Average Error: 0.0 → 0.1
Time: 1.1m
Precision: 64
Internal Precision: 320
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{{\left(\frac{0.5}{e^{im}}\right)}^{3} + {\left(0.5 \cdot e^{im}\right)}^{3}}{\left(\left(0.5 \cdot e^{im}\right) \cdot \left(0.5 \cdot e^{im}\right) - \frac{0.5}{e^{im}} \cdot \left(0.5 \cdot e^{im}\right)\right) + \frac{0.5}{e^{im}} \cdot \frac{0.5}{e^{im}}} \cdot \cos re\]

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

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

  2. Initial simplification0.0

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

  4. Applied flip3-+0.1

    \[\leadsto \color{blue}{\frac{{\left(\frac{0.5}{e^{im}}\right)}^{3} + {\left(0.5 \cdot e^{im}\right)}^{3}}{\frac{0.5}{e^{im}} \cdot \frac{0.5}{e^{im}} + \left(\left(0.5 \cdot e^{im}\right) \cdot \left(0.5 \cdot e^{im}\right) - \frac{0.5}{e^{im}} \cdot \left(0.5 \cdot e^{im}\right)\right)}} \cdot \cos re\]

  5. Final simplification0.1

    \[\leadsto \frac{{\left(\frac{0.5}{e^{im}}\right)}^{3} + {\left(0.5 \cdot e^{im}\right)}^{3}}{\left(\left(0.5 \cdot e^{im}\right) \cdot \left(0.5 \cdot e^{im}\right) - \frac{0.5}{e^{im}} \cdot \left(0.5 \cdot e^{im}\right)\right) + \frac{0.5}{e^{im}} \cdot \frac{0.5}{e^{im}}} \cdot \cos re\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018255 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))