rsin A (should all be same)

1. Initial program 81.6%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-*r/81.7%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. *-commutative81.7%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

   3. +-commutative81.7%

      \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

3. Simplified81.7%

   \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]
4. Step-by-step derivation

   1. cos-sum99.6%

      \[\leadsto \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \cdot r \]

5. Applied egg-rr99.6%

   \[\leadsto \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \cdot r \]

6. Final simplification99.6%

   \[\leadsto \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot r \]

1. Initial program 81.6%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l*81.5%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(a + b\right)}{\sin b}}} \]

   2. +-commutative81.5%

      \[\leadsto \frac{r}{\frac{\cos \color{blue}{\left(b + a\right)}}{\sin b}} \]

3. Simplified81.5%

   \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]
4. Step-by-step derivation

   1. associate-/r/81.6%

      \[\leadsto \color{blue}{\frac{r}{\cos \left(b + a\right)} \cdot \sin b} \]

5. Applied egg-rr81.6%

   \[\leadsto \color{blue}{\frac{r}{\cos \left(b + a\right)} \cdot \sin b} \]
6. Step-by-step derivation

   1. cos-sum99.6%

      \[\leadsto \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \cdot r \]

7. Applied egg-rr99.5%

   \[\leadsto \frac{r}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \cdot \sin b \]

8. Final simplification99.5%

   \[\leadsto \sin b \cdot \frac{r}{\cos b \cdot \cos a - \sin b \cdot \sin a} \]

1. Split input into 2 regimes

2. if a < -6.5 or 5.7e14 < a

   1. Initial program 62.3%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l*62.3%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(a + b\right)}{\sin b}}} \]

      2. +-commutative62.3%

         \[\leadsto \frac{r}{\frac{\cos \color{blue}{\left(b + a\right)}}{\sin b}} \]

   3. Simplified62.3%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   4. Taylor expanded in b around 0 62.8%

      \[\leadsto \frac{r}{\frac{\color{blue}{\cos a}}{\sin b}} \]

   if -6.5 < a < 5.7e14

   1. Initial program 97.4%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-*r/97.5%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. *-commutative97.5%

         \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

      3. +-commutative97.5%

         \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

   3. Simplified97.5%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

   4. Taylor expanded in a around 0 97.5%

      \[\leadsto \frac{\sin b}{\color{blue}{\cos b}} \cdot r \]
   5. Step-by-step derivation

      1. expm1-log1p-u87.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)\right)} \cdot r \]

      2. expm1-udef50.9%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)} - 1\right)} \cdot r \]

      3. quot-tan50.9%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\tan b}\right)} - 1\right) \cdot r \]

   6. Applied egg-rr50.9%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\tan b\right)} - 1\right)} \cdot r \]
   7. Step-by-step derivation

      1. expm1-def87.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan b\right)\right)} \cdot r \]

      2. expm1-log1p97.6%

         \[\leadsto \color{blue}{\tan b} \cdot r \]

   8. Simplified97.6%

      \[\leadsto \color{blue}{\tan b} \cdot r \]
3. Recombined 2 regimes into one program.

4. Final simplification81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \lor \neg \left(a \leq 5.7 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{r}{\frac{\cos a}{\sin b}}\\ \mathbf{else}:\\ \;\;\;\;r \cdot \tan b\\ \end{array} \]

1. Split input into 3 regimes

2. if a < -6.5

   1. Initial program 67.3%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. +-commutative67.3%

         \[\leadsto \frac{r \cdot \sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified67.3%

      \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos \left(b + a\right)}} \]

   4. Taylor expanded in b around 0 67.4%

      \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a}} \]

   if -6.5 < a < 5.7e14

   1. Initial program 97.4%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-*r/97.5%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. *-commutative97.5%

         \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

      3. +-commutative97.5%

         \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

   3. Simplified97.5%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

   4. Taylor expanded in a around 0 97.5%

      \[\leadsto \frac{\sin b}{\color{blue}{\cos b}} \cdot r \]
   5. Step-by-step derivation

      1. expm1-log1p-u87.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)\right)} \cdot r \]

      2. expm1-udef50.9%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)} - 1\right)} \cdot r \]

      3. quot-tan50.9%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\tan b}\right)} - 1\right) \cdot r \]

   6. Applied egg-rr50.9%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\tan b\right)} - 1\right)} \cdot r \]
   7. Step-by-step derivation

      1. expm1-def87.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan b\right)\right)} \cdot r \]

      2. expm1-log1p97.6%

         \[\leadsto \color{blue}{\tan b} \cdot r \]

   8. Simplified97.6%

      \[\leadsto \color{blue}{\tan b} \cdot r \]

   if 5.7e14 < a

   1. Initial program 55.6%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l*55.6%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(a + b\right)}{\sin b}}} \]

