Details

analyze361.0ms (4.5%)

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

sample145.0ms (1.8%)

Algorithm

1×

intervals

Results

76.0ms	143×	body	1280	valid
22.0ms	70×	body	640	valid
12.0ms	38×	body	1280	invalid
8.0ms	34×	body	640	invalid
5.0ms	27×	body	320	valid
3.0ms	21×	body	320	invalid
2.0ms	17×	body	160	invalid
2.0ms	13×	body	160	valid
1.0ms	17×	body	80	invalid
0.0ms	3×	body	80	valid

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5348	12

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 58.6b

Counts

2 → 1

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
6.1b	(- (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))

series22.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
5.0ms	(- (exp (- 0.0 im)) (exp im))

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5332	526

prune94.0ms (1.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	1	44

Merged error: 0.1b

Counts

44 → 1

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

10.0ms	(* (* 0.5 (cos re)) (+ (* (pow im 3) -1/3) (+ (* im -2) (* (pow im 5) -1/60))))
8.0ms	(+ (* (pow im 3) -1/3) (+ (* im -2) (* (pow im 5) -1/60)))
5.0ms	(* (pow im 3) -1/3)
5.0ms	(* (pow im 5) -1/60)

series50.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* 0.5 (cos re)) (+ (* (pow im 3) -1/3) (+ (* im -2) (* (pow im 5) -1/60))))
6.0ms	(+ (* (pow im 3) -1/3) (+ (* im -2) (* (pow im 5) -1/60)))
4.0ms	(* (pow im 5) -1/60)
4.0ms	(* (pow im 3) -1/3)

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5943	1256

prune278.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

17.0ms	(* (cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))) (cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))))
7.0ms	(cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))
7.0ms	(cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))
7.0ms	(cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))

series87.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))) (cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))))
23.0ms	(cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))
20.0ms	(cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))
20.0ms	(cbrt (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5025	2775

prune655.0ms (8.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	97	11	108

Merged error: 0.0b

Counts

108 → 11

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`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:

12.0ms	(cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))))
10.0ms	(cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))))
10.0ms	(cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))))
9.0ms	(* (cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))))) (cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))))))

series417.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))))) (cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60)))))))
81.0ms	(cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))))
79.0ms	(cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))))
79.0ms	(cbrt (* 0.5 (* (cos re) (+ (* -1/3 (pow im 3)) (+ (* im -2) (* (pow im 5) -1/60))))))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5239	2668

prune518.0ms (6.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

regimes448.0ms (5.5%)

Accuracy

Total 0.1b remaining (10.8%)

Threshold costs 0.1b (10.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	20
1	25	20

end0.0ms (0%)

sample4.5s (55.7%)

Algorithm

1×

intervals

Results

2.2s	4278×	body	1280	valid
732.0ms	2344×	body	640	valid
527.0ms	1534×	body	1280	invalid
295.0ms	1302×	body	640	invalid
179.0ms	869×	body	320	valid
111.0ms	621×	body	320	invalid
47.0ms	369×	body	160	valid
36.0ms	319×	body	160	invalid
35.0ms	561×	body	80	invalid
9.0ms	140×	body	80	valid

Details

analyze361.0ms (4.5%)

sample145.0ms (1.8%)

simplify60.0ms (0.7%)

prune7.0ms (0.1%)

localize14.0ms (0.2%)

rewrite19.0ms (0.2%)

series22.0ms (0.3%)

simplify54.0ms (0.7%)

prune94.0ms (1.2%)

localize15.0ms (0.2%)

rewrite31.0ms (0.4%)

series50.0ms (0.6%)

simplify32.0ms (0.4%)

prune278.0ms (3.5%)

localize20.0ms (0.3%)

rewrite40.0ms (0.5%)

series87.0ms (1.1%)

simplify85.0ms (1.1%)

prune655.0ms (8.1%)

localize21.0ms (0.3%)

rewrite43.0ms (0.5%)

series417.0ms (5.2%)

simplify55.0ms (0.7%)

prune518.0ms (6.4%)

regimes448.0ms (5.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample4.5s (55.7%)

Profiling