Average Error: 0.0 → 0.0

Time: 16.0s

Precision: 64

Internal Precision: 576

\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

↓

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

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Initial program 0.0
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
Initial simplification0.0
\[\leadsto \sin re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]
Using strategy rm
Applied add-sqr-sqrt0.0
\[\leadsto \sin re \cdot \color{blue}{\left(\sqrt{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}} \cdot \sqrt{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}}\right)}\]
Applied associate-*r*0.0
\[\leadsto \color{blue}{\left(\sin re \cdot \sqrt{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}}\right) \cdot \sqrt{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}}}\]
Final simplification0.0
\[\leadsto \left(\sqrt{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5} \cdot \sin re\right) \cdot \sqrt{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5}\]

herbie shell --seed 2018225 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))