Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
Internal Precision: 320
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\cos im \cdot \sqrt{e^{re}}\right)\]

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

    \[e^{re} \cdot \cos im\]

  2. Initial simplification0.0

    \[\leadsto \cos im \cdot e^{re}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.0

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

  5. Applied associate-*r*0.0

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

  6. Final simplification0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\cos im \cdot \sqrt{e^{re}}\right)\]

Runtime

Time bar (total: 5.5s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.00%
herbie shell --seed 2018274 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))