Average Error: 0.0 → 0.0
Time: 21.3s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[0.5 \cdot (\left(\cos re\right) \cdot \left(e^{im}\right) + \left(\frac{\cos re}{e^{im}}\right))_*\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

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

  2. Initial simplification0.0

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

  3. Final simplification0.0

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

Runtime

Time bar (total: 21.3s)Debug logProfile

herbie shell --seed 2018217 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))