Average Error: 0.3 → 0.3
Time: 29.8s
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \frac{\sin x \cdot \tan x}{\cos x}}{1 + \frac{\sin x \cdot \tan x}{\cos x}}\]

Error

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Results

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Derivation

  1. Initial program 0.3

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

  2. Initial simplification0.3

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

  4. Applied tan-quot0.4

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

  5. Applied associate-*l/0.4

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

  7. Applied tan-quot0.4

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

  8. Applied associate-*l/0.3

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

  9. 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: 29.8s)Debug logProfile

herbie shell --seed 2018225 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))