Average Error: 0.3 → 0.5
Time: 39.4s
Precision: 64
Internal Precision: 384
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \tan x \cdot \tan x}{1 - {\left(\tan x\right)}^{\left(3 + 1\right)}} \cdot \left(1 - \tan x \cdot \tan x\right)\]

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

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

  4. Applied associate-/r/0.4

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

  5. Applied simplify0.5

    \[\leadsto \color{blue}{\frac{1 - \tan x \cdot \tan x}{1 - {\left(\tan x\right)}^{\left(3 + 1\right)}}} \cdot \left(1 - \tan x \cdot \tan x\right)\]

Runtime

Time bar (total: 39.4s)Debug logProfile

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))