Error

Derivation

1. Split input into 2 regimes

2. if x < -0.0006848976318816709 or 4185100.604392328 < x

   1. Initial program 0.1

      \[\frac{x - \sin x}{x - \tan x}\]

   if -0.0006848976318816709 < x < 4185100.604392328

   1. Initial program 62.7

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

   3. Applied add-cbrt-cube62.7

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

   4. Applied add-cbrt-cube62.7

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

   5. Applied cbrt-undiv62.7

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

   6. Applied simplify62.7

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

   7. Taylor expanded around 0 63.6

      \[\leadsto \color{blue}{\left({\left({\frac{-1}{2}}^{3}\right)}^{\frac{1}{3}} + \frac{27}{1400} \cdot \left({\frac{-1}{8}}^{\frac{1}{3}} \cdot {x}^{4}\right)\right) - \frac{9}{20} \cdot \left({\frac{-1}{8}}^{\frac{1}{3}} \cdot {x}^{2}\right)}\]

   8. Applied simplify0.0

      \[\leadsto \color{blue}{\frac{-1}{2} + \sqrt[3]{\frac{-1}{8}} \cdot \left({x}^{4} \cdot \frac{27}{1400} - x \cdot \left(\frac{9}{20} \cdot x\right)\right)}\]
3. Recombined 2 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed '#(1062930989 876886121 3990119081 3032829768 3060892583 1929069376)' 
(FPCore (x)
  :name "sintan (problem 3.4.5)"
  (/ (- x (sin x)) (- x (tan x))))