if i < -8.1852f-14

1. Started with
   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
   5.8
2. Applied simplify to get
   \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
   5.8
3. Using strategy rm
   5.8
4. Applied sub-neg to get
   \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \color{red}{\left(c \cdot z - i \cdot a\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\]
   5.8
5. Applied distribute-lft-in to get
   \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{red}{b \cdot \left(c \cdot z + \left(-i \cdot a\right)\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{blue}{\left(b \cdot \left(c \cdot z\right) + b \cdot \left(-i \cdot a\right)\right)}\]
   5.8
6. Applied associate--r+ to get
   \[\color{red}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \left(b \cdot \left(c \cdot z\right) + b \cdot \left(-i \cdot a\right)\right)} \leadsto \color{blue}{\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \left(-i \cdot a\right)}\]
   5.8
7. Using strategy rm
   5.8
8. Applied distribute-lft-neg-in to get
   \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \color{red}{\left(-i \cdot a\right)} \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-i\right) \cdot a\right)}\]
   5.8
9. Applied associate-*r* to get
   \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{red}{b \cdot \left(\left(-i\right) \cdot a\right)} \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{blue}{\left(b \cdot \left(-i\right)\right) \cdot a}\]
   6.2
10. Applied taylor to get
    \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \left(b \cdot \left(-i\right)\right) \cdot a \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - -1 \cdot \left(b \cdot \left(a \cdot i\right)\right)\]
    5.8
11. Taylor expanded around inf to get
    \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{red}{-1 \cdot \left(b \cdot \left(a \cdot i\right)\right)} \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{blue}{-1 \cdot \left(b \cdot \left(a \cdot i\right)\right)}\]
    5.8
12. Applied simplify to get
    \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - -1 \cdot \left(b \cdot \left(a \cdot i\right)\right) \leadsto (\left(t \cdot c - y \cdot i\right) * j + \left(x \cdot \left(z \cdot y - a \cdot t\right)\right))_* - (\left(b \cdot c\right) * z + \left(\left(a \cdot b\right) \cdot \left(-i\right)\right))_*\]
    5.1

---

13. Applied final simplification

if -8.1852f-14 < i < 6.7191024f-08

1. Started with
   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
   4.6
2. Applied simplify to get
   \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
   4.6
3. Using strategy rm
   4.6
4. Applied sub-neg to get
   \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \color{red}{\left(c \cdot z - i \cdot a\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\]
   4.6
5. Applied distribute-lft-in to get
   \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{red}{b \cdot \left(c \cdot z + \left(-i \cdot a\right)\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{blue}{\left(b \cdot \left(c \cdot z\right) + b \cdot \left(-i \cdot a\right)\right)}\]
   4.6
6. Applied associate--r+ to get
   \[\color{red}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \left(b \cdot \left(c \cdot z\right) + b \cdot \left(-i \cdot a\right)\right)} \leadsto \color{blue}{\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \left(-i \cdot a\right)}\]
   4.6
7. Using strategy rm
   4.6
8. Applied add-cube-cbrt to get
   \[\color{red}{\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \left(-i \cdot a\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \left(-i \cdot a\right)}\right)}^3}\]
   5.0
9. Applied simplify to get
   \[{\color{red}{\left(\sqrt[3]{\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \left(-i \cdot a\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{(\left(t \cdot c - y \cdot i\right) * j + \left(x \cdot \left(z \cdot y - a \cdot t\right)\right))_* - (i * \left(-a\right) + \left(c \cdot z\right))_* \cdot b}\right)}}^3\]
   5.0
10. Applied taylor to get
    \[{\left(\sqrt[3]{(\left(t \cdot c - y \cdot i\right) * j + \left(x \cdot \left(z \cdot y - a \cdot t\right)\right))_* - (i * \left(-a\right) + \left(c \cdot z\right))_* \cdot b}\right)}^3 \leadsto {\left(\sqrt[3]{(\left(t \cdot c - y \cdot i\right) * j + \left(y \cdot \left(x \cdot z\right) - t \cdot \left(a \cdot x\right)\right))_* - (i * \left(-a\right) + \left(c \cdot z\right))_* \cdot b}\right)}^3\]
    4.6
11. Taylor expanded around inf to get
    \[{\left(\sqrt[3]{(\left(t \cdot c - y \cdot i\right) * j + \color{red}{\left(y \cdot \left(x \cdot z\right) - t \cdot \left(a \cdot x\right)\right)})_* - (i * \left(-a\right) + \left(c \cdot z\right))_* \cdot b}\right)}^3 \leadsto {\left(\sqrt[3]{(\left(t \cdot c - y \cdot i\right) * j + \color{blue}{\left(y \cdot \left(x \cdot z\right) - t \cdot \left(a \cdot x\right)\right)})_* - (i * \left(-a\right) + \left(c \cdot z\right))_* \cdot b}\right)}^3\]
    4.6
12. Applied simplify to get
    \[{\left(\sqrt[3]{(\left(t \cdot c - y \cdot i\right) * j + \left(y \cdot \left(x \cdot z\right) - t \cdot \left(a \cdot x\right)\right))_* - (i * \left(-a\right) + \left(c \cdot z\right))_* \cdot b}\right)}^3 \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right))_* - b \cdot (i * \left(-a\right) + \left(c \cdot z\right))_*\]
    4.0

