Error

Derivation

1. Split input into 3 regimes.

2. if x < -0.009369761232765748

   1. Initial program 0.1

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

   3. Applied div-sub 0.1

      \[\leadsto \color{blue}{\frac{x}{x - \tan x} - \frac{\sin x}{x - \tan x}}\]

   if -0.009369761232765748 < x < 0.06423521200938427

   1. Initial program 62.7

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

   3. Applied div-sub 62.6

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

   5. Applied add-cube-cbrt 62.6

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{x}{x - \tan x} - \frac{\sin x}{x - \tan x}}\right)}^3}\]

   6. Applied taylor 1.0

      \[\leadsto {\left(\sqrt[3]{\frac{9}{40} \cdot {x}^2 - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right)}\right)}^3\]

   7. Taylor expanded around 0 1.0

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{9}{40} \cdot {x}^2 - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right)}}\right)}^3\]

   8. Applied simplify 0.0

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

   if 0.06423521200938427 < x

   1. Initial program 0.0

      \[\frac{x - \sin x}{x - \tan x}\]
3. Recombined 3 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 18.5s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067488128 1186562765 67428877 2948030040 4169093828 3206893112)'
(FPCore (x)
  :name "sintan (problem 3.4.5)"
  (/ (- x (sin x)) (- x (tan x))))