Error

Derivation

1. Initial program 13.2

   \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
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 add-log-exp0.2

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

6. Applied add-log-exp0.3

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

7. Applied diff-log0.3

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

8. Applied add-log-exp0.3

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

9. Applied sum-log0.3

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

10. Simplified0.3

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

12. Applied *-un-lft-identity0.3

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

13. Applied *-un-lft-identity0.3

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

14. Applied distribute-lft-out--0.3

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

15. Applied *-un-lft-identity0.3

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

16. Applied distribute-lft-out0.3

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

17. Applied exp-prod0.3

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

18. Simplified0.3

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

19. Final simplification0.3

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

Reproduce

herbie shell --seed 2019090 
(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))))