Average Error: 0.3 → 0.4
Time: 36.8s
Precision: 64
Internal Precision: 384
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1}{1 + \frac{\sin x \cdot \sin x}{\cos x \cdot \cos x}} - \frac{\tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]

Error

Bits error versus x

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 div-sub0.4

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

  5. Applied tan-quot0.4

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

  6. Applied tan-quot0.4

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

  7. Applied frac-times0.4

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

Runtime

Time bar (total: 36.8s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))