Average Error: 15.3 → 0.6
Time: 12.0s
Precision: 64
Internal Precision: 1344
\[1 - \cos x\]
\[\left(\sin x \cdot \sin x\right) \cdot \frac{1}{1 + \cos x}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.3

    \[1 - \cos x\]
  2. Using strategy rm
  3. Applied flip--15.6

    \[\leadsto \color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{1 + \cos x}}\]
  4. Applied simplify0.6

    \[\leadsto \frac{\color{blue}{\sin x \cdot \sin x}}{1 + \cos x}\]
  5. Using strategy rm
  6. Applied div-inv0.6

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

Runtime

Time bar (total: 12.0s)Debug log

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