Linear.Quaternion:$ccosh from linear-1.19.1.3

1. Initial program 85.6%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-*l/99.9%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

3. Simplified99.9%

   \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

4. Final simplification99.9%

   \[\leadsto \frac{\sin x}{x} \cdot \sinh y \]

1. Split input into 3 regimes

2. if (sinh.f64 y) < -inf.0

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   4. Taylor expanded in x around 0 86.5%

      \[\leadsto \color{blue}{1} \cdot \sinh y \]

   if -inf.0 < (sinh.f64 y) < 4.9999999999999997e104

   1. Initial program 72.5%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 71.4%

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

      1. *-commutative71.4%

         \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

      2. associate-/l*98.1%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   6. Simplified98.1%

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

      1. associate-/r/98.7%

         \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot y} \]

   8. Applied egg-rr98.7%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot y} \]

   if 4.9999999999999997e104 < (sinh.f64 y)

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   4. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{\left(1 + -0.16666666666666666 \cdot {x}^{2}\right)} \cdot \sinh y \]
   5. Step-by-step derivation

      1. *-commutative81.4%

         \[\leadsto \left(1 + \color{blue}{{x}^{2} \cdot -0.16666666666666666}\right) \cdot \sinh y \]

      2. unpow281.4%

         \[\leadsto \left(1 + \color{blue}{\left(x \cdot x\right)} \cdot -0.16666666666666666\right) \cdot \sinh y \]

   6. Simplified81.4%

      \[\leadsto \color{blue}{\left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)} \cdot \sinh y \]
3. Recombined 3 regimes into one program.

4. Final simplification91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 5 \cdot 10^{+104}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \end{array} \]

1. Initial program 85.6%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-*r/99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Final simplification99.9%

   \[\leadsto \sin x \cdot \frac{\sinh y}{x} \]

1. Split input into 2 regimes

2. if y < -4.8000000000000001e-5 or 2.4e9 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   4. Taylor expanded in x around 0 78.5%

      \[\leadsto \color{blue}{1} \cdot \sinh y \]

   if -4.8000000000000001e-5 < y < 2.4e9

   1. Initial program 72.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 70.9%

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

      1. *-commutative70.9%

         \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

      2. associate-/l*97.4%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   6. Simplified97.4%

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

      1. clear-num97.4%

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

      2. associate-/r/97.3%

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

      3. clear-num98.0%

         \[\leadsto \color{blue}{\frac{y}{x}} \cdot \sin x \]

   8. Applied egg-rr98.0%

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

4. Final simplification88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;y \leq 2400000000:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

1. Split input into 2 regimes

2. if y < -1.06e-4 or 2.4e9 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   4. Taylor expanded in x around 0 78.5%

      \[\leadsto \color{blue}{1} \cdot \sinh y \]

   if -1.06e-4 < y < 2.4e9

   1. Initial program 72.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 70.9%

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

      1. *-commutative70.9%

         \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

      2. associate-/l*97.4%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   6. Simplified97.4%

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

      1. associate-/r/98.0%

         \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot y} \]

   8. Applied egg-rr98.0%

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

4. Final simplification88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000106:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;y \leq 2400000000:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

1. Split input into 2 regimes

2. if y < -4.0000000000000001e-8 or 2.4e9 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*l/100.0%

         \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y} \]

   4. Taylor expanded in x around 0 78.5%

      \[\leadsto \color{blue}{1} \cdot \sinh y \]

   if -4.0000000000000001e-8 < y < 2.4e9

   1. Initial program 72.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
   4. Step-by-step derivation

      1. associate-*r/72.7%

         \[\leadsto \color{blue}{\frac{\sin x \cdot \sinh y}{x}} \]

      2. associate-/l*99.2%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}} \]

      3. clear-num99.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{\sinh y}}{\sin x}}} \]

   5. Applied egg-rr99.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{\sinh y}}{\sin x}}} \]

   6. Taylor expanded in y around 0 70.3%

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

      1. associate-/r*97.4%

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

   8. Simplified97.4%

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

   9. Taylor expanded in x around 0 74.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{{x}^{2}}{y}}} \]
   10. Step-by-step derivation

       1. unpow274.9%

          \[\leadsto \frac{1}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{\color{blue}{x \cdot x}}{y}} \]

   11. Simplified74.9%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{x \cdot x}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;y \leq 2400000000:\\ \;\;\;\;\frac{1}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{x \cdot x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

1. Split input into 3 regimes

2. if y < -660

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 4.3%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 13.3%

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

   if -660 < y < 0.0051999999999999998

   1. Initial program 72.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
   4. Step-by-step derivation

      1. associate-*r/72.1%

         \[\leadsto \color{blue}{\frac{\sin x \cdot \sinh y}{x}} \]

      2. associate-/l*99.2%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}} \]

      3. clear-num99.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{\sinh y}}{\sin x}}} \]

   5. Applied egg-rr99.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{\sinh y}}{\sin x}}} \]

   6. Taylor expanded in y around 0 71.5%

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

      1. associate-/r*99.2%

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

   8. Simplified99.2%

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

   9. Taylor expanded in x around 0 76.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{{x}^{2}}{y}}} \]
   10. Step-by-step derivation

       1. unpow276.6%

          \[\leadsto \frac{1}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{\color{blue}{x \cdot x}}{y}} \]

   11. Simplified76.6%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{x \cdot x}{y}}} \]

   if 0.0051999999999999998 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.0%

