Average Error: 0.3 → 0.4
Time: 26.1s
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1}{\tan x \cdot \tan x + 1} - \frac{\tan x \cdot \tan x}{\tan x \cdot \tan x + 1}\]

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 div-sub0.4

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

  5. Final simplification0.4

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

Runtime

Time bar (total: 26.1s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.40.40.10.30%
herbie shell --seed 2018296 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))