Error

Try it out

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 flip3--0.2

   \[\leadsto x + \left(\frac{\tan y + \tan z}{\color{blue}{\frac{{1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}}{1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)}}} - \tan a\right)\]

6. Applied associate-/r/0.2

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{{1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)\right)} - \tan a\right)\]

7. Simplified0.2

   \[\leadsto x + \left(\frac{\tan y + \tan z}{{1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}} \cdot \color{blue}{\left(\left(1 + \tan z \cdot \tan y\right) + \left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right)} - \tan a\right)\]

8. Final simplification0.2

   \[\leadsto \left(\frac{\tan y + \tan z}{1 - {\left(\tan z \cdot \tan y\right)}^{3}} \cdot \left(\left(1 + \tan z \cdot \tan y\right) + \left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right) - \tan a\right) + x\]

Runtime

Time bar (total: 2.1m)Debug logProfile

herbie shell --seed 2018263 
(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))))