Average Error: 14.0 → 14.0
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{\frac{1 - {\left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3} \cdot {\left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{{\left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3} + 1}}{1 + \left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}} + \frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\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{\frac{1 - {\left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3} \cdot {\left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{{\left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3} + 1}}{1 + \left(\frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}} + \frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\sqrt{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}} \cdot \frac{\sqrt{\log \left(e^{0.254829592 + \frac{\frac{\frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{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}}\right)}}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}
double f(double x) {
        double r4435991 = 1.0;
        double r4435992 = 0.3275911;
        double r4435993 = x;
        double r4435994 = fabs(r4435993);
        double r4435995 = r4435992 * r4435994;
        double r4435996 = r4435991 + r4435995;
        double r4435997 = r4435991 / r4435996;
        double r4435998 = 0.254829592;
        double r4435999 = -0.284496736;
        double r4436000 = 1.421413741;
        double r4436001 = -1.453152027;
        double r4436002 = 1.061405429;
        double r4436003 = r4435997 * r4436002;
        double r4436004 = r4436001 + r4436003;
        double r4436005 = r4435997 * r4436004;
        double r4436006 = r4436000 + r4436005;
        double r4436007 = r4435997 * r4436006;
        double r4436008 = r4435999 + r4436007;
        double r4436009 = r4435997 * r4436008;
        double r4436010 = r4435998 + r4436009;
        double r4436011 = r4435997 * r4436010;
        double r4436012 = r4435994 * r4435994;
        double r4436013 = -r4436012;
        double r4436014 = exp(r4436013);
        double r4436015 = r4436011 * r4436014;
        double r4436016 = r4435991 - r4436015;
        return r4436016;
}
↓
double f(double x) {
        double r4436017 = 1.0;
        double r4436018 = 0.254829592;
        double r4436019 = -1.453152027;
        double r4436020 = 1.061405429;
        double r4436021 = x;
        double r4436022 = fabs(r4436021);
        double r4436023 = 0.3275911;
        double r4436024 = r4436022 * r4436023;
        double r4436025 = r4436017 + r4436024;
        double r4436026 = r4436020 / r4436025;
        double r4436027 = r4436019 + r4436026;
        double r4436028 = r4436027 / r4436025;
        double r4436029 = 1.421413741;
        double r4436030 = r4436028 + r4436029;
        double r4436031 = r4436030 / r4436025;
        double r4436032 = -0.284496736;
        double r4436033 = r4436031 + r4436032;
        double r4436034 = r4436033 / r4436025;
        double r4436035 = r4436018 + r4436034;
        double r4436036 = sqrt(r4436035);
        double r4436037 = cbrt(r4436025);
        double r4436038 = r4436037 * r4436037;
        double r4436039 = r4436036 / r4436038;
        double r4436040 = exp(r4436035);
        double r4436041 = log(r4436040);
        double r4436042 = sqrt(r4436041);
        double r4436043 = r4436042 / r4436037;
        double r4436044 = r4436039 * r4436043;
        double r4436045 = r4436022 * r4436022;
        double r4436046 = exp(r4436045);
        double r4436047 = r4436044 / r4436046;
        double r4436048 = 3.0;
        double r4436049 = pow(r4436047, r4436048);
        double r4436050 = r4436049 * r4436049;
        double r4436051 = r4436017 - r4436050;
        double r4436052 = r4436049 + r4436017;
        double r4436053 = r4436051 / r4436052;
        double r4436054 = r4436047 * r4436047;
        double r4436055 = r4436047 + r4436054;
        double r4436056 = r4436017 + r4436055;
        double r4436057 = r4436053 / r4436056;
        return r4436057;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.0

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

  2. Simplified14.0

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

  4. Applied add-cube-cbrt14.0

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

  5. Applied add-sqr-sqrt14.0

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

  6. Applied times-frac14.0

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

  8. Applied add-log-exp14.0

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

  10. Applied flip3--14.0

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

  12. Applied flip--14.0

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

  13. Final simplification14.0

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

Reproduce

herbie shell --seed 2019154 
(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)))))))