Average Error: 0.3 → 0.4
Time: 46.5s
Precision: 64
Internal Precision: 384
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[(e^{\log_* (1 + \frac{(\left(\tan x\right) \cdot \left(\tan x\right) + \left(-1\right))_*}{-(\left(\tan x\right) \cdot \left(\tan x\right) + 1)_*})} - 1)^*\]

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 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

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

  7. Applied expm1-log1p-u0.4

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

Runtime

Time bar (total: 46.5s)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' +o rules:numerics
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))