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Derivation

1. Initial program 13.0

   \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
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 tan-quot0.2

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

6. Applied associate-*r/0.2

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

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

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

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

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

10. Applied distribute-lft-out0.2

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

11. Applied associate-/l*0.2

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

12. Final simplification0.2

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018249 +o rules:numerics
(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))))