Details

analyze655.0ms (5.7%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
31.2%	68.7%	0.1%	5
31.2%	59.3%	9.5%	6
34.3%	54.6%	11%	7
34.3%	49.2%	16.5%	8
35.9%	46.4%	17.7%	9
35.9%	42.1%	22%	10
36.7%	40.6%	22.7%	11
36.7%	39.1%	24.2%	12
37.1%	38.3%	24.7%	13
37.1%	36.7%	26.2%	14

sample523.0ms (4.5%)

Algorithm

1×

intervals

Results

424.0ms	153×	body	5120	exit
38.0ms	90×	body	1280	nan
20.0ms	72×	body	640	nan
16.0ms	256×	body	80	valid
6.0ms	35×	body	320	nan
1.0ms	13×	body	160	nan
0.0ms	9×	body	80	nan
0.0ms	2×	body	80	overflowed
0.0ms	2×	body	80	invalid

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4891	7
1	4891	7

prune9.0ms (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: 0.3b

Counts

2 → 2

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(* (exp (neg w)) (pow l (exp w)))
0.3b	(pow l (exp w))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `unpow-prod-down` `-un-lft-identity` `associate-r*`
5×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*l/` `pow-exp` `add-log-exp`
1×	`neg-sub0` `exp-neg` `pow-pow` `exp-diff` `*-commutative` `cbrt-unprod`

Counts

2 → 44

Calls

2 calls:

8.0ms	(* (exp (neg w)) (pow l (exp w)))
2.0ms	(pow l (exp w))

series44.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

23.0ms	(* (exp (neg w)) (pow l (exp w)))
21.0ms	(pow l (exp w))

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5150	472

prune80.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.1b

Counts

52 → 5

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp w))
0.0b	(* (exp (neg w)) (pow (pow l (sqrt (exp w))) (sqrt (exp w))))
0.3b	(pow l (sqrt (exp w)))
0.3b	(pow (pow l (sqrt (exp w))) (sqrt (exp w)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`unpow-prod-down`
26×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow-unpow`
11×	`associate-r`
10×	`add-exp-log`
9×	`pow-exp` `sqrt-prod`
7×	`sqr-pow`
6×	`pow1` `add-cbrt-cube`
5×	`pow-to-exp` `prod-exp` `unswap-sqr`
4×	`sqrt-pow1` `add-log-exp`
3×	`exp-prod` `associate-l`
2×	`pow-pow` `associate-*l/`
1×	`neg-sub0` `exp-neg` `rem-sqrt-square` `pow1/2` `exp-diff` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

10.0ms	(* (exp (neg w)) (pow (pow l (sqrt (exp w))) (sqrt (exp w))))
5.0ms	(pow (pow l (sqrt (exp w))) (sqrt (exp w)))
3.0ms	(pow l (sqrt (exp w)))
2.0ms	(sqrt (exp w))

series92.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (exp (neg w)) (pow (pow l (sqrt (exp w))) (sqrt (exp w))))
30.0ms	(pow (pow l (sqrt (exp w))) (sqrt (exp w)))
19.0ms	(pow l (sqrt (exp w)))
3.0ms	(sqrt (exp w))

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4977	1080
1	4977	1080

prune151.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 0.1b

Counts

114 → 6

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* (exp (neg w)) (pow (pow l (sqrt (exp w))) (pow (exp 1) (/ w 2))))
0.0b	(pow (exp 1) (/ w 2))
0.3b	(pow l (sqrt (exp w)))
0.3b	(pow (pow l (sqrt (exp w))) (pow (exp 1) (/ w 2)))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`unpow-prod-down`
32×	`add-sqr-sqrt`
26×	`pow-unpow`
24×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r`
10×	`add-exp-log` `pow-exp`
9×	`times-frac` `sqr-pow`
6×	`pow1` `pow-to-exp` `pow-pow` `add-cbrt-cube`
5×	`prod-exp` `unswap-sqr`
4×	`add-log-exp`
3×	`exp-prod` `associate-l` `sqrt-prod`
2×	`associate-*l/`
1×	`neg-sub0` `exp-neg` `exp-diff` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 112

