Average Error: 0.0 → 0.0
Time: 10.6s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]

Error

Bits error versus re

Bits error versus im

Try it out

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. Final simplification0.0

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

Runtime

Time bar (total: 10.6s)Debug logProfile

start678.0ms

Algorithm
intervals

setup483.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ 0.5 (exp im))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

1.0ms
(/ 0.5 (exp im))

series11.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

11.0ms
(/ 0.5 (exp im))

simplify72.0ms

Counts
6 → 16
Calls

6 calls. Slowest were:

62.0ms
(- (+ (* 0.25 (pow im 2)) 0.5) (* 0.5 im))
5.0ms
(sqrt (exp im))
2.0ms
(/ 0.5 (exp im))

prune158.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

herbie shell --seed 2018357 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))