1. Split input into 2 regimes

2. if y < -1.4e68

   1. Initial program 79.2%

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

      1. associate-*r/97.8%

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

   3. Simplified97.8%

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

   if -1.4e68 < y

   1. Initial program 99.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]

1. Split input into 5 regimes

2. if a < -6.3999999999999997e34 or -1.6e5 < a < -5.6000000000000001e-14 or 2.59999999999999997e34 < a

   1. Initial program 90.4%

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

      1. associate-*r/98.9%

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

   3. Simplified98.9%

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

   4. Taylor expanded in z around inf 74.4%

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

      1. associate-*l/78.0%

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

      2. *-commutative78.0%

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

   6. Simplified78.0%

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

   7. Taylor expanded in x around inf 63.5%

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

   if -6.3999999999999997e34 < a < -1.6e5

   1. Initial program 74.7%

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

      1. associate-*r/100.0%

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

   3. Simplified100.0%

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

   4. Taylor expanded in z around inf 74.7%

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

      1. associate-*l/99.6%

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

      2. *-commutative99.6%

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

   6. Simplified99.6%

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

   7. Taylor expanded in x around 0 60.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-*l/85.5%

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

      2. *-commutative85.5%

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

      3. neg-mul-185.5%

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

      4. distribute-rgt-neg-in85.5%

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

      5. distribute-frac-neg85.5%

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

   9. Simplified85.5%

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

   if -5.6000000000000001e-14 < a < -6.60000000000000037e-190

   1. Initial program 99.8%

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

      1. associate-*r/80.5%

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

   3. Simplified80.5%

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

   4. Taylor expanded in z around 0 63.9%

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

      1. neg-mul-163.9%

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

      2. distribute-neg-frac63.9%

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

   6. Simplified63.9%

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

   7. Taylor expanded in x around 0 48.8%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   8. Step-by-step derivation

      1. *-commutative48.8%

         \[\leadsto \frac{\color{blue}{t \cdot y}}{a} \]

      2. associate-*r/48.8%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified48.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. clear-num48.9%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv50.7%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   11. Applied egg-rr50.7%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if -6.60000000000000037e-190 < a < 7.2000000000000003e-304 or 7.50000000000000005e-202 < a < 2.59999999999999997e34

   1. Initial program 99.8%

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

      1. associate-*r/91.0%

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

   3. Simplified91.0%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. associate-*l/74.7%

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

      2. *-commutative74.7%

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

   6. Simplified74.7%

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

   7. Taylor expanded in x around 0 63.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg63.2%

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

   9. Simplified63.2%

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

   if 7.2000000000000003e-304 < a < 7.50000000000000005e-202

   1. Initial program 99.9%

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

      1. associate-*r/81.8%

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

   3. Simplified81.8%

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

   4. Taylor expanded in z around 0 70.3%

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

      1. neg-mul-170.3%

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

      2. distribute-neg-frac70.3%

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

   6. Simplified70.3%

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

   7. Taylor expanded in x around 0 63.0%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -160000:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-304}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

1. Split input into 5 regimes

2. if a < -2.55000000000000009e35 or -3.2e6 < a < -1.84999999999999994e-13 or 1.6e28 < a