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

      1. *-commutative5.0%

         \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

      2. associate-/l*33.5%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   6. Simplified33.5%

      \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   7. Taylor expanded in x around 0 23.0%

      \[\leadsto \color{blue}{y + -0.16666666666666666 \cdot \left(y \cdot {x}^{2}\right)} \]
   8. Step-by-step derivation

      1. unpow223.0%

         \[\leadsto y + -0.16666666666666666 \cdot \left(y \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

   9. Simplified23.0%

      \[\leadsto \color{blue}{y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -660:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq 0.0052:\\ \;\;\;\;\frac{1}{\frac{1}{y} + 0.16666666666666666 \cdot \frac{x \cdot x}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \end{array} \]

1. Split input into 3 regimes

2. if y < -1e94

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 20.1%

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

   if -1e94 < y < 0.0051999999999999998

   1. Initial program 75.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 62.7%

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

      1. *-commutative62.7%

         \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

      2. associate-/l*89.2%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   6. Simplified89.2%

      \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   7. Taylor expanded in x around 0 52.4%

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

   if 0.0051999999999999998 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.0%

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

      1. *-commutative5.0%

         \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

      2. associate-/l*33.5%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   6. Simplified33.5%

      \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   7. Taylor expanded in x around 0 23.0%

      \[\leadsto \color{blue}{y + -0.16666666666666666 \cdot \left(y \cdot {x}^{2}\right)} \]
   8. Step-by-step derivation

      1. +-commutative23.0%

         \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left(y \cdot {x}^{2}\right) + y} \]

      2. *-commutative23.0%

         \[\leadsto -0.16666666666666666 \cdot \color{blue}{\left({x}^{2} \cdot y\right)} + y \]

      3. associate-*r*23.0%

         \[\leadsto \color{blue}{\left(-0.16666666666666666 \cdot {x}^{2}\right) \cdot y} + y \]

      4. *-commutative23.0%

         \[\leadsto \color{blue}{\left({x}^{2} \cdot -0.16666666666666666\right)} \cdot y + y \]

      5. unpow223.0%

         \[\leadsto \left(\color{blue}{\left(x \cdot x\right)} \cdot -0.16666666666666666\right) \cdot y + y \]

      6. associate-*r*23.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot -0.16666666666666666\right)\right)} \cdot y + y \]

      7. *-lft-identity23.0%

         \[\leadsto \left(x \cdot \left(x \cdot -0.16666666666666666\right)\right) \cdot y + \color{blue}{1 \cdot y} \]

      8. distribute-rgt-in23.0%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot \left(x \cdot -0.16666666666666666\right) + 1\right)} \]

      9. fma-udef23.0%

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(x, x \cdot -0.16666666666666666, 1\right)} \]

   9. Simplified23.0%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(x, x \cdot -0.16666666666666666, 1\right)} \]

   10. Taylor expanded in x around inf 20.8%

       \[\leadsto y \cdot \color{blue}{\left(-0.16666666666666666 \cdot {x}^{2}\right)} \]
   11. Step-by-step derivation

       1. unpow220.8%

          \[\leadsto y \cdot \left(-0.16666666666666666 \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. *-commutative20.8%

          \[\leadsto y \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot -0.16666666666666666\right)} \]

       3. associate-*l*20.8%

          \[\leadsto y \cdot \color{blue}{\left(x \cdot \left(x \cdot -0.16666666666666666\right)\right)} \]

   12. Simplified20.8%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot \left(x \cdot -0.16666666666666666\right)\right)} \]

   13. Taylor expanded in y around 0 20.8%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left(y \cdot {x}^{2}\right)} \]
   14. Step-by-step derivation

       1. unpow220.8%

          \[\leadsto -0.16666666666666666 \cdot \left(y \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

   15. Simplified20.8%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq 0.0052:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \end{array} \]

1. Split input into 2 regimes

2. if x < -3.3e193 or 5.0000000000000004e96 < x

   1. Initial program 99.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 45.8%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 21.2%

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

   if -3.3e193 < x < 5.0000000000000004e96

   1. Initial program 81.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 37.5%

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

      1. *-commutative37.5%

         \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

      2. associate-/l*74.6%

         \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   6. Simplified74.6%

      \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

   7. Taylor expanded in x around 0 42.0%

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

4. Final simplification37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+193} \lor \neg \left(x \leq 5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

1. Initial program 85.6%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-*r/99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Taylor expanded in y around 0 39.5%

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

   1. *-commutative39.5%

      \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

   2. associate-/l*67.7%

      \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

6. Simplified67.7%

   \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

7. Taylor expanded in x around 0 38.9%

   \[\leadsto \color{blue}{y + -0.16666666666666666 \cdot \left(y \cdot {x}^{2}\right)} \]
8. Step-by-step derivation

   1. unpow238.9%

      \[\leadsto y + -0.16666666666666666 \cdot \left(y \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

9. Simplified38.9%

   \[\leadsto \color{blue}{y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)} \]

10. Final simplification38.9%

    \[\leadsto y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right) \]

1. Initial program 85.6%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-*r/99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Taylor expanded in y around 0 39.5%

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

   1. *-commutative39.5%

      \[\leadsto \frac{\color{blue}{\sin x \cdot y}}{x} \]

   2. associate-/l*67.7%

      \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

6. Simplified67.7%

   \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{y}}} \]

7. Taylor expanded in x around 0 33.0%

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

8. Final simplification33.0%

   \[\leadsto y \]

herbie shell --seed 2023167 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))