Average Error: 0.2 → 0.2
Time: 26.0s
Precision: 64
Internal Precision: 576
\[1 + \left(\sin x \cdot \cos x\right) \cdot \tan^{-1} x\]
\[e^{\log \left(1 + \frac{\tan^{-1} x \cdot \sin \left(x + x\right)}{2}\right)}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[1 + \left(\sin x \cdot \cos x\right) \cdot \tan^{-1} x\]
  2. Using strategy rm
  3. Applied sin-cos-mult0.2

    \[\leadsto 1 + \color{blue}{\frac{\sin \left(x - x\right) + \sin \left(x + x\right)}{2}} \cdot \tan^{-1} x\]
  4. Applied associate-*l/0.2

    \[\leadsto 1 + \color{blue}{\frac{\left(\sin \left(x - x\right) + \sin \left(x + x\right)\right) \cdot \tan^{-1} x}{2}}\]
  5. Applied simplify0.2

    \[\leadsto 1 + \frac{\color{blue}{\tan^{-1} x \cdot \sin \left(x + x\right)}}{2}\]
  6. Using strategy rm
  7. Applied add-exp-log0.2

    \[\leadsto \color{blue}{e^{\log \left(1 + \frac{\tan^{-1} x \cdot \sin \left(x + x\right)}{2}\right)}}\]

Runtime

Time bar (total: 26.0s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "1+sin(x)*cos(x)*atan(x)"
  (+ 1 (* (* (sin x) (cos x)) (atan x))))