Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

Details

Time bar (total: 11.6s)Debug log

sample224.0ms

Algorithm
intervals

simplify333.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

333.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (exp (- im)) (exp im))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

12.0ms
(+ (exp (- im)) (exp im))

series48.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

48.0ms
(+ (exp (- im)) (exp im))

simplify38.0ms

Counts
5 → 15
Calls

5 calls. Slowest were:

10.0ms
(+ (pow im 2) (+ (* 1/12 (pow im 4)) 2))
10.0ms
(* (exp (exp (- im))) (exp (exp im)))
7.0ms
(+ (exp im) (exp (* -1 im)))

prune134.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/12 (pow im 4))
0.0b
(* (* 0.5 (cos re)) (+ (pow im 2) (+ (* 1/12 (pow im 4)) 2)))
0.0b
(+ (pow im 2) (+ (* 1/12 (pow im 4)) 2))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
3 → 44
Calls

3 calls. Slowest were:

12.0ms
(* (* 0.5 (cos re)) (+ (pow im 2) (+ (* 1/12 (pow im 4)) 2)))
6.0ms
(+ (pow im 2) (+ (* 1/12 (pow im 4)) 2))
1.0ms
(* 1/12 (pow im 4))

series167.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

122.0ms
(* (* 0.5 (cos re)) (+ (pow im 2) (+ (* 1/12 (pow im 4)) 2)))
28.0ms
(* 1/12 (pow im 4))
17.0ms
(+ (pow im 2) (+ (* 1/12 (pow im 4)) 2))

simplify1.5s

Counts
25 → 53
Calls

25 calls. Slowest were:

330.0ms
(+ (* (pow im 2) (pow im 2)) (- (* (+ (* 1/12 (pow im 4)) 2) (+ (* 1/12 (pow im 4)) 2)) (* (pow im 2) (+ (* 1/12 (pow im 4)) 2))))
309.0ms
(* (* 0.5 (cos re)) (+ (pow im 2) (+ (* 1/12 (pow im 4)) 2)))
278.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (+ (pow im 2) (+ (* 1/12 (pow im 4)) 2)) (+ (pow im 2) (+ (* 1/12 (pow im 4)) 2))) (+ (pow im 2) (+ (* 1/12 (pow im 4)) 2))))

prune729.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes202.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch3.0ms

end0.0ms

sample8.1s

Algorithm
intervals