Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \cos im\]
↓
\[\cos im \cdot e^{re}\]

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

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 5.9s)Debug log

sample114.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

2.0ms
(* (exp re) (cos im))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (exp re) (cos im))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

4.0ms
(* (exp re) (cos im))

series77.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

77.0ms
(* (exp re) (cos im))

simplify122.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

83.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
22.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (exp re) (cos im))

prune164.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
0.0b
(sqrt (exp re))
0.0b
(sqrt (exp re))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
3 → 45
Calls

3 calls. Slowest were:

10.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series85.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

48.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
19.0ms
(sqrt (exp re))
18.0ms
(sqrt (exp re))

simplify991.0ms

Counts
29 → 54
Calls

29 calls. Slowest were:

464.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (cos im)) (* (sqrt (exp re)) (cos im))) (* (sqrt (exp re)) (cos im))))
321.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im))))
45.0ms
(+ (* 1/2 re) (+ (* 1/8 (pow re 2)) 1))

prune579.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes138.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm
intervals