   1. Initial program 90.4%

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

      1. associate-*r/98.9%

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

   3. Simplified98.9%

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

   4. Taylor expanded in z around inf 74.4%

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

      1. associate-*l/78.0%

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

      2. *-commutative78.0%

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

   6. Simplified78.0%

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

   7. Taylor expanded in x around inf 63.5%

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

   if -2.55000000000000009e35 < a < -3.2e6

   1. Initial program 74.7%

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

      1. associate-*r/100.0%

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

   3. Simplified100.0%

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

   4. Taylor expanded in z around inf 74.7%

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

      1. associate-*l/99.6%

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

      2. *-commutative99.6%

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

   6. Simplified99.6%

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

   7. Taylor expanded in x around 0 60.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-*l/85.5%

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

      2. *-commutative85.5%

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

      3. neg-mul-185.5%

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

      4. distribute-rgt-neg-in85.5%

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

      5. distribute-frac-neg85.5%

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

   9. Simplified85.5%

      \[\leadsto \color{blue}{z \cdot \frac{-y}{a}} \]
   10. Step-by-step derivation

       1. *-commutative85.5%

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

       2. distribute-frac-neg85.5%

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

       3. distribute-lft-neg-in85.5%

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

       4. associate-/r/85.5%

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

       5. frac-2neg85.5%

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

       6. distribute-neg-frac85.5%

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

       7. remove-double-neg85.5%

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

       8. distribute-neg-frac85.5%

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

   11. Applied egg-rr85.5%

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

   12. Taylor expanded in y around 0 60.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   13. Step-by-step derivation

       1. associate-*r/85.9%

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

       2. neg-mul-185.9%

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

       3. distribute-lft-neg-in85.9%

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

   14. Simplified85.9%

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

   if -1.84999999999999994e-13 < a < -1.1000000000000001e-189

   1. Initial program 99.8%

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

      1. associate-*r/80.5%

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

   3. Simplified80.5%

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

   4. Taylor expanded in z around 0 63.9%

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

      1. neg-mul-163.9%

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

      2. distribute-neg-frac63.9%

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

   6. Simplified63.9%

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

   7. Taylor expanded in x around 0 48.8%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   8. Step-by-step derivation

      1. *-commutative48.8%

         \[\leadsto \frac{\color{blue}{t \cdot y}}{a} \]

      2. associate-*r/48.8%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified48.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. clear-num48.9%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv50.7%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   11. Applied egg-rr50.7%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if -1.1000000000000001e-189 < a < 9.00000000000000009e-306 or 1.45e-200 < a < 1.6e28

   1. Initial program 99.8%

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

      1. associate-*r/91.0%

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

   3. Simplified91.0%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. associate-*l/74.7%

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

      2. *-commutative74.7%

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

   6. Simplified74.7%

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

   7. Taylor expanded in x around 0 63.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg63.2%

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

   9. Simplified63.2%

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

   if 9.00000000000000009e-306 < a < 1.45e-200

   1. Initial program 99.9%

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

      1. associate-*r/81.8%

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

   3. Simplified81.8%

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

   4. Taylor expanded in z around 0 70.3%

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

      1. neg-mul-170.3%

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

      2. distribute-neg-frac70.3%

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

   6. Simplified70.3%

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

   7. Taylor expanded in x around 0 63.0%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3200000:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-189}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-306}:\\ \;\;\;\;-\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-200}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;-\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

1. Split input into 4 regimes

2. if a < -3.10000000000000005e-9 or 2.09999999999999989e28 < a

   1. Initial program 89.4%

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

      1. associate-*r/99.0%

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

   3. Simplified99.0%

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

   4. Taylor expanded in z around inf 74.4%

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

      1. associate-*l/79.4%

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

      2. *-commutative79.4%

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

   6. Simplified79.4%

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

   7. Taylor expanded in x around inf 60.4%

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

   if -3.10000000000000005e-9 < a < -1.05000000000000008e-189

   1. Initial program 99.8%

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

      1. associate-*r/80.5%

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

   3. Simplified80.5%

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

   4. Taylor expanded in z around 0 63.9%

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

      1. neg-mul-163.9%

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

      2. distribute-neg-frac63.9%

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

   6. Simplified63.9%

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

   7. Taylor expanded in x around 0 48.8%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   8. Step-by-step derivation

      1. *-commutative48.8%

         \[\leadsto \frac{\color{blue}{t \cdot y}}{a} \]

      2. associate-*r/48.8%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified48.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. clear-num48.9%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv50.7%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   11. Applied egg-rr50.7%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if -1.05000000000000008e-189 < a < 1.01999999999999992e-304 or 2.9499999999999999e-201 < a < 2.09999999999999989e28

   1. Initial program 99.8%

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

      1. associate-*r/91.0%

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

   3. Simplified91.0%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. associate-*l/74.7%

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

      2. *-commutative74.7%

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

   6. Simplified74.7%

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

   7. Taylor expanded in x around 0 63.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg63.2%

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

   9. Simplified63.2%

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

   if 1.01999999999999992e-304 < a < 2.9499999999999999e-201

   1. Initial program 99.9%

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

      1. associate-*r/81.8%

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

   3. Simplified81.8%

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

   4. Taylor expanded in z around 0 70.3%

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

      1. neg-mul-170.3%

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

      2. distribute-neg-frac70.3%

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

   6. Simplified70.3%

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

   7. Taylor expanded in x around 0 63.0%

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

4. Final simplification60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-189}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-304}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-201}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -6.5999999999999998e109 or 2.5500000000000001e92 < z

