Error

Derivation

1. Split input into 2 regimes.

2. if x < -0.01003190387316039 or 7.988163388129748 < x

   1. Initial program 0.0

      \[\frac{x - \sin x}{x - \tan x}\]
   2. Using strategy rm

   3. Applied div-sub 0.0

      \[\leadsto \color{blue}{\frac{x}{x - \tan x} - \frac{\sin x}{x - \tan x}}\]
   4. Using strategy rm

   5. Applied add-log-exp 0.1

      \[\leadsto \frac{x}{x - \tan x} - \color{blue}{\log \left(e^{\frac{\sin x}{x - \tan x}}\right)}\]

   6. Applied add-log-exp 0.1

      \[\leadsto \color{blue}{\log \left(e^{\frac{x}{x - \tan x}}\right)} - \log \left(e^{\frac{\sin x}{x - \tan x}}\right)\]

   7. Applied diff-log 0.1

      \[\leadsto \color{blue}{\log \left(\frac{e^{\frac{x}{x - \tan x}}}{e^{\frac{\sin x}{x - \tan x}}}\right)}\]

   8. Applied simplify 0.0

      \[\leadsto \log \color{blue}{\left(e^{\frac{x}{x - \tan x} - \frac{\sin x}{x - \tan x}}\right)}\]

   if -0.01003190387316039 < x < 7.988163388129748

   1. Initial program 62.6

      \[\frac{x - \sin x}{x - \tan x}\]
   2. Using strategy rm

   3. Applied div-sub 62.5

      \[\leadsto \color{blue}{\frac{x}{x - \tan x} - \frac{\sin x}{x - \tan x}}\]
   4. Using strategy rm

   5. Applied add-log-exp 63.5

      \[\leadsto \frac{x}{x - \tan x} - \color{blue}{\log \left(e^{\frac{\sin x}{x - \tan x}}\right)}\]

   6. Applied add-log-exp 63.5

      \[\leadsto \color{blue}{\log \left(e^{\frac{x}{x - \tan x}}\right)} - \log \left(e^{\frac{\sin x}{x - \tan x}}\right)\]

   7. Applied diff-log 63.5

      \[\leadsto \color{blue}{\log \left(\frac{e^{\frac{x}{x - \tan x}}}{e^{\frac{\sin x}{x - \tan x}}}\right)}\]

   8. Applied simplify 62.5

      \[\leadsto \log \color{blue}{\left(e^{\frac{x}{x - \tan x} - \frac{\sin x}{x - \tan x}}\right)}\]

   9. Applied taylor 0.0

      \[\leadsto \log \left(e^{\frac{9}{40} \cdot {x}^2 - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right)}\right)\]

   10. Taylor expanded around 0 0.0

       \[\leadsto \log \left(e^{\color{blue}{\frac{9}{40} \cdot {x}^2 - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right)}}\right)\]

   11. Applied simplify 0.0

       \[\leadsto \color{blue}{\left(\frac{9}{40} \cdot {x}^2 - \frac{1}{2}\right) - \frac{27}{2800} \cdot {x}^{4}}\]
3. Recombined 2 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 22.9s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (x)
  :name "sintan (problem 3.4.5)"
  (/ (- x (sin x)) (- x (tan x))))