Average Error: 0.3 → 0.4
Time: 44.7s
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\log_* (1 + (e^{\frac{1 - \tan x \cdot \tan x}{(\left(\tan x\right) \cdot \left(\tan x\right) + 1)_*}} - 1)^*)\]

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 log1p-expm1-u0.4

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

  4. Applied simplify0.4

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

Runtime

Time bar (total: 44.7s)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' +o rules:numerics
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))