Average Error: 0.4 → 0.4
Time: 16.3s
Precision: 64
Internal Precision: 576
\[\frac{1}{1 - 3 \cdot {\left(\tan x\right)}^{2}}\]
\[\frac{1}{1 - \frac{\sin x \cdot \left(\tan x \cdot 3\right)}{\cos x}}\]

Error

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Results

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Derivation

  1. Initial program 0.4

    \[\frac{1}{1 - 3 \cdot {\left(\tan x\right)}^{2}}\]
  2. Initial simplification0.4

    \[\leadsto \frac{1}{1 - \left(\tan x \cdot \tan x\right) \cdot 3}\]
  3. Using strategy rm
  4. Applied tan-quot0.4

    \[\leadsto \frac{1}{1 - \left(\color{blue}{\frac{\sin x}{\cos x}} \cdot \tan x\right) \cdot 3}\]
  5. Applied associate-*l/0.4

    \[\leadsto \frac{1}{1 - \color{blue}{\frac{\sin x \cdot \tan x}{\cos x}} \cdot 3}\]
  6. Applied associate-*l/0.4

    \[\leadsto \frac{1}{1 - \color{blue}{\frac{\left(\sin x \cdot \tan x\right) \cdot 3}{\cos x}}}\]
  7. Using strategy rm
  8. Applied associate-*l*0.4

    \[\leadsto \frac{1}{1 - \frac{\color{blue}{\sin x \cdot \left(\tan x \cdot 3\right)}}{\cos x}}\]
  9. Final simplification0.4

    \[\leadsto \frac{1}{1 - \frac{\sin x \cdot \left(\tan x \cdot 3\right)}{\cos x}}\]

Runtime

Time bar (total: 16.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "1/ (1- 3*tan(x)^2)"
  (/ 1 (- 1 (* 3 (pow (tan x) 2)))))