Details

analyze376.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

sample153.0ms (1.9%)

Algorithm

1×

intervals

Results

71.0ms	137×	body	1280	valid
27.0ms	75×	body	640	valid
15.0ms	45×	body	1280	invalid
13.0ms	58×	body	640	invalid
7.0ms	31×	body	320	valid
3.0ms	17×	body	320	invalid
1.0ms	10×	body	160	valid
1.0ms	10×	body	160	invalid
1.0ms	13×	body	80	invalid
0.0ms	3×	body	80	valid

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5348	12

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 58.3b

Counts

2 → 1

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
5.7b	(- (exp (- 0.0 im)) (exp im))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`add-cube-cbrt` `sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-l` `*-commutative`

Counts

2 → 37

Calls

2 calls:

11.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
7.0ms	(- (exp (- 0.0 im)) (exp im))

series25.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

19.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
5.0ms	(- (exp (- 0.0 im)) (exp im))

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5332	526

prune103.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	3	44

Merged error: 0.1b

Counts

44 → 3

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))) (* im -2))
0.0b	(* 1/60 (pow im 5))
0.1b	(* (* 0.5 (cos re)) (+ (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))) (* im -2)))
0.1b	(* (pow im 3) -1/3)

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-exp-log`
16×	`associate-l`
13×	`associate-r` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `prod-exp` `add-log-exp`
8×	`unpow-prod-down`
7×	`unswap-sqr`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `sum-log` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `associate-+l-` `sub-neg` `associate-+l+` `distribute-lft-in` `diff-log` `unpow3`

Counts

4 → 92

Calls

4 calls:

11.0ms	(* (* 0.5 (cos re)) (+ (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))) (* im -2)))
8.0ms	(+ (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))) (* im -2))
6.0ms	(* (pow im 3) -1/3)
5.0ms	(* 1/60 (pow im 5))

series51.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 0.5 (cos re)) (+ (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))) (* im -2)))
6.0ms	(* 1/60 (pow im 5))
6.0ms	(+ (- (* (pow im 3) -1/3) (* 1/60 (pow im 5))) (* im -2))
4.0ms	(* (pow im 3) -1/3)

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5469	1284

prune292.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	98	9	107

Merged error: 0.0b

Counts

107 → 9

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))) (cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))))
0.6b	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
0.6b	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
0.6b	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

10.0ms	(* (cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))) (cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))))
9.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
9.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
9.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))

series430.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))) (cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))))
84.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
82.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
81.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4926	2709
1	4926	2709

prune624.0ms (7.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	83	10	93

Merged error: 0.0b

Counts

93 → 10

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
0.7b	(cbrt (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))
0.7b	(cbrt (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))
0.7b	(* (cbrt (* 0.5 (cos re))) (cbrt (* 0.5 (cos re))))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`pow1` `cbrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1/3`
6×	`add-exp-log` `cbrt-div`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`associate-*r/` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

9.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
7.0ms	(cbrt (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))
7.0ms	(cbrt (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))
5.0ms	(* (cbrt (* 0.5 (cos re))) (cbrt (* 0.5 (cos re))))

series160.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (* (* 0.5 (cos re)) (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2))))
36.0ms	(* (cbrt (* 0.5 (cos re))) (cbrt (* 0.5 (cos re))))
21.0ms	(cbrt (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))
21.0ms	(cbrt (+ (- (* -1/3 (pow im 3)) (* 1/60 (pow im 5))) (* im -2)))

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5168	1519

prune550.0ms (6.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	79	11	90

Merged error: 0.0b

Counts

90 → 11

regimes482.0ms (5.8%)

Accuracy

Total 0.7b remaining (92.3%)

Threshold costs 0.7b (92.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	20
1	50	20

end0.0ms (0%)

sample4.5s (55%)

Algorithm

1×

intervals

Results

2.3s	4291×	body	1280	valid
752.0ms	2322×	body	640	valid
512.0ms	1493×	body	1280	invalid
289.0ms	1198×	body	640	invalid
186.0ms	882×	body	320	valid
109.0ms	658×	body	320	invalid
52.0ms	359×	body	160	valid
34.0ms	299×	body	160	invalid
32.0ms	496×	body	80	invalid
10.0ms	146×	body	80	valid

Details

analyze376.0ms (4.6%)

sample153.0ms (1.9%)

simplify69.0ms (0.8%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite19.0ms (0.2%)

series25.0ms (0.3%)

simplify56.0ms (0.7%)

prune103.0ms (1.3%)

localize15.0ms (0.2%)

rewrite32.0ms (0.4%)

series51.0ms (0.6%)

simplify29.0ms (0.4%)

prune292.0ms (3.5%)

localize23.0ms (0.3%)

rewrite41.0ms (0.5%)

series430.0ms (5.2%)

simplify73.0ms (0.9%)

prune624.0ms (7.6%)

localize26.0ms (0.3%)

rewrite29.0ms (0.4%)

series160.0ms (1.9%)

simplify39.0ms (0.5%)

prune550.0ms (6.7%)

regimes482.0ms (5.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample4.5s (55%)

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