if z < -32602426.0f0

1. Started with
   \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
   30.4
2. Using strategy rm
   30.4
3. Applied add-cube-cbrt to get
   \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{{\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3}\]
   30.1
4. Applied taylor to get
   \[(x * y + z)_* - {\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3 \leadsto (\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1\]
   0.2
5. Taylor expanded around -inf to get
   \[\color{red}{(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1} \leadsto \color{blue}{(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1}\]
   0.2
6. Applied simplify to get
   \[(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1 \leadsto (\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1\]
   0.2

---

7. Applied final simplification

if -32602426.0f0 < z < 161.79059f0

1. Started with
   \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
   12.5
2. Using strategy rm
   12.5
3. Applied associate--r+ to get
   \[\color{red}{(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \leadsto \color{blue}{\left((x * y + z)_* - 1\right) - \left(x \cdot y + z\right)}\]
   9.6
4. Using strategy rm
   9.6
5. Applied add-log-exp to get
   \[\left((x * y + z)_* - 1\right) - \color{red}{\left(x \cdot y + z\right)} \leadsto \left((x * y + z)_* - 1\right) - \color{blue}{\log \left(e^{x \cdot y + z}\right)}\]
   15.6
6. Applied add-log-exp to get
   \[\color{red}{\left((x * y + z)_* - 1\right)} - \log \left(e^{x \cdot y + z}\right) \leadsto \color{blue}{\log \left(e^{(x * y + z)_* - 1}\right)} - \log \left(e^{x \cdot y + z}\right)\]
   15.9
7. Applied diff-log to get
   \[\color{red}{\log \left(e^{(x * y + z)_* - 1}\right) - \log \left(e^{x \cdot y + z}\right)} \leadsto \color{blue}{\log \left(\frac{e^{(x * y + z)_* - 1}}{e^{x \cdot y + z}}\right)}\]
   15.9
8. Applied simplify to get
   \[\log \color{red}{\left(\frac{e^{(x * y + z)_* - 1}}{e^{x \cdot y + z}}\right)} \leadsto \log \color{blue}{\left(e^{\left((x * y + z)_* - \left(1 + z\right)\right) - y \cdot x}\right)}\]
   10.2
9. Applied taylor to get
   \[\log \left(e^{\left((x * y + z)_* - \left(1 + z\right)\right) - y \cdot x}\right) \leadsto \log \left(e^{(x * y + z)_* - \left(y \cdot x + \left(1 + z\right)\right)}\right)\]
   12.5
10. Taylor expanded around 0 to get
    \[\log \left(e^{\color{red}{(x * y + z)_* - \left(y \cdot x + \left(1 + z\right)\right)}}\right) \leadsto \log \left(e^{\color{blue}{(x * y + z)_* - \left(y \cdot x + \left(1 + z\right)\right)}}\right)\]
    12.5
11. Applied simplify to get
    \[\log \left(e^{(x * y + z)_* - \left(y \cdot x + \left(1 + z\right)\right)}\right) \leadsto \left((x * y + z)_* - y \cdot x\right) - \left(z + 1\right)\]
    5.6

---

12. Applied final simplification

if 161.79059f0 < z

1. Started with
   \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
   30.1
2. Using strategy rm
   30.1
3. Applied add-cube-cbrt to get
   \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{{\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3}\]
   29.9
4. Applied taylor to get
   \[(x * y + z)_* - {\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3 \leadsto (\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1\]
   0.2
5. Taylor expanded around -inf to get
   \[\color{red}{(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1} \leadsto \color{blue}{(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1}\]
   0.2
6. Applied simplify to get
   \[(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1 \leadsto (\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - 1\]
   0.2

---

7. Applied final simplification