Average Error: 0.3 → 0.4
Time: 57.2s
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \tan x \cdot \tan x}{1 + \sqrt[3]{{\left(\tan x \cdot \tan x\right)}^{3}}}\]

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-cbrt-cube0.4

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

  4. Applied add-cbrt-cube0.5

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

  5. Applied cbrt-unprod0.4

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

  6. Applied simplify0.4

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

Runtime

Time bar (total: 57.2s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' +o rules:numerics
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))