Average Error: 0.3 → 0.4
Time: 2.4m
Precision: 64
Internal Precision: 576
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{\frac{1 - \left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)}{\tan x \cdot \tan x + 1}}{\tan x \cdot \tan x + 1}\]

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. Final simplification0.4

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

Runtime

Time bar (total: 2.4m)Debug logProfile

herbie shell --seed 2018214 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))