Average Error: 0.3 → 0.4
Time: 19.1s
Precision: 64
Internal Precision: 128
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{\frac{1 - \left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)}{1 + \tan x \cdot \tan x}}{1 + \tan x \cdot \tan x}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 flip--0.4

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

  5. Applied *-commutative0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019026 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))