   1. Initial program 92.5%

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

      1. associate-*r/86.2%

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

   3. Simplified86.2%

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

   4. Taylor expanded in z around inf 86.1%

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

      1. associate-*l/91.2%

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

      2. *-commutative91.2%

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

   6. Simplified91.2%

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

   7. Taylor expanded in x around 0 63.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-*l/67.2%

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

      2. *-commutative67.2%

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

      3. neg-mul-167.2%

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

      4. distribute-rgt-neg-in67.2%

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

      5. distribute-frac-neg67.2%

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

   9. Simplified67.2%

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

   if -6.5999999999999998e109 < z < 2.5500000000000001e92

   1. Initial program 97.4%

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

      1. associate-*r/95.6%

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

   3. Simplified95.6%

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

   4. Taylor expanded in z around 0 81.7%

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

      1. neg-mul-181.7%

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

      2. distribute-neg-frac81.7%

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

   6. Simplified81.7%

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

      1. *-commutative81.7%

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

      2. distribute-frac-neg81.7%

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

      3. cancel-sign-sub81.7%

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

      4. add-sqr-sqrt42.6%

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

      5. sqrt-unprod53.1%

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

      6. sqr-neg53.1%

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

      7. sqrt-unprod18.7%

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

      8. add-sqr-sqrt41.5%

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

      9. *-commutative41.5%

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

      10. associate-*r/40.5%

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

      11. associate-*l/42.7%

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

      12. +-commutative42.7%

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

      13. associate-*l/40.5%

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

      14. associate-*r/41.5%

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

      15. add-sqr-sqrt18.7%

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

      16. sqrt-unprod53.1%

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

      17. sqr-neg53.1%

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

      18. sqrt-unprod42.6%

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

      19. add-sqr-sqrt81.7%

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

   8. Applied egg-rr81.7%

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

4. Final simplification75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+109} \lor \neg \left(z \leq 2.55 \cdot 10^{+92}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -6.00000000000000031e109 or 1.2500000000000001e91 < z

   1. Initial program 92.5%

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

      1. associate-*r/86.2%

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

   3. Simplified86.2%

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

   4. Taylor expanded in z around inf 86.1%

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

      1. associate-*l/91.2%

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

      2. *-commutative91.2%

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

   6. Simplified91.2%

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

   7. Taylor expanded in x around 0 63.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-*l/67.2%

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

      2. *-commutative67.2%

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

      3. neg-mul-167.2%

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

      4. distribute-rgt-neg-in67.2%

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

      5. distribute-frac-neg67.2%

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

   9. Simplified67.2%

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

   if -6.00000000000000031e109 < z < 1.2500000000000001e91

   1. Initial program 97.4%

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

      1. associate-*r/95.6%

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

   3. Simplified95.6%

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

   4. Taylor expanded in z around 0 81.7%

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

      1. neg-mul-181.7%

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

      2. distribute-neg-frac81.7%

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

   6. Simplified81.7%

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

   7. Taylor expanded in x around 0 82.3%

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

      1. associate-*l/81.8%

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

   9. Applied egg-rr81.8%

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

4. Final simplification76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+109} \lor \neg \left(z \leq 1.25 \cdot 10^{+91}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -6.00000000000000031e109 or 5.09999999999999988e87 < z

   1. Initial program 92.5%

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

      1. associate-*r/86.2%

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

   3. Simplified86.2%

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

   4. Taylor expanded in z around inf 86.1%

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

      1. associate-*l/91.2%

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

      2. *-commutative91.2%

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

   6. Simplified91.2%

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

   7. Taylor expanded in x around 0 63.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   8. Step-by-step derivation

      1. associate-*l/67.2%

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

      2. *-commutative67.2%

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

      3. neg-mul-167.2%

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

      4. distribute-rgt-neg-in67.2%

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

      5. distribute-frac-neg67.2%

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

   9. Simplified67.2%

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

   if -6.00000000000000031e109 < z < 5.09999999999999988e87

   1. Initial program 97.4%

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

      1. associate-*r/95.6%

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

   3. Simplified95.6%

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

   4. Taylor expanded in z around 0 81.7%

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

      1. neg-mul-181.7%

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

      2. distribute-neg-frac81.7%

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

   6. Simplified81.7%

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

   7. Taylor expanded in x around 0 82.3%

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

4. Final simplification76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+109} \lor \neg \left(z \leq 5.1 \cdot 10^{+87}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -1.05e-32 or 2.05e83 < z

   1. Initial program 93.0%

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

      1. associate-*r/87.8%

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

   3. Simplified87.8%

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

   4. Taylor expanded in z around inf 80.1%

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

   if -1.05e-32 < z < 2.05e83

   1. Initial program 97.8%

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

      1. associate-*r/95.6%

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

   3. Simplified95.6%

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

   4. Taylor expanded in z around 0 84.5%

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

      1. neg-mul-184.5%

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

      2. distribute-neg-frac84.5%

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

   6. Simplified84.5%

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

   7. Taylor expanded in x around 0 85.9%

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

4. Final simplification83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-32} \lor \neg \left(z \leq 2.05 \cdot 10^{+83}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < -1.59999999999999988e-33 or 2.05e83 < z

