if z < -3.46539097027431e-21 or 5.232316343847364e-09 < z

1. Started with
   \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
   59.2
2. Using strategy rm
   59.2
3. Applied add-cube-cbrt to get
   \[\color{red}{(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \leadsto \color{blue}{{\left(\sqrt[3]{(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\right)}^3}\]
   59.2
4. Using strategy rm
   59.2
5. Applied add-cube-cbrt to get
   \[{\left(\sqrt[3]{(x * y + z)_* - \left(1 + \color{red}{\left(x \cdot y + z\right)}\right)}\right)}^3 \leadsto {\left(\sqrt[3]{(x * y + z)_* - \left(1 + \color{blue}{{\left(\sqrt[3]{x \cdot y + z}\right)}^3}\right)}\right)}^3\]
   59.7
6. Using strategy rm
   59.7
7. Applied pow3 to get
   \[{\left(\sqrt[3]{(x * y + z)_* - \left(1 + \color{red}{{\left(\sqrt[3]{x \cdot y + z}\right)}^3}\right)}\right)}^3 \leadsto {\left(\sqrt[3]{(x * y + z)_* - \left(1 + \color{blue}{{\left(\sqrt[3]{x \cdot y + z}\right)}^{3}}\right)}\right)}^3\]
   59.8
8. Applied taylor to get
   \[{\left(\sqrt[3]{(x * y + z)_* - \left(1 + {\left(\sqrt[3]{x \cdot y + z}\right)}^{3}\right)}\right)}^3 \leadsto {\left(\sqrt[3]{(\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \left(1 + {\left(\sqrt[3]{\frac{1}{z} + \frac{1}{y \cdot x}}\right)}^{3}\right)}\right)}^3\]
   30.5
9. Taylor expanded around inf to get
   \[{\left(\sqrt[3]{\color{red}{(\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \left(1 + {\left(\sqrt[3]{\frac{1}{z} + \frac{1}{y \cdot x}}\right)}^{3}\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{(\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \left(1 + {\left(\sqrt[3]{\frac{1}{z} + \frac{1}{y \cdot x}}\right)}^{3}\right)}}\right)}^3\]
   30.5
10. Applied simplify to get
    \[{\left(\sqrt[3]{(\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \left(1 + {\left(\sqrt[3]{\frac{1}{z} + \frac{1}{y \cdot x}}\right)}^{3}\right)}\right)}^3 \leadsto \left((\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1\right) - \left(\frac{1}{y \cdot x} + \frac{1}{z}\right)\]
    30.0

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11. Applied final simplification

if -3.46539097027431e-21 < z < 5.232316343847364e-09

1. Started with
   \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
   29.2
2. Using strategy rm
   29.2
3. Applied add-cube-cbrt to get
   \[\color{red}{(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \leadsto \color{blue}{{\left(\sqrt[3]{(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\right)}^3}\]
   29.2
4. Using strategy rm
   29.2
5. Applied add-cube-cbrt to get
   \[{\left(\sqrt[3]{(x * y + z)_* - \left(1 + \color{red}{\left(x \cdot y + z\right)}\right)}\right)}^3 \leadsto {\left(\sqrt[3]{(x * y + z)_* - \left(1 + \color{blue}{{\left(\sqrt[3]{x \cdot y + z}\right)}^3}\right)}\right)}^3\]
   29.8
6. Using strategy rm
   29.8
7. Applied add-cube-cbrt to get
   \[{\left(\sqrt[3]{(x * y + z)_* - \left(1 + {\left(\sqrt[3]{\color{red}{x \cdot y + z}}\right)}^3\right)}\right)}^3 \leadsto {\left(\sqrt[3]{(x * y + z)_* - \left(1 + {\left(\sqrt[3]{\color{blue}{{\left(\sqrt[3]{x \cdot y + z}\right)}^3}}\right)}^3\right)}\right)}^3\]
   29.8