Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

1. Initial program 84.8%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Step-by-step derivation

   1. associate-*l/97.6%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

3. Simplified97.6%

   \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

4. Final simplification97.6%

   \[\leadsto x + \frac{y - z}{a - z} \cdot t \]

1. Split input into 4 regimes

2. if z < -3.5999999999999997e83 or 1.3e44 < z

   1. Initial program 68.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/99.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 81.6%

      \[\leadsto x + \color{blue}{t} \]

   if -3.5999999999999997e83 < z < -2.3000000000000002e22

   1. Initial program 82.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 82.3%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]

   5. Taylor expanded in a around 0 77.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{z} + x} \]
   6. Step-by-step derivation

      1. +-commutative77.6%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot t}{z}} \]

      2. mul-1-neg77.6%

         \[\leadsto x + \color{blue}{\left(-\frac{y \cdot t}{z}\right)} \]

      3. unsub-neg77.6%

         \[\leadsto \color{blue}{x - \frac{y \cdot t}{z}} \]

      4. associate-/l*77.6%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{z}{t}}} \]

   7. Simplified77.6%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{z}{t}}} \]

   8. Taylor expanded in y around 0 77.6%

      \[\leadsto x - \color{blue}{\frac{y \cdot t}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/77.6%

         \[\leadsto x - \color{blue}{y \cdot \frac{t}{z}} \]

   10. Simplified77.6%

       \[\leadsto x - \color{blue}{y \cdot \frac{t}{z}} \]

   if -2.3000000000000002e22 < z < -1.10000000000000001e-24

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. add-cube-cbrt99.6%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}{a - z} \]

      2. pow399.6%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]

   3. Applied egg-rr99.6%

      \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]
   4. Step-by-step derivation

      1. clear-num99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}} \]

      2. inv-pow99.6%

         \[\leadsto x + \color{blue}{{\left(\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}\right)}^{-1}} \]

      3. unpow399.6%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}\right)}^{-1} \]

      4. add-cube-cbrt99.9%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(y - z\right) \cdot t}}\right)}^{-1} \]

      5. *-commutative99.9%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{t \cdot \left(y - z\right)}}\right)}^{-1} \]

      6. associate-/r*100.0%

         \[\leadsto x + {\color{blue}{\left(\frac{\frac{a - z}{t}}{y - z}\right)}}^{-1} \]

   5. Applied egg-rr100.0%

      \[\leadsto x + \color{blue}{{\left(\frac{\frac{a - z}{t}}{y - z}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   7. Simplified100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   8. Taylor expanded in z around inf 80.9%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{t}}} \]

   if -1.10000000000000001e-24 < z < 1.3e44

   1. Initial program 94.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/95.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified95.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 88.8%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]
   5. Step-by-step derivation

      1. *-commutative88.8%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

      2. clear-num88.7%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a - z}{y}}} \]

      3. un-div-inv89.5%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   6. Applied egg-rr89.5%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   7. Taylor expanded in a around inf 77.0%

      \[\leadsto x + \frac{t}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+83}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+22}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{1}{\frac{1}{t}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

1. Split input into 4 regimes

2. if z < -8.4000000000000001e83 or 1.08e42 < z

   1. Initial program 68.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/99.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 81.6%

      \[\leadsto x + \color{blue}{t} \]

   if -8.4000000000000001e83 < z < -5.3999999999999997e-45

   1. Initial program 93.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 81.9%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]

   5. Taylor expanded in a around 0 76.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{z} + x} \]
   6. Step-by-step derivation

      1. +-commutative76.5%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot t}{z}} \]

      2. mul-1-neg76.5%

         \[\leadsto x + \color{blue}{\left(-\frac{y \cdot t}{z}\right)} \]

      3. unsub-neg76.5%

         \[\leadsto \color{blue}{x - \frac{y \cdot t}{z}} \]

      4. associate-/l*76.5%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{z}{t}}} \]

   7. Simplified76.5%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{z}{t}}} \]

   8. Taylor expanded in y around 0 76.5%

      \[\leadsto x - \color{blue}{\frac{y \cdot t}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/76.5%

         \[\leadsto x - \color{blue}{y \cdot \frac{t}{z}} \]

