Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

sample37.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5022	33

prune12.0ms (0.3%)

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: 0.1b

Counts

2 → 2

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 5) 5.0)
0.1b	(/ (pow (fabs x) 3) 3.0)
0.1b	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
1.0b	(sqrt PI)

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`times-frac`
69×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-*r/`
24×	`unpow-prod-down`
22×	`associate-l`
19×	`add-exp-log` `associate-/l*`
16×	`frac-add`
13×	`sqrt-prod` `add-cbrt-cube`
12×	`flip3-+` `cube-prod` `flip-+`
8×	`frac-times` `sqr-pow`
7×	`pow1` `div-exp`
6×	`associate-/r*`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`cbrt-undiv` `associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `prod-exp` `clear-num` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 183

Calls

4 calls:

26.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
5.0ms	(/ (pow (fabs x) 3) 3.0)
5.0ms	(/ (pow (fabs x) 5) 5.0)
1.0ms	(sqrt PI)

series71.0ms (1.6%)

Counts

4 → 10

Calls

4 calls:

52.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
10.0ms	(/ (pow (fabs x) 5) 5.0)
9.0ms	(/ (pow (fabs x) 3) 3.0)
0.0ms	(sqrt PI)

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4975	4274
1	4975	4274

prune798.0ms (17.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	191	4	195

Merged error: 0b

Counts

195 → 4

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(* (pow (fabs x) 7) 0.047619047619047616)
0.1b	(* (pow (fabs x) 5) 0.2)
0.1b	(* (pow (fabs x) 3) 0.6666666666666666)
0.1b	(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) 0.047619047619047616)))))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
42×	`associate-l`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`add-exp-log`
16×	`sqrt-prod`
14×	`unswap-sqr`
12×	`unpow-prod-down` `associate-r` `add-cbrt-cube`
11×	`times-frac`
10×	`prod-exp`
6×	`pow1` `sqr-pow`
4×	`cube-prod` `*-commutative` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `sqrt-div` `pow-exp`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `pow-prod-down` `associate-*l/` `div-inv`

Counts

4 → 122

Calls

4 calls:

18.0ms	(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) 0.047619047619047616)))))
5.0ms	(* (pow (fabs x) 3) 0.6666666666666666)
5.0ms	(* (pow (fabs x) 7) 0.047619047619047616)
5.0ms	(* (pow (fabs x) 5) 0.2)

series74.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* 2.0 (fabs x)) (* (pow (fabs x) 7) 0.047619047619047616)))))
12.0ms	(* (pow (fabs x) 7) 0.047619047619047616)
10.0ms	(* (pow (fabs x) 3) 0.6666666666666666)
9.0ms	(* (pow (fabs x) 5) 0.2)

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	2304
1	4958	2304

prune505.0ms (11.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	134	4	138

Merged error: 0b

Counts

138 → 4

localize27.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* (cbrt PI) (cbrt PI)))
1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 52

Calls

4 calls:

4.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4951	327
1	4951	327

prune167.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	56	4	60

Merged error: 0b

Counts

60 → 4

localize26.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
0.3b	(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite208.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`associate-*r/`
72×	`sqrt-prod`
48×	`frac-add`
47×	`add-sqr-sqrt`
45×	`sqrt-div`
41×	`frac-times`
38×	`times-frac`
36×	`flip3-+` `flip-+`
35×	`add-cube-cbrt` `*-un-lft-identity`
28×	`associate-l`
26×	`associate-r`
25×	`associate-*l/`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `div-inv`

Counts

4 → 161

Calls

4 calls:

32.0ms	(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
25.0ms	(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series130.0ms (2.9%)

Counts

4 → 8

Calls

4 calls:

73.0ms	(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
57.0ms	(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5128	7602

prune977.0ms (21.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	169	4	173

Merged error: 0b

Counts

173 → 4

regimes87.0ms (1.9%)

Accuracy

Total 0.1b remaining (79.6%)

Threshold costs 0.1b (79.6%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	33
1	37	33

end0.0ms (0%)

sample938.0ms (20.9%)

Algorithm

1×

intervals

Results

745.0ms	8000×	body	80	valid
85.0ms	8001×	pre	80	true
0.0ms	1×	body	80	invalid

Details

analyze5.0ms (0.1%)

sample37.0ms (0.8%)

simplify42.0ms (0.9%)

prune12.0ms (0.3%)

localize20.0ms (0.5%)

rewrite45.0ms (1%)

series71.0ms (1.6%)

simplify71.0ms (1.6%)

prune798.0ms (17.8%)

localize20.0ms (0.4%)

rewrite38.0ms (0.8%)

series74.0ms (1.7%)

simplify60.0ms (1.3%)

prune505.0ms (11.2%)

localize27.0ms (0.6%)

rewrite8.0ms (0.2%)

series0.0ms (0%)

simplify59.0ms (1.3%)

prune167.0ms (3.7%)

localize26.0ms (0.6%)

rewrite208.0ms (4.6%)

series130.0ms (2.9%)

simplify70.0ms (1.5%)

prune977.0ms (21.7%)

regimes87.0ms (1.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample938.0ms (20.9%)

Profiling