Average Error: 0.0 → 0.0
Time: 15.4s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[(\left(e^{im}\right) \cdot \left(\cos re \cdot 0.5\right) + \left(\frac{\frac{\cos re \cdot 0.5}{\sqrt{e^{im}}}}{\sqrt{e^{im}}}\right))_*\]

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied associate-/r*0.0

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

  6. Final simplification0.0

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

Runtime

Time bar (total: 15.4s)Debug logProfile

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