Average Error: 13.9 → 10.7
Time: 31.2s
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{1 \cdot 1 - \frac{\sqrt[3]{\frac{\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) \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)}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{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)}} \cdot \frac{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)}{\frac{\sqrt{e^{{\left(\left|x\right|\right)}^{2}}}}{\sqrt{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)}}}} \cdot \frac{\frac{1 \cdot 1}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}}}{\frac{\sqrt{e^{{\left(\left|x\right|\right)}^{2}}}}{\sqrt{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)}}}}{e^{{\left(\left|x\right|\right)}^{2}}}}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\left(\left(\left(0.25482959199999999 + \frac{1.42141374100000006}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}\right) + \frac{1.0614054289999999}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right) - \frac{0.284496735999999972}{0.32759110000000002 \cdot \left|x\right| + 1}\right) - \frac{1.45315202700000001}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}\]
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{1 \cdot 1 - \frac{\sqrt[3]{\frac{\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) \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)}{\frac{e^{{\left(\left|x\right|\right)}^{2}}}{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)}} \cdot \frac{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)}{\frac{\sqrt{e^{{\left(\left|x\right|\right)}^{2}}}}{\sqrt{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)}}}} \cdot \frac{\frac{1 \cdot 1}{{\left(1 + 0.32759110000000002 \cdot \left|x\right|\right)}^{2}}}{\frac{\sqrt{e^{{\left(\left|x\right|\right)}^{2}}}}{\sqrt{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)}}}}{e^{{\left(\left|x\right|\right)}^{2}}}}{\frac{\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(\left(\left(\left(0.25482959199999999 + \frac{1.42141374100000006}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{2}}\right) + \frac{1.0614054289999999}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{4}}\right) - \frac{0.284496735999999972}{0.32759110000000002 \cdot \left|x\right| + 1}\right) - \frac{1.45315202700000001}{{\left(0.32759110000000002 \cdot \left|x\right| + 1\right)}^{3}}\right)}{e^{{\left(\left|x\right|\right)}^{2}}} + 1}
double f(double x) {
        double r189925 = 1.0;
        double r189926 = 0.3275911;
        double r189927 = x;
        double r189928 = fabs(r189927);
        double r189929 = r189926 * r189928;
        double r189930 = r189925 + r189929;
        double r189931 = r189925 / r189930;
        double r189932 = 0.254829592;
        double r189933 = -0.284496736;
        double r189934 = 1.421413741;
        double r189935 = -1.453152027;
        double r189936 = 1.061405429;
        double r189937 = r189931 * r189936;
        double r189938 = r189935 + r189937;
        double r189939 = r189931 * r189938;
        double r189940 = r189934 + r189939;
        double r189941 = r189931 * r189940;
        double r189942 = r189933 + r189941;
        double r189943 = r189931 * r189942;
        double r189944 = r189932 + r189943;
        double r189945 = r189931 * r189944;
        double r189946 = r189928 * r189928;
        double r189947 = -r189946;
        double r189948 = exp(r189947);
        double r189949 = r189945 * r189948;
        double r189950 = r189925 - r189949;
        return r189950;
}
↓
double f(double x) {
        double r189951 = 1.0;
        double r189952 = r189951 * r189951;
        double r189953 = 0.254829592;
        double r189954 = 0.3275911;
        double r189955 = x;
        double r189956 = fabs(r189955);
        double r189957 = r189954 * r189956;
        double r189958 = r189951 + r189957;
        double r189959 = r189951 / r189958;
        double r189960 = -0.284496736;
        double r189961 = 1.421413741;
        double r189962 = -1.453152027;
        double r189963 = 1.061405429;
        double r189964 = r189959 * r189963;
        double r189965 = r189962 + r189964;
        double r189966 = r189959 * r189965;
        double r189967 = r189961 + r189966;
        double r189968 = r189959 * r189967;
        double r189969 = r189960 + r189968;
        double r189970 = r189959 * r189969;
        double r189971 = r189953 + r189970;
        double r189972 = r189971 * r189971;
        double r189973 = 2.0;
        double r189974 = pow(r189956, r189973);
        double r189975 = exp(r189974);
        double r189976 = r189975 / r189971;
        double r189977 = r189972 / r189976;
        double r189978 = sqrt(r189975);
        double r189979 = sqrt(r189971);
        double r189980 = r189978 / r189979;
        double r189981 = r189971 / r189980;
        double r189982 = r189977 * r189981;
        double r189983 = cbrt(r189982);
        double r189984 = pow(r189958, r189973);
        double r189985 = r189952 / r189984;
        double r189986 = r189985 / r189980;
        double r189987 = r189983 * r189986;
        double r189988 = r189987 / r189975;
        double r189989 = r189952 - r189988;
        double r189990 = r189957 + r189951;
        double r189991 = pow(r189990, r189973);
        double r189992 = r189961 / r189991;
        double r189993 = r189953 + r189992;
        double r189994 = 4.0;
        double r189995 = pow(r189990, r189994);
        double r189996 = r189963 / r189995;
        double r189997 = r189993 + r189996;
        double r189998 = 0.284496736;
        double r189999 = r189998 / r189990;
        double r190000 = r189997 - r189999;
        double r190001 = 1.453152027;
        double r190002 = 3.0;
        double r190003 = pow(r189990, r190002);
        double r190004 = r190001 / r190003;
        double r190005 = r190000 - r190004;
        double r190006 = r189959 * r190005;
        double r190007 = r190006 / r189975;
        double r190008 = r190007 + r189951;
        double r190009 = r189989 / r190008;
        return r190009;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.9

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

  2. Simplified13.9

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

  4. Applied flip--13.9

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

  5. Simplified10.7

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

  6. Simplified10.7

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

  7. Taylor expanded around 0 10.7

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

  8. Simplified10.7

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

  10. Applied add-sqr-sqrt10.7

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

  11. Applied add-sqr-sqrt10.7

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

  12. Applied times-frac10.7

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

  13. Applied times-frac10.7

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

  15. Applied add-cbrt-cube10.7

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

  16. Applied add-cbrt-cube10.7

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

  17. Applied cbrt-undiv14.4

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

  18. Applied add-cbrt-cube13.9

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

  19. Applied cbrt-undiv10.7

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

  20. Simplified10.7

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

  21. Final simplification10.7

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

Reproduce

herbie shell --seed 2020046 
(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)))))))