Average Error: 0.3 → 0.3
Time: 45.7s
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{(\left(\tan x\right) \cdot \left(\tan x\right) + \left(-1\right))_*}{-(\left(\tan x\right) \cdot \left(\tan x\right) + 1)_*}\]

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 frac-2neg0.3

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

  4. Applied simplify0.3

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

  5. Applied simplify0.3

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

Runtime

Time bar (total: 45.7s)Debug logProfile

herbie shell --seed 2018201 +o rules:numerics
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))