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Derivation

1. Initial program 13.3

   \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
2. Using strategy rm

3. Applied tan-sum0.2

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right)\]
4. Using strategy rm

5. Applied clear-num0.2

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right)\]
6. Using strategy rm

7. Applied tan-quot0.2

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

8. Applied frac-sub0.2

   \[\leadsto x + \color{blue}{\frac{1 \cdot \cos a - \frac{1 - \tan y \cdot \tan z}{\tan y + \tan z} \cdot \sin a}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z} \cdot \cos a}}\]

9. Simplified0.2

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

10. Final simplification0.2

    \[\leadsto x + \frac{\cos a - \frac{\sin a}{\tan y + \tan z} \cdot \left(1 - \tan z \cdot \tan y\right)}{\frac{1 - \tan z \cdot \tan y}{\tan y + \tan z} \cdot \cos a}\]

Runtime

Time bar (total: 37.3s)Debug logProfile

herbie shell --seed 2018296 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.751224e+308)) (or (<= -1.776707e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.751224e+308)))
  (+ x (- (tan (+ y z)) (tan a))))