   10. Simplified76.5%

       \[\leadsto x - \color{blue}{y \cdot \frac{t}{z}} \]

   if -5.3999999999999997e-45 < z < -1.0500000000000001e-75

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. add-cube-cbrt100.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}{a - z} \]

      2. pow399.8%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]

   3. Applied egg-rr99.8%

      \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]
   4. Step-by-step derivation

      1. clear-num99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}} \]

      2. inv-pow99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}\right)}^{-1}} \]

      3. unpow399.8%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}\right)}^{-1} \]

      4. add-cube-cbrt99.8%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(y - z\right) \cdot t}}\right)}^{-1} \]

      5. *-commutative99.8%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{t \cdot \left(y - z\right)}}\right)}^{-1} \]

      6. associate-/r*100.0%

         \[\leadsto x + {\color{blue}{\left(\frac{\frac{a - z}{t}}{y - z}\right)}}^{-1} \]

   5. Applied egg-rr100.0%

      \[\leadsto x + \color{blue}{{\left(\frac{\frac{a - z}{t}}{y - z}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   7. Simplified100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   8. Taylor expanded in y around 0 100.0%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{t \cdot z}{a - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg100.0%

         \[\leadsto x + \color{blue}{\left(-\frac{t \cdot z}{a - z}\right)} \]

      2. associate-/l*100.0%

         \[\leadsto x + \left(-\color{blue}{\frac{t}{\frac{a - z}{z}}}\right) \]

      3. distribute-neg-frac100.0%

         \[\leadsto x + \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]

   10. Simplified100.0%

       \[\leadsto x + \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]

   11. Taylor expanded in a around inf 100.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a} + x} \]
   12. Step-by-step derivation

       1. +-commutative100.0%

          \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot z}{a}} \]

       2. mul-1-neg100.0%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot z}{a}\right)} \]

       3. *-commutative100.0%

          \[\leadsto x + \left(-\frac{\color{blue}{z \cdot t}}{a}\right) \]

       4. associate-*r/100.0%

          \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t}{a}}\right) \]

       5. sub-neg100.0%

          \[\leadsto \color{blue}{x - z \cdot \frac{t}{a}} \]

   13. Simplified100.0%

       \[\leadsto \color{blue}{x - z \cdot \frac{t}{a}} \]

   if -1.0500000000000001e-75 < z < 1.08e42

   1. Initial program 94.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/95.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified95.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 88.7%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]
   5. Step-by-step derivation

      1. *-commutative88.7%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

      2. clear-num88.7%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a - z}{y}}} \]

      3. un-div-inv89.5%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   6. Applied egg-rr89.5%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   7. Taylor expanded in a around inf 76.8%

      \[\leadsto x + \frac{t}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+83}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-45}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

1. Split input into 4 regimes

2. if z < -2.20000000000000003e86 or 7.00000000000000047e42 < z

   1. Initial program 68.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/99.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 81.6%

      \[\leadsto x + \color{blue}{t} \]

   if -2.20000000000000003e86 < z < -8.6000000000000007e-46

   1. Initial program 93.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 81.9%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]

   5. Taylor expanded in a around 0 76.5%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{y \cdot t}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/76.5%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(y \cdot t\right)}{z}} \]

      2. neg-mul-176.5%

         \[\leadsto x + \frac{\color{blue}{-y \cdot t}}{z} \]

      3. distribute-rgt-neg-in76.5%

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(-t\right)}}{z} \]

   7. Simplified76.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(-t\right)}{z}} \]

   if -8.6000000000000007e-46 < z < -2.6e-75

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. add-cube-cbrt100.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}{a - z} \]

      2. pow399.8%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]

   3. Applied egg-rr99.8%

      \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]
   4. Step-by-step derivation

      1. clear-num99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}} \]

      2. inv-pow99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}\right)}^{-1}} \]

      3. unpow399.8%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}\right)}^{-1} \]

      4. add-cube-cbrt99.8%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(y - z\right) \cdot t}}\right)}^{-1} \]

