Average Error: 0.0 → 0.0

Time: 17.3s

Precision: 64

Internal Precision: 320

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

↓

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

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

herbie shell --seed 2018221 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))