Average Error: 0.0 → 0.0
Time: 1.4m
Precision: 64
Internal Precision: 320
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot (\left(\sqrt{e^{-im}}\right) \cdot \left(\sqrt{e^{-im}}\right) + \left(e^{im}\right))_*\]

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied fma-def0.0

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018178 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))