1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -0.0050000000000000001

   1. Initial program 76.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative76.6%

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

   3. Simplified76.6%

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

   4. Taylor expanded in y around inf 76.4%

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

      1. *-commutative76.4%

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

      2. *-commutative76.4%

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

      3. times-frac94.9%

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

      4. +-commutative94.9%

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

      5. *-commutative94.9%

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

   6. Simplified94.9%

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

   if -0.0050000000000000001 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1e266

   1. Initial program 97.9%

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

   if 1e266 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 18.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative18.6%

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

   3. Simplified18.6%

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

   4. Taylor expanded in z around inf 81.3%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq -0.005:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{+266}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

1. Split input into 3 regimes

2. if x < -1.25e-39 or 1.05e-95 < x < 2.6e-75 or 1.79999999999999987e-20 < x

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative89.5%

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

   3. Simplified89.5%

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

   4. Taylor expanded in z around inf 66.8%

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

   5. Taylor expanded in x around inf 84.2%

      \[\leadsto \color{blue}{1} \]

   if -1.25e-39 < x < 1.05e-95

   1. Initial program 88.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative88.0%

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

   3. Simplified88.0%

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

   4. Taylor expanded in z around inf 77.9%

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

   5. Taylor expanded in x around 0 64.2%

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

   if 2.6e-75 < x < 1.79999999999999987e-20

   1. Initial program 83.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative83.5%

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

   3. Simplified83.5%

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

   4. Taylor expanded in y around inf 67.4%

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

      1. times-frac67.7%

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

      2. +-commutative67.7%

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

   6. Simplified67.7%

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

   7. Taylor expanded in x around 0 67.7%

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

4. Final simplification75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-95}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

1. Split input into 2 regimes

2. if t < -9.30000000000000052e-138 or 7.0000000000000004e-98 < t

   1. Initial program 87.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative87.1%

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

   3. Simplified87.1%

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

   4. Taylor expanded in z around inf 84.3%

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

   if -9.30000000000000052e-138 < t < 7.0000000000000004e-98

   1. Initial program 92.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative92.3%

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

   3. Simplified92.3%

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

   4. Taylor expanded in x around -inf 62.6%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]
   5. Step-by-step derivation

      1. mul-1-neg62.6%

         \[\leadsto 1 + \color{blue}{\left(-\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)} \]

      2. unsub-neg62.6%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out--62.6%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot \left(y - t\right)}}{{x}^{2}} \]

      4. unpow262.6%

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

      5. times-frac70.1%

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

   6. Simplified70.1%

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

      1. *-commutative70.1%

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

      2. clear-num70.2%

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

      3. frac-2neg70.2%

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

      4. frac-times70.2%

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

      5. *-un-lft-identity70.2%

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

   8. Applied egg-rr70.2%

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

      1. *-commutative70.2%

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

      2. associate-*r/70.2%

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

      3. associate-/l*62.6%

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

      4. *-commutative62.6%

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

      5. associate-/l*70.2%

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

      6. *-commutative70.2%

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

   10. Simplified70.2%

       \[\leadsto 1 - \color{blue}{\frac{y - t}{\frac{x \cdot \left(-x\right)}{-z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.3 \cdot 10^{-138} \lor \neg \left(t \leq 7 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{t - y}{\frac{x \cdot \left(-x\right)}{-z}}\\ \end{array} \]

1. Split input into 2 regimes

2. if t < -6.20000000000000029e-105 or 8.00000000000000041e-101 < t

   1. Initial program 86.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative86.8%

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

   3. Simplified86.8%

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

   4. Taylor expanded in z around inf 84.0%

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

   if -6.20000000000000029e-105 < t < 8.00000000000000041e-101

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative92.7%

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

   3. Simplified92.7%

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

   4. Taylor expanded in t around 0 81.7%

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

      1. +-commutative81.7%

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

      2. mul-1-neg81.7%

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

      3. unsub-neg81.7%

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

      4. associate-/l*85.3%

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

      5. +-commutative85.3%

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

   6. Simplified85.3%

      \[\leadsto \color{blue}{\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-105} \lor \neg \left(t \leq 8 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

1. Split input into 2 regimes

2. if t < -1.30000000000000002e-135 or 9.20000000000000002e-98 < t

   1. Initial program 87.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative87.1%

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

   3. Simplified87.1%

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

   4. Taylor expanded in z around inf 84.3%

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

   if -1.30000000000000002e-135 < t < 9.20000000000000002e-98

   1. Initial program 92.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative92.3%

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

   3. Simplified92.3%

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

   4. Taylor expanded in x around -inf 62.6%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]
   5. Step-by-step derivation

