Average Error: 0.0 → 0.0
Time: 6.7s
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 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 6.3s)Debug log

sample105.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune6.0ms

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 → 19
Calls

1 calls. Slowest were:

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

series53.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

53.0ms
(* (exp re) (cos im))

simplify154.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

96.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
35.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (exp re) (cos im))

prune212.0ms

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))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
3 → 51
Calls

3 calls. Slowest were:

11.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series75.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

48.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
15.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify1.3s

Counts
29 → 60
Calls

29 calls. Slowest were:

760.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (cos im)) (* (sqrt (exp re)) (cos im))) (* (sqrt (exp re)) (cos im))))
367.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im))))
53.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))

prune510.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes127.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm
intervals