Average Error: 14.1 → 10.8
Time: 1.3m
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\left(\sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}} \cdot \sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}\right) \cdot \sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}}{1 + \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}\]
1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\frac{\left(\sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}} \cdot \sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}\right) \cdot \sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}}{1 + \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}
double f(double x) {
        double r8225066 = 1.0;
        double r8225067 = 0.3275911;
        double r8225068 = x;
        double r8225069 = fabs(r8225068);
        double r8225070 = r8225067 * r8225069;
        double r8225071 = r8225066 + r8225070;
        double r8225072 = r8225066 / r8225071;
        double r8225073 = 0.254829592;
        double r8225074 = -0.284496736;
        double r8225075 = 1.421413741;
        double r8225076 = -1.453152027;
        double r8225077 = 1.061405429;
        double r8225078 = r8225072 * r8225077;
        double r8225079 = r8225076 + r8225078;
        double r8225080 = r8225072 * r8225079;
        double r8225081 = r8225075 + r8225080;
        double r8225082 = r8225072 * r8225081;
        double r8225083 = r8225074 + r8225082;
        double r8225084 = r8225072 * r8225083;
        double r8225085 = r8225073 + r8225084;
        double r8225086 = r8225072 * r8225085;
        double r8225087 = r8225069 * r8225069;
        double r8225088 = -r8225087;
        double r8225089 = exp(r8225088);
        double r8225090 = r8225086 * r8225089;
        double r8225091 = r8225066 - r8225090;
        return r8225091;
}
↓
double f(double x) {
        double r8225092 = 1.0;
        double r8225093 = 0.254829592;
        double r8225094 = 1.061405429;
        double r8225095 = x;
        double r8225096 = fabs(r8225095);
        double r8225097 = 0.3275911;
        double r8225098 = r8225096 * r8225097;
        double r8225099 = r8225092 + r8225098;
        double r8225100 = r8225094 / r8225099;
        double r8225101 = r8225099 * r8225099;
        double r8225102 = r8225100 / r8225101;
        double r8225103 = 1.453152027;
        double r8225104 = r8225103 / r8225101;
        double r8225105 = 0.284496736;
        double r8225106 = r8225104 + r8225105;
        double r8225107 = r8225102 - r8225106;
        double r8225108 = 1.421413741;
        double r8225109 = r8225108 / r8225099;
        double r8225110 = r8225107 + r8225109;
        double r8225111 = r8225110 / r8225099;
        double r8225112 = r8225093 + r8225111;
        double r8225113 = r8225096 * r8225096;
        double r8225114 = exp(r8225113);
        double r8225115 = r8225114 * r8225099;
        double r8225116 = r8225112 / r8225115;
        double r8225117 = -1.453152027;
        double r8225118 = r8225100 + r8225117;
        double r8225119 = r8225118 / r8225099;
        double r8225120 = r8225108 + r8225119;
        double r8225121 = r8225120 / r8225099;
        double r8225122 = -0.284496736;
        double r8225123 = r8225121 + r8225122;
        double r8225124 = cbrt(r8225123);
        double r8225125 = r8225124 * r8225124;
        double r8225126 = r8225099 / r8225124;
        double r8225127 = r8225125 / r8225126;
        double r8225128 = r8225127 + r8225093;
        double r8225129 = r8225128 / r8225115;
        double r8225130 = r8225116 * r8225129;
        double r8225131 = r8225092 - r8225130;
        double r8225132 = cbrt(r8225131);
        double r8225133 = r8225132 * r8225132;
        double r8225134 = r8225133 * r8225132;
        double r8225135 = r8225092 + r8225129;
        double r8225136 = r8225134 / r8225135;
        return r8225136;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  2. Simplified14.1

    \[\leadsto \color{blue}{1 - \frac{\frac{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt14.1

    \[\leadsto 1 - \frac{\frac{\color{blue}{\left(\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}\right) \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\]

  5. Applied associate-/l*14.1

    \[\leadsto 1 - \frac{\color{blue}{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\]
  6. Using strategy rm

  7. Applied flip--14.1

    \[\leadsto \color{blue}{\frac{1 \cdot 1 - \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}{1 + \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}}\]

  8. Taylor expanded around 0 10.8

    \[\leadsto \frac{1 \cdot 1 - \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\color{blue}{\frac{\left(1.421413741 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 0.284496736\right)}{0.3275911 \cdot \left|x\right| + 1}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}{1 + \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}\]

  9. Simplified10.8

    \[\leadsto \frac{1 \cdot 1 - \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\color{blue}{\frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(0.284496736 + \frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right)}{1 + \left|x\right| \cdot 0.3275911}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}{1 + \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt10.8

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1 \cdot 1 - \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(0.284496736 + \frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right)}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}} \cdot \sqrt[3]{1 \cdot 1 - \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(0.284496736 + \frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right)}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}\right) \cdot \sqrt[3]{1 \cdot 1 - \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} + \left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(0.284496736 + \frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right)\right)}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}}}{1 + \frac{\frac{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}\]

  12. Final simplification10.8

    \[\leadsto \frac{\left(\sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}} \cdot \sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}\right) \cdot \sqrt[3]{1 - \frac{0.254829592 + \frac{\left(\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \left(\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + 0.284496736\right)\right) + \frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} \cdot \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}}{1 + \frac{\frac{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736} \cdot \sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}{\frac{1 + \left|x\right| \cdot 0.3275911}{\sqrt[3]{\frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + -0.284496736}}} + 0.254829592}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))