Error

Derivation

1. Initial program 13.1

   \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
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-exp0.3

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

7. Applied add-cube-cbrt0.4

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

8. Applied flip--0.4

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

9. Applied associate-/r/0.4

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

10. Applied prod-diff0.4

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

11. Simplified0.3

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

12. Simplified0.3

    \[\leadsto \log \left(e^{x + \left(\left(\frac{(\left(\tan z + \tan y\right) \cdot \left(\tan y \cdot \tan z\right) + \left(\tan z + \tan y\right))_*}{1 - \left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)} - \tan a\right) + \color{blue}{0}\right)}\right)\]

13. Final simplification0.3

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

Reproduce

herbie shell --seed 2018360 +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))))

Details

Time bar (total: 48.2s)Debug log