   1. Initial program 93.0%

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

      1. associate-*r/87.8%

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

   3. Simplified87.8%

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

   4. Taylor expanded in z around inf 85.4%

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

      1. associate-*l/89.7%

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

      2. *-commutative89.7%

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

   6. Simplified89.7%

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

   if -1.59999999999999988e-33 < z < 2.05e83

   1. Initial program 97.8%

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

      1. associate-*r/95.6%

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

   3. Simplified95.6%

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

   4. Taylor expanded in z around 0 84.5%

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

      1. neg-mul-184.5%

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

      2. distribute-neg-frac84.5%

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

   6. Simplified84.5%

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

   7. Taylor expanded in x around 0 85.9%

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

4. Final simplification87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-33} \lor \neg \left(z \leq 2.05 \cdot 10^{+83}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

1. Split input into 2 regimes

2. if z < 2.5999999999999998e212

   1. Initial program 96.2%

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

      1. associate-*r/93.7%

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

   3. Simplified93.7%

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

   if 2.5999999999999998e212 < z

   1. Initial program 90.2%

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

      1. associate-*r/77.4%

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

   3. Simplified77.4%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. associate-*l/96.3%

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

      2. *-commutative96.3%

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

   6. Simplified96.3%

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

4. Final simplification94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.6 \cdot 10^{+212}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \]

1. Split input into 2 regimes

2. if a < -3.8000000000000002e-15 or 3.89999999999999985e-8 < a

   1. Initial program 90.1%

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

      1. associate-*r/99.0%

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

   3. Simplified99.0%

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

   4. Taylor expanded in z around inf 75.4%

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

      1. associate-*l/80.0%

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

      2. *-commutative80.0%

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

   6. Simplified80.0%

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

   7. Taylor expanded in x around inf 58.2%

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

   if -3.8000000000000002e-15 < a < 3.89999999999999985e-8

   1. Initial program 99.9%

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

      1. associate-*r/86.0%

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

   3. Simplified86.0%

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

   4. Taylor expanded in z around 0 56.5%

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

      1. neg-mul-156.5%

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

      2. distribute-neg-frac56.5%

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

   6. Simplified56.5%

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

   7. Taylor expanded in x around 0 44.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   8. Step-by-step derivation

      1. *-commutative44.7%

         \[\leadsto \frac{\color{blue}{t \cdot y}}{a} \]

      2. associate-*r/45.4%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified45.4%

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

4. Final simplification51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

1. Split input into 2 regimes

2. if a < -4.3999999999999997e-9 or 3.8499999999999998e-4 < a

   1. Initial program 90.1%

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

      1. associate-*r/99.0%

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

   3. Simplified99.0%

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

   4. Taylor expanded in z around inf 75.4%

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

      1. associate-*l/80.0%

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

      2. *-commutative80.0%

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

   6. Simplified80.0%

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

   7. Taylor expanded in x around inf 58.2%

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

   if -4.3999999999999997e-9 < a < 3.8499999999999998e-4

   1. Initial program 99.9%

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

      1. associate-*r/86.0%

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

   3. Simplified86.0%

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

   4. Taylor expanded in z around 0 56.5%

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

      1. neg-mul-156.5%

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

      2. distribute-neg-frac56.5%

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

   6. Simplified56.5%

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

   7. Taylor expanded in x around 0 44.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   8. Step-by-step derivation

      1. *-commutative44.7%

         \[\leadsto \frac{\color{blue}{t \cdot y}}{a} \]

      2. associate-*r/45.4%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified45.4%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. clear-num45.4%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv45.9%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   11. Applied egg-rr45.9%

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

4. Final simplification51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.000385:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

1. Initial program 95.5%

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

   1. associate-*l/95.9%

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

3. Simplified95.9%

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

4. Final simplification95.9%

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

1. Initial program 95.5%

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

   1. associate-*r/91.8%

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

3. Simplified91.8%

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

4. Taylor expanded in z around inf 68.8%

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

   1. associate-*l/71.3%

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

   2. *-commutative71.3%

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

6. Simplified71.3%

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

7. Taylor expanded in x around inf 35.6%

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

8. Final simplification35.6%

   \[\leadsto x \]

herbie shell --seed 2023166 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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