      2. +-commutative55.6%

         \[\leadsto \frac{r}{\frac{\cos \color{blue}{\left(b + a\right)}}{\sin b}} \]

   3. Simplified55.6%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   4. Taylor expanded in b around 0 56.6%

      \[\leadsto \frac{r}{\frac{\color{blue}{\cos a}}{\sin b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5:\\ \;\;\;\;\frac{\sin b \cdot r}{\cos a}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+14}:\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;\frac{r}{\frac{\cos a}{\sin b}}\\ \end{array} \]

1. Initial program 81.6%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l*81.5%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(a + b\right)}{\sin b}}} \]

   2. +-commutative81.5%

      \[\leadsto \frac{r}{\frac{\cos \color{blue}{\left(b + a\right)}}{\sin b}} \]

3. Simplified81.5%

   \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]
4. Step-by-step derivation

   1. associate-/r/81.6%

      \[\leadsto \color{blue}{\frac{r}{\cos \left(b + a\right)} \cdot \sin b} \]

5. Applied egg-rr81.6%

   \[\leadsto \color{blue}{\frac{r}{\cos \left(b + a\right)} \cdot \sin b} \]

6. Final simplification81.6%

   \[\leadsto \sin b \cdot \frac{r}{\cos \left(b + a\right)} \]

1. Initial program 81.6%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-*r/81.7%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. *-commutative81.7%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

   3. +-commutative81.7%

      \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

3. Simplified81.7%

   \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

4. Final simplification81.7%

   \[\leadsto r \cdot \frac{\sin b}{\cos \left(b + a\right)} \]

1. Split input into 2 regimes

2. if b < -4.00000000000000033e-5 or 7.19999999999999967e-6 < b

   1. Initial program 60.5%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-*r/60.6%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. *-commutative60.6%

         \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

      3. +-commutative60.6%

         \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

   3. Simplified60.6%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

   4. Taylor expanded in a around 0 60.9%

      \[\leadsto \frac{\sin b}{\color{blue}{\cos b}} \cdot r \]
   5. Step-by-step derivation

      1. expm1-log1p-u47.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)\right)} \cdot r \]

      2. expm1-udef46.9%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)} - 1\right)} \cdot r \]

      3. quot-tan46.9%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\tan b}\right)} - 1\right) \cdot r \]

   6. Applied egg-rr46.9%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\tan b\right)} - 1\right)} \cdot r \]
   7. Step-by-step derivation

      1. expm1-def47.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan b\right)\right)} \cdot r \]

      2. expm1-log1p60.9%

         \[\leadsto \color{blue}{\tan b} \cdot r \]

   8. Simplified60.9%

      \[\leadsto \color{blue}{\tan b} \cdot r \]

   if -4.00000000000000033e-5 < b < 7.19999999999999967e-6

   1. Initial program 99.1%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-*r/99.1%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. *-commutative99.1%

         \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

      3. +-commutative99.1%

         \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

   3. Simplified99.1%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

   4. Taylor expanded in b around 0 99.1%

      \[\leadsto \color{blue}{\frac{b}{\cos a}} \cdot r \]
3. Recombined 2 regimes into one program.

4. Final simplification81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-5} \lor \neg \left(b \leq 7.2 \cdot 10^{-6}\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;r \cdot \frac{b}{\cos a}\\ \end{array} \]

1. Split input into 2 regimes

2. if b < -9.2e-6 or 5.09999999999999996e-5 < b

   1. Initial program 60.5%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-*r/60.6%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. *-commutative60.6%

         \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

      3. +-commutative60.6%

         \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

   3. Simplified60.6%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

   4. Taylor expanded in a around 0 60.9%

      \[\leadsto \frac{\sin b}{\color{blue}{\cos b}} \cdot r \]
   5. Step-by-step derivation

      1. expm1-log1p-u47.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)\right)} \cdot r \]

      2. expm1-udef46.9%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)} - 1\right)} \cdot r \]

      3. quot-tan46.9%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\tan b}\right)} - 1\right) \cdot r \]

   6. Applied egg-rr46.9%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\tan b\right)} - 1\right)} \cdot r \]
   7. Step-by-step derivation

      1. expm1-def47.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan b\right)\right)} \cdot r \]

      2. expm1-log1p60.9%

         \[\leadsto \color{blue}{\tan b} \cdot r \]

   8. Simplified60.9%

      \[\leadsto \color{blue}{\tan b} \cdot r \]

   if -9.2e-6 < b < 5.09999999999999996e-5

   1. Initial program 99.1%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-*r/99.1%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. *-commutative99.1%

         \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

      3. +-commutative99.1%

         \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

   3. Simplified99.1%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

   4. Taylor expanded in b around 0 99.1%

      \[\leadsto \color{blue}{\frac{b \cdot r}{\cos a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-6} \lor \neg \left(b \leq 5.1 \cdot 10^{-5}\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot r}{\cos a}\\ \end{array} \]