---

13. Applied final simplification
14. Applied simplify to get
    \[\color{red}{(\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - \left(t \cdot x\right) \cdot a\right))_* - b \cdot (i * \left(-a\right) + \left(c \cdot z\right))_*} \leadsto \color{blue}{(\left(t \cdot c - y \cdot i\right) * j + \left(\left(z \cdot y - t \cdot a\right) \cdot x\right))_* - b \cdot (i * \left(-a\right) + \left(z \cdot c\right))_*}\]
    4.6

if 6.7191024f-08 < i

1. Started with
   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
   6.7
2. Applied simplify to get
   \[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
   6.7
3. Using strategy rm
   6.7
4. Applied sub-neg to get
   \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \color{red}{\left(c \cdot z - i \cdot a\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\]
   6.7
5. Applied distribute-lft-in to get
   \[(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{red}{b \cdot \left(c \cdot z + \left(-i \cdot a\right)\right)} \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \color{blue}{\left(b \cdot \left(c \cdot z\right) + b \cdot \left(-i \cdot a\right)\right)}\]
   6.7
6. Applied associate--r+ to get
   \[\color{red}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - \left(b \cdot \left(c \cdot z\right) + b \cdot \left(-i \cdot a\right)\right)} \leadsto \color{blue}{\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \left(-i \cdot a\right)}\]
   6.7
7. Using strategy rm
   6.7
8. Applied distribute-lft-neg-in to get
   \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \color{red}{\left(-i \cdot a\right)} \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-i\right) \cdot a\right)}\]
   6.7
9. Applied associate-*r* to get
   \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{red}{b \cdot \left(\left(-i\right) \cdot a\right)} \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{blue}{\left(b \cdot \left(-i\right)\right) \cdot a}\]
   7.0
10. Applied taylor to get
    \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \left(b \cdot \left(-i\right)\right) \cdot a \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - -1 \cdot \left(b \cdot \left(a \cdot i\right)\right)\]
    6.7
11. Taylor expanded around inf to get
    \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{red}{-1 \cdot \left(b \cdot \left(a \cdot i\right)\right)} \leadsto \left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - \color{blue}{-1 \cdot \left(b \cdot \left(a \cdot i\right)\right)}\]
    6.7
12. Applied simplify to get
    \[\left((\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z\right)\right) - -1 \cdot \left(b \cdot \left(a \cdot i\right)\right) \leadsto (\left(t \cdot c - y \cdot i\right) * j + \left(x \cdot \left(z \cdot y - a \cdot t\right)\right))_* - (\left(b \cdot c\right) * z + \left(\left(a \cdot b\right) \cdot \left(-i\right)\right))_*\]
    5.3

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13. Applied final simplification