Average Error: 0.0 → 0.0
Time: 8.2s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right)\]

Error

Bits error versus re

Bits error versus im

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]

  2. Initial simplification0.0

    \[\leadsto \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right) \cdot \cos re\]

  3. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot e^{im} + 0.5 \cdot \frac{1}{e^{im}}\right) \cdot \cos re}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{\cos re}{e^{im}} + e^{im} \cdot \cos re\right) \cdot 0.5}\]

  5. Final simplification0.0

    \[\leadsto 0.5 \cdot \left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right)\]

Runtime

Time bar (total: 8.2s)Debug logProfile

herbie shell --seed 2018249 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))