Average Error: 0.0 → 0.0
Time: 22.7s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\sin re \cdot e^{im} + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]

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. Initial simplification0.0

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

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Runtime

Time bar (total: 22.7s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.00%
herbie shell --seed 2018296 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))