Error

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 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. Applied simplify0.2

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

9. Applied unpow-prod-down0.2

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

11. Applied add-cbrt-cube0.2

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

12. Applied add-cbrt-cube0.2

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

13. Applied cbrt-unprod0.2

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

14. Applied add-cbrt-cube0.2

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

15. Applied add-cbrt-cube0.2

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

16. Applied cbrt-unprod0.2

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

17. Applied cbrt-unprod0.2

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

18. Applied simplify0.2

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

Runtime

Time bar (total: 56.2s)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' 
(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))))