      5. *-commutative99.8%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{t \cdot \left(y - z\right)}}\right)}^{-1} \]

      6. associate-/r*100.0%

         \[\leadsto x + {\color{blue}{\left(\frac{\frac{a - z}{t}}{y - z}\right)}}^{-1} \]

   5. Applied egg-rr100.0%

      \[\leadsto x + \color{blue}{{\left(\frac{\frac{a - z}{t}}{y - z}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   7. Simplified100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   8. Taylor expanded in y around 0 100.0%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{t \cdot z}{a - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg100.0%

         \[\leadsto x + \color{blue}{\left(-\frac{t \cdot z}{a - z}\right)} \]

      2. associate-/l*100.0%

         \[\leadsto x + \left(-\color{blue}{\frac{t}{\frac{a - z}{z}}}\right) \]

      3. distribute-neg-frac100.0%

         \[\leadsto x + \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]

   10. Simplified100.0%

       \[\leadsto x + \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]

   11. Taylor expanded in a around inf 100.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a} + x} \]
   12. Step-by-step derivation

       1. +-commutative100.0%

          \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot z}{a}} \]

       2. mul-1-neg100.0%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot z}{a}\right)} \]

       3. *-commutative100.0%

          \[\leadsto x + \left(-\frac{\color{blue}{z \cdot t}}{a}\right) \]

       4. associate-*r/100.0%

          \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t}{a}}\right) \]

       5. sub-neg100.0%

          \[\leadsto \color{blue}{x - z \cdot \frac{t}{a}} \]

   13. Simplified100.0%

       \[\leadsto \color{blue}{x - z \cdot \frac{t}{a}} \]

   if -2.6e-75 < z < 7.00000000000000047e42

   1. Initial program 94.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/95.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified95.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 88.7%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]
   5. Step-by-step derivation

      1. *-commutative88.7%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

      2. clear-num88.7%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a - z}{y}}} \]

      3. un-div-inv89.5%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   6. Applied egg-rr89.5%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   7. Taylor expanded in a around inf 76.8%

      \[\leadsto x + \frac{t}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+86}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -3.1e78 or 7.49999999999999974e143 < z

   1. Initial program 62.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/99.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 83.1%

      \[\leadsto x + \color{blue}{t} \]

   if -3.1e78 < z < 7.49999999999999974e143

   1. Initial program 94.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/96.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified96.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 87.4%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+78} \lor \neg \left(z \leq 7.5 \cdot 10^{+143}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -4.4999999999999999e78 or 1.74999999999999995e140 < z

   1. Initial program 62.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/99.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 83.1%

      \[\leadsto x + \color{blue}{t} \]

   if -4.4999999999999999e78 < z < 1.74999999999999995e140

   1. Initial program 94.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/96.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified96.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 87.4%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]
   5. Step-by-step derivation

      1. *-commutative87.4%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

      2. clear-num87.4%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a - z}{y}}} \]

      3. un-div-inv87.9%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   6. Applied egg-rr87.9%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+78} \lor \neg \left(z \leq 1.75 \cdot 10^{+140}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -3.8999999999999998e77 or 5.20000000000000044e139 < z

   1. Initial program 62.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. add-cube-cbrt61.6%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}{a - z} \]

      2. pow361.6%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]

   3. Applied egg-rr61.6%

      \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}{a - z} \]
   4. Step-by-step derivation

      1. clear-num61.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}}} \]

      2. inv-pow61.7%

         \[\leadsto x + \color{blue}{{\left(\frac{a - z}{{\left(\sqrt[3]{\left(y - z\right) \cdot t}\right)}^{3}}\right)}^{-1}} \]

      3. unpow361.6%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot t} \cdot \sqrt[3]{\left(y - z\right) \cdot t}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot t}}}\right)}^{-1} \]

      4. add-cube-cbrt62.0%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{\left(y - z\right) \cdot t}}\right)}^{-1} \]

      5. *-commutative62.0%

         \[\leadsto x + {\left(\frac{a - z}{\color{blue}{t \cdot \left(y - z\right)}}\right)}^{-1} \]

