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Derivation

1. Initial program 0.3

   \[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
2. Using strategy rm

3. Applied tan-quot0.4

   \[\leadsto \frac{1 - \tan x \cdot \tan x}{1 + \color{blue}{\frac{\sin x}{\cos x}} \cdot \tan x}\]

4. Applied associate-*l/0.4

   \[\leadsto \frac{1 - \tan x \cdot \tan x}{1 + \color{blue}{\frac{\sin x \cdot \tan x}{\cos x}}}\]
5. Using strategy rm

6. Applied tan-quot0.4

   \[\leadsto \frac{1 - \color{blue}{\frac{\sin x}{\cos x}} \cdot \tan x}{1 + \frac{\sin x \cdot \tan x}{\cos x}}\]

7. Applied associate-*l/0.3

   \[\leadsto \frac{1 - \color{blue}{\frac{\sin x \cdot \tan x}{\cos x}}}{1 + \frac{\sin x \cdot \tan x}{\cos x}}\]

8. Final simplification0.3

   \[\leadsto \frac{1 - \frac{\sin x \cdot \tan x}{\cos x}}{1 + \frac{\sin x \cdot \tan x}{\cos x}}\]

Runtime

Time bar (total: 26.3s)Debug logProfile

herbie shell --seed 2018274 +o rules:numerics
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))