Average Error: 0.3 → 0.4
Time: 38.9s
Precision: 64
Internal Precision: 384
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\log \left(e^{\frac{1 - \tan x \cdot \tan x}{(\left(\tan x\right) \cdot \left(\tan x\right) + 1)_*}}\right)\]

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 add-log-exp0.4

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

  4. Applied simplify0.4

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

Runtime

Time bar (total: 38.9s)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' +o rules:numerics
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))