Average Error: 0.3 → 0.5
Time: 51.0s
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{\frac{1 - {\left(\tan x\right)}^{4}}{1 + \tan x \cdot \tan x}}{1 + \tan x \cdot \tan x}\]

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 flip--0.4

    \[\leadsto \frac{\color{blue}{\frac{1 \cdot 1 - \left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)}{1 + \tan x \cdot \tan x}}}{1 + \tan x \cdot \tan x}\]

  4. Applied simplify0.5

    \[\leadsto \frac{\frac{\color{blue}{1 - {\left(\tan x\right)}^{4}}}{1 + \tan x \cdot \tan x}}{1 + \tan x \cdot \tan x}\]

Runtime

Time bar (total: 51.0s)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))