Error

Derivation

1. Initial program 0.2

   \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]

2. Simplified0.1

   \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
3. Using strategy rm

4. Applied tan-quot0.2

   \[\leadsto \frac{1}{\sin B} - \frac{x}{\color{blue}{\frac{\sin B}{\cos B}}}\]

5. Applied associate-/r/0.2

   \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x}{\sin B} \cdot \cos B}\]
6. Using strategy rm

7. Applied *-un-lft-identity0.2

   \[\leadsto \frac{1}{\sin B} - \frac{x}{\color{blue}{1 \cdot \sin B}} \cdot \cos B\]

8. Applied associate-/r*0.2

   \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{\frac{x}{1}}{\sin B}} \cdot \cos B\]

9. Applied associate-*l/0.2

   \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{\frac{x}{1} \cdot \cos B}{\sin B}}\]

10. Applied *-un-lft-identity0.2

    \[\leadsto \frac{1}{\color{blue}{1 \cdot \sin B}} - \frac{\frac{x}{1} \cdot \cos B}{\sin B}\]

11. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\sin B}} - \frac{\frac{x}{1} \cdot \cos B}{\sin B}\]

12. Applied sub-div0.2

    \[\leadsto \color{blue}{\frac{\frac{1}{1} - \frac{x}{1} \cdot \cos B}{\sin B}}\]

13. Simplified0.2

    \[\leadsto \frac{\color{blue}{1 - x \cdot \cos B}}{\sin B}\]

14. Final simplification0.2

    \[\leadsto \frac{1 - \cos B \cdot x}{\sin B}\]

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))