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Derivation

1. Initial program 0.2

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

2. Initial simplification0.1

   \[\leadsto \frac{1}{\sin B} - \frac{x}{\tan B}\]
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 associate-*l/0.2

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

8. Applied sub-div0.2

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

9. Final simplification0.2

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))

Details

Time bar (total: 13.0s)Debug log