Average Error: 0.0 → 0.0
Time: 27.8s
Precision: 64
Internal Precision: 320
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{0.5 \cdot \sin re}{e^{im}}\]

Error

Bits error versus re

Bits error versus im

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]
  4. Using strategy rm

  5. Applied pow10.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{{\left(e^{0 - im}\right)}^{1}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

  6. Applied pow10.0

    \[\leadsto \color{blue}{{\left(0.5 \cdot \sin re\right)}^{1}} \cdot {\left(e^{0 - im}\right)}^{1} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

  7. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(\left(0.5 \cdot \sin re\right) \cdot e^{0 - im}\right)}^{1}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

  8. Simplified0.0

    \[\leadsto {\color{blue}{\left(\frac{\sin re \cdot 0.5}{e^{im}}\right)}}^{1} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

  9. Final simplification0.0

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

Runtime

Time bar (total: 27.8s)Debug logProfile

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