double r251277 = 2.0;
        double r251278 = pow(r251264, r251277);
        double r251279 = exp(r251278);
        double r251280 = r251276 / r251279;
        double r251281 = r251267 * r251280;
        double r251282 = pow(r251281, r251260);
        double r251283 = sqrt(r251282);
        double r251284 = r251266 * r251279;
        double r251285 = pow(r251284, r251260);
        double r251286 = 4.0;
        double r251287 = pow(r251266, r251286);
        double r251288 = r251268 / r251287;
        double r251289 = pow(r251266, r251277);
        double r251290 = r251271 / r251289;
        double r251291 = r251290 + r251275;
        double r251292 = 1.453152027;
        double r251293 = pow(r251266, r251260);
        double r251294 = r251292 / r251293;
        double r251295 = r251291 - r251294;
        double r251296 = 0.284496736;
        double r251297 = r251296 / r251266;
        double r251298 = r251295 - r251297;
        double r251299 = r251288 + r251298;
        double r251300 = pow(r251299, r251260);
        double r251301 = r251285 / r251300;
        double r251302 = r251259 / r251301;
        double r251303 = sqrt(r251302);
        double r251304 = r251283 * r251303;
        double r251305 = -r251304;
        double r251306 = fma(r251262, r251262, r251305);
        double r251307 = -r251283;
        double r251308 = fma(r251307, r251303, r251304);
        double r251309 = r251306 + r251308;
        double r251310 = fma(r251267, r251280, r251259);
        double r251311 = r251259 * r251259;
        double r251312 = fma(r251281, r251310, r251311);
        double r251313 = r251309 / r251312;
        return r251313;
}

Error

Bits error versus x

Derivation

  1. Initial program 13.8

    \[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  2. Simplified13.8

    \[\leadsto \color{blue}{1 - \frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}}\]
  3. Using strategy rm

  4. Applied flip3--13.8

    \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{1 \cdot 1 + \left(\frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}} + 1 \cdot \frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}}\]

  5. Simplified13.8

    \[\leadsto \frac{\color{blue}{{1}^{3} - {\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}{1 \cdot 1 + \left(\frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}} + 1 \cdot \frac{\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}\]

  6. Simplified13.8

    \[\leadsto \frac{{1}^{3} - {\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}{\color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt13.0

    \[\leadsto \frac{{1}^{3} - \color{blue}{\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}\]

  9. Taylor expanded around 0 14.1

    \[\leadsto \frac{{1}^{3} - \sqrt{\color{blue}{1 \cdot \frac{{\left(\left(1.0614054289999999 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.42141374100000006 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}} + 0.25482959199999999\right)\right) - \left(1.45315202700000001 \cdot \frac{1}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}} + 0.284496735999999972 \cdot \frac{1}{0.32759110000000002 \cdot \left|x\right| + 1}\right)\right)}^{3}}{{\left(e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3} \cdot {\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}}} \cdot \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}\]

  10. Simplified13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{\color{blue}{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}} \cdot \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}\]
  11. Using strategy rm

  12. Applied add-sqr-sqrt13.1

    \[\leadsto \frac{\color{blue}{\sqrt{{1}^{3}} \cdot \sqrt{{1}^{3}}} - \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}} \cdot \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}\]

  13. Applied prod-diff13.0

    \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt{{1}^{3}}, \sqrt{{1}^{3}}, -\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right) + \mathsf{fma}\left(-\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}, \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}, \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right)}}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}\]

  14. Final simplification13.0

    \[\leadsto \frac{\mathsf{fma}\left(\sqrt{{1}^{3}}, \sqrt{{1}^{3}}, -\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right) + \mathsf{fma}\left(-\sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}, \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}, \sqrt{{\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{\frac{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3}}{{\left(\frac{1.0614054289999999}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{4}} + \left(\left(\left(\frac{1.42141374100000006}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{2}} + 0.25482959199999999\right) - \frac{1.45315202700000001}{{\left(\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)\right)}^{3}}\right) - \frac{0.284496735999999972}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}\right)\right)}^{3}}}}\right)}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)} \cdot \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \frac{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.32759110000000002, 1\right)}, -0.284496735999999972\right), 0.25482959199999999\right)}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right), 1 \cdot 1\right)}\]

Reproduce

herbie shell --seed 2020042 +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)))))))