Average Error: 0.0 → 0.0
Time: 8.5s
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 2019002 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 8.1s)Debug log

sample80.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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))

series44.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

44.0ms
(* (exp re) (cos im))

simplify94.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

60.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
20.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
3.0ms
(* (exp re) (cos im))

prune190.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

13.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
8.0ms
(* (sqrt (exp re)) (cos im))
1.0ms
(sqrt (exp re))

series111.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

53.0ms
(* (sqrt (exp re)) (cos im))
32.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
14.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify1.1s

Counts
43 → 77
Calls

43 calls. Slowest were:

429.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (cos im)) (* (sqrt (exp re)) (cos im))) (* (sqrt (exp re)) (cos im))))
413.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im))))
87.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im)))

prune726.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (sqrt (exp re)))
0.3b
(cbrt (sqrt (exp re)))
0.3b
(cbrt (sqrt (exp re)))
0.0b
(* (cbrt (sqrt (exp re))) (cbrt (sqrt (exp re))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 76
Calls

4 calls. Slowest were:

12.0ms
(* (cbrt (sqrt (exp re))) (cbrt (sqrt (exp re))))
2.0ms
(cbrt (sqrt (exp re)))
2.0ms
(cbrt (sqrt (exp re)))

series563.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

161.0ms
(cbrt (sqrt (exp re)))
152.0ms
(cbrt (sqrt (exp re)))
146.0ms
(cbrt (sqrt (exp re)))
104.0ms
(* (cbrt (sqrt (exp re))) (cbrt (sqrt (exp re))))

simplify250.0ms

Counts
56 → 88
Calls

56 calls. Slowest were:

40.0ms
(+ (* 1/6 re) (+ (* 1/72 (pow re 2)) 1))
38.0ms
(+ (* 1/6 re) (+ (* 1/72 (pow re 2)) 1))
29.0ms
(+ (* 1/6 re) (+ (* 1/72 (pow re 2)) 1))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes261.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.4s

Algorithm
intervals