      1. mul-1-neg62.6%

         \[\leadsto 1 + \color{blue}{\left(-\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)} \]

      2. unsub-neg62.6%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out--62.6%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot \left(y - t\right)}}{{x}^{2}} \]

      4. unpow262.6%

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

      5. times-frac70.1%

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

   6. Simplified70.1%

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

      1. clear-num70.2%

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

      2. frac-times70.2%

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

      3. *-un-lft-identity70.2%

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

   8. Applied egg-rr70.2%

      \[\leadsto 1 - \color{blue}{\frac{y - t}{\frac{x}{z} \cdot x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-135} \lor \neg \left(t \leq 9.2 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{t - y}{x \cdot \frac{x}{z}}\\ \end{array} \]

1. Split input into 2 regimes

2. if t < -1.85000000000000003e-139 or 4.9999999999999995e-97 < t

   1. Initial program 87.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative87.1%

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

   3. Simplified87.1%

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

   4. Taylor expanded in z around inf 84.3%

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

   if -1.85000000000000003e-139 < t < 4.9999999999999995e-97

   1. Initial program 92.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative92.3%

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

   3. Simplified92.3%

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

   4. Taylor expanded in x around -inf 62.6%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]
   5. Step-by-step derivation

      1. mul-1-neg62.6%

         \[\leadsto 1 + \color{blue}{\left(-\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)} \]

      2. unsub-neg62.6%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out--62.6%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot \left(y - t\right)}}{{x}^{2}} \]

      4. unpow262.6%

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

      5. times-frac70.1%

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

   6. Simplified70.1%

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

   7. Taylor expanded in y around inf 70.1%

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

   8. Taylor expanded in z around 0 62.6%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{{x}^{2}}} \]
   9. Step-by-step derivation

      1. *-commutative62.6%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot y}}{{x}^{2}} \]

      2. unpow262.6%

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

      3. associate-*l/70.2%

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

      4. *-commutative70.2%

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

   10. Simplified70.2%

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

       1. clear-num70.2%

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

       2. un-div-inv70.2%

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

   12. Applied egg-rr70.2%

       \[\leadsto 1 - \color{blue}{\frac{y}{\frac{x \cdot x}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-139} \lor \neg \left(t \leq 5 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \]

1. Split input into 2 regimes

2. if x < -1.04999999999999997e-39 or 9e-103 < x < 2.45e-83 or 4.49999999999999968e-21 < x

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative89.5%

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

   3. Simplified89.5%

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

   4. Taylor expanded in z around inf 66.8%

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

   5. Taylor expanded in x around inf 84.2%

      \[\leadsto \color{blue}{1} \]

   if -1.04999999999999997e-39 < x < 9e-103 or 2.45e-83 < x < 4.49999999999999968e-21

   1. Initial program 87.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative87.5%

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

   3. Simplified87.5%

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

   4. Taylor expanded in z around inf 74.9%

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

   5. Taylor expanded in x around 0 62.7%

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

4. Final simplification75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-103}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

1. Split input into 2 regimes

2. if x < -4.50000000000000008e-138 or 6.20000000000000004e-97 < x

   1. Initial program 88.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative88.9%

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

   3. Simplified88.9%

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

   4. Taylor expanded in z around inf 65.4%

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

   5. Taylor expanded in x around inf 69.9%

      \[\leadsto \color{blue}{1} \]

   if -4.50000000000000008e-138 < x < 6.20000000000000004e-97

   1. Initial program 88.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative88.0%

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

   3. Simplified88.0%

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

   4. Taylor expanded in t around inf 18.7%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   5. Step-by-step derivation

      1. +-commutative18.7%

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

   6. Simplified18.7%

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

   7. Taylor expanded in x around 0 18.7%

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

4. Final simplification55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-138}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

1. Initial program 88.6%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Step-by-step derivation

   1. *-commutative88.6%

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

3. Simplified88.6%

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

4. Taylor expanded in z around inf 70.3%

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

5. Taylor expanded in x around inf 51.1%

   \[\leadsto \color{blue}{1} \]

6. Final simplification51.1%

   \[\leadsto 1 \]

herbie shell --seed 2023166 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))