Average Error: 0.4 → 0.4
Time: 17.1s
Precision: 64
Internal Precision: 576
\[\frac{\tan a}{1 - \tan a \cdot \tan a}\]
\[\frac{\tan a}{1 - \frac{\sin a \cdot \tan a}{\cos a}}\]

Error

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{\tan a}{1 - \tan a \cdot \tan a}\]
  2. Using strategy rm
  3. Applied tan-quot0.4

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

    \[\leadsto \frac{\tan a}{1 - \color{blue}{\frac{\sin a \cdot \tan a}{\cos a}}}\]
  5. Using strategy rm
  6. Applied *-commutative0.4

    \[\leadsto \frac{\tan a}{1 - \frac{\color{blue}{\tan a \cdot \sin a}}{\cos a}}\]
  7. Final simplification0.4

    \[\leadsto \frac{\tan a}{1 - \frac{\sin a \cdot \tan a}{\cos a}}\]

Runtime

Time bar (total: 17.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a)
  :name "(tan(a))/(1-tan(a)*tan(a))"
  (/ (tan a) (- 1 (* (tan a) (tan a)))))