Calls

4 calls:

10.0ms	(* (exp (neg w)) (pow (pow l (sqrt (exp w))) (pow (exp 1) (/ w 2))))
4.0ms	(pow (exp 1) (/ w 2))
4.0ms	(pow (pow l (sqrt (exp w))) (pow (exp 1) (/ w 2)))
2.0ms	(pow l (sqrt (exp w)))

series100.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (exp (neg w)) (pow (pow l (sqrt (exp w))) (pow (exp 1) (/ w 2))))
35.0ms	(pow (pow l (sqrt (exp w))) (pow (exp 1) (/ w 2)))
21.0ms	(pow l (sqrt (exp w)))
3.0ms	(pow (exp 1) (/ w 2))

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5268	1561

prune246.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 0.1b

Counts

130 → 6

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp w))
0.3b	(pow (pow (pow l (sqrt (exp w))) (fabs (cbrt (exp w)))) (sqrt (cbrt (exp w))))
0.3b	(pow l (sqrt (exp w)))
0.3b	(pow (pow l (sqrt (exp w))) (fabs (cbrt (exp w))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`unpow-prod-down`
18×	`pow-unpow`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`pow-exp`
10×	`add-exp-log`
9×	`sqrt-prod`
6×	`cbrt-prod` `pow-to-exp` `sqr-pow`
5×	`pow1`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-pow`
1×	`pow1/3`

Counts

4 → 89

Calls

4 calls:

6.0ms	(pow (pow (pow l (sqrt (exp w))) (fabs (cbrt (exp w)))) (sqrt (cbrt (exp w))))
3.0ms	(pow (pow l (sqrt (exp w))) (fabs (cbrt (exp w))))
2.0ms	(pow l (sqrt (exp w)))
2.0ms	(cbrt (exp w))

series132.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (pow (pow l (sqrt (exp w))) (fabs (cbrt (exp w)))) (sqrt (cbrt (exp w))))
36.0ms	(pow (pow l (sqrt (exp w))) (fabs (cbrt (exp w))))
21.0ms	(pow l (sqrt (exp w)))
16.0ms	(cbrt (exp w))

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5289	1633

prune134.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	101	6	107

Merged error: 0.0b

Counts

107 → 6

regimes105.0ms (0.9%)

Accuracy

Total 0.2b remaining (72.4%)

Threshold costs 0.2b (72.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	25
1	23	25

end0.0ms (0%)

sample8.9s (76.6%)

Algorithm

1×

intervals

Results

6.1s	4843×	body	5120	exit
1.0s	2377×	body	1280	nan
541.0ms	1966×	body	640	nan
498.0ms	8000×	body	80	valid
175.0ms	1006×	body	320	nan
30.0ms	302×	body	160	nan
10.0ms	237×	body	80	nan
9.0ms	147×	body	80	overflowed
6.0ms	108×	body	80	invalid
6.0ms	3×	body	5120	nan
2.0ms	2×	body	2560	nan

Details

analyze655.0ms (5.7%)

sample523.0ms (4.5%)

simplify88.0ms (0.8%)

prune9.0ms (0.1%)

localize8.0ms (0.1%)

rewrite11.0ms (0.1%)

series44.0ms (0.4%)

simplify57.0ms (0.5%)

prune80.0ms (0.7%)

localize13.0ms (0.1%)

rewrite22.0ms (0.2%)

series92.0ms (0.8%)

simplify48.0ms (0.4%)

prune151.0ms (1.3%)

localize18.0ms (0.2%)

rewrite24.0ms (0.2%)

series100.0ms (0.9%)

simplify52.0ms (0.4%)

prune246.0ms (2.1%)

localize17.0ms (0.1%)

rewrite16.0ms (0.1%)

series132.0ms (1.1%)

simplify50.0ms (0.4%)

prune134.0ms (1.2%)

regimes105.0ms (0.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample8.9s (76.6%)

Profiling