      6. associate-/r*96.0%

         \[\leadsto x + {\color{blue}{\left(\frac{\frac{a - z}{t}}{y - z}\right)}}^{-1} \]

   5. Applied egg-rr96.0%

      \[\leadsto x + \color{blue}{{\left(\frac{\frac{a - z}{t}}{y - z}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-196.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   7. Simplified96.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}} \]

   8. Taylor expanded in y around 0 62.0%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{t \cdot z}{a - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg62.0%

         \[\leadsto x + \color{blue}{\left(-\frac{t \cdot z}{a - z}\right)} \]

      2. associate-/l*94.5%

         \[\leadsto x + \left(-\color{blue}{\frac{t}{\frac{a - z}{z}}}\right) \]

      3. distribute-neg-frac94.5%

         \[\leadsto x + \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]

   10. Simplified94.5%

       \[\leadsto x + \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]

   11. Taylor expanded in x around 0 62.0%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot z}{a - z}} \]
   12. Step-by-step derivation

       1. mul-1-neg62.0%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot z}{a - z}\right)} \]

       2. associate-*r/94.6%

          \[\leadsto x + \left(-\color{blue}{t \cdot \frac{z}{a - z}}\right) \]

       3. sub-neg94.6%

          \[\leadsto \color{blue}{x - t \cdot \frac{z}{a - z}} \]

   13. Simplified94.6%

       \[\leadsto \color{blue}{x - t \cdot \frac{z}{a - z}} \]

   if -3.8999999999999998e77 < z < 5.20000000000000044e139

   1. Initial program 94.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/96.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified96.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 87.4%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]
   5. Step-by-step derivation

      1. *-commutative87.4%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

      2. clear-num87.4%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a - z}{y}}} \]

      3. un-div-inv87.9%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   6. Applied egg-rr87.9%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+77} \lor \neg \left(z \leq 5.2 \cdot 10^{+139}\right):\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -1.90000000000000005e-28 or 1.95000000000000013e47 < z

   1. Initial program 74.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/99.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 77.7%

      \[\leadsto x + \color{blue}{t} \]

   if -1.90000000000000005e-28 < z < 1.95000000000000013e47

   1. Initial program 94.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/95.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified95.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around 0 76.2%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+47}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -7.20000000000000038e-35 or 6.6000000000000003e43 < z

   1. Initial program 74.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/99.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 77.7%

      \[\leadsto x + \color{blue}{t} \]

   if -7.20000000000000038e-35 < z < 6.6000000000000003e43

   1. Initial program 94.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/95.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified95.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in y around inf 88.8%

      \[\leadsto x + \color{blue}{\frac{y}{a - z}} \cdot t \]
   5. Step-by-step derivation

      1. *-commutative88.8%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

      2. clear-num88.7%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a - z}{y}}} \]

      3. un-div-inv89.5%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   6. Applied egg-rr89.5%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y}}} \]

   7. Taylor expanded in a around inf 77.0%

      \[\leadsto x + \frac{t}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-35}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

1. Split input into 2 regimes

2. if a < -2.39999999999999983e113 or 1.6500000000000001e187 < a

   1. Initial program 83.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative83.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot t}{a - z} + x} \]

      2. associate-*r/98.2%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} + x \]

      3. fma-def98.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

   3. Simplified98.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

   4. Taylor expanded in t around 0 67.4%

      \[\leadsto \color{blue}{x} \]

   if -2.39999999999999983e113 < a < 1.6500000000000001e187

   1. Initial program 85.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/97.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   3. Simplified97.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]

   4. Taylor expanded in z around inf 60.3%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+187}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

1. Initial program 84.8%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Step-by-step derivation

   1. +-commutative84.8%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot t}{a - z} + x} \]

   2. associate-*r/96.5%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} + x \]

   3. fma-def96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

3. Simplified96.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

4. Taylor expanded in t around 0 48.6%

   \[\leadsto \color{blue}{x} \]

5. Final simplification48.6%

   \[\leadsto x \]

herbie shell --seed 2023167 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

  (+ x (/ (* (- y z) t) (- a z))))