1. Initial program 81.6%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-*r/81.7%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. *-commutative81.7%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

   3. +-commutative81.7%

      \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

3. Simplified81.7%

   \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

4. Taylor expanded in a around 0 63.3%

   \[\leadsto \frac{\sin b}{\color{blue}{\cos b}} \cdot r \]
5. Step-by-step derivation

   1. expm1-log1p-u57.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)\right)} \cdot r \]

   2. expm1-udef36.1%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\sin b}{\cos b}\right)} - 1\right)} \cdot r \]

   3. quot-tan36.1%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\tan b}\right)} - 1\right) \cdot r \]

6. Applied egg-rr36.1%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\tan b\right)} - 1\right)} \cdot r \]
7. Step-by-step derivation

   1. expm1-def57.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan b\right)\right)} \cdot r \]

   2. expm1-log1p63.3%

      \[\leadsto \color{blue}{\tan b} \cdot r \]

8. Simplified63.3%

   \[\leadsto \color{blue}{\tan b} \cdot r \]

9. Final simplification63.3%

   \[\leadsto r \cdot \tan b \]

1. Initial program 81.6%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l*81.5%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(a + b\right)}{\sin b}}} \]

   2. +-commutative81.5%

      \[\leadsto \frac{r}{\frac{\cos \color{blue}{\left(b + a\right)}}{\sin b}} \]

3. Simplified81.5%

   \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

4. Taylor expanded in b around 0 57.6%

   \[\leadsto \frac{r}{\color{blue}{b \cdot \left(-0.5 \cdot \cos a - -0.16666666666666666 \cdot \cos a\right) + \left(-1 \cdot \sin a + \frac{\cos a}{b}\right)}} \]
5. Step-by-step derivation

   1. fma-def57.6%

      \[\leadsto \frac{r}{\color{blue}{\mathsf{fma}\left(b, -0.5 \cdot \cos a - -0.16666666666666666 \cdot \cos a, -1 \cdot \sin a + \frac{\cos a}{b}\right)}} \]

   2. distribute-rgt-out--57.6%

      \[\leadsto \frac{r}{\mathsf{fma}\left(b, \color{blue}{\cos a \cdot \left(-0.5 - -0.16666666666666666\right)}, -1 \cdot \sin a + \frac{\cos a}{b}\right)} \]

   3. metadata-eval57.6%

      \[\leadsto \frac{r}{\mathsf{fma}\left(b, \cos a \cdot \color{blue}{-0.3333333333333333}, -1 \cdot \sin a + \frac{\cos a}{b}\right)} \]

   4. neg-mul-157.6%

      \[\leadsto \frac{r}{\mathsf{fma}\left(b, \cos a \cdot -0.3333333333333333, \color{blue}{\left(-\sin a\right)} + \frac{\cos a}{b}\right)} \]

   5. +-commutative57.6%

      \[\leadsto \frac{r}{\mathsf{fma}\left(b, \cos a \cdot -0.3333333333333333, \color{blue}{\frac{\cos a}{b} + \left(-\sin a\right)}\right)} \]

   6. unsub-neg57.6%

      \[\leadsto \frac{r}{\mathsf{fma}\left(b, \cos a \cdot -0.3333333333333333, \color{blue}{\frac{\cos a}{b} - \sin a}\right)} \]

6. Simplified57.6%

   \[\leadsto \frac{r}{\color{blue}{\mathsf{fma}\left(b, \cos a \cdot -0.3333333333333333, \frac{\cos a}{b} - \sin a\right)}} \]

7. Taylor expanded in a around 0 38.7%

   \[\leadsto \frac{r}{\color{blue}{-0.3333333333333333 \cdot b + \frac{1}{b}}} \]

8. Final simplification38.7%

   \[\leadsto \frac{r}{b \cdot -0.3333333333333333 + \frac{1}{b}} \]

1. Initial program 81.6%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-*r/81.7%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. *-commutative81.7%

      \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(a + b\right)} \cdot r} \]

   3. +-commutative81.7%

      \[\leadsto \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \cdot r \]

3. Simplified81.7%

   \[\leadsto \color{blue}{\frac{\sin b}{\cos \left(b + a\right)} \cdot r} \]

4. Taylor expanded in b around 0 56.2%

   \[\leadsto \color{blue}{\frac{b}{\cos a}} \cdot r \]

5. Taylor expanded in a around 0 37.7%

   \[\leadsto \color{blue}{b} \cdot r \]

6. Final simplification37.7%

   \[\leadsto b \cdot r \]

herbie shell --seed 2023167 
(FPCore (r a b)
  :name "rsin A (should all be same)"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))