Details

analyze1.0s (15.8%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

sample63.0ms (1%)

Algorithm

1×

intervals

Results

17.0ms	196×	body	80	valid
8.0ms	17×	body	1280	valid
6.0ms	64×	body	80	invalid
5.0ms	15×	body	640	valid
5.0ms	7×	body	640	invalid
5.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	invalid
0.0ms	1×	body	1280	invalid
0.0ms	3×	body	160	invalid

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4845	16
1	4845	16

prune13.0ms (0.2%)

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: 25.7b

Counts

2 → 2

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
4.7b	(* x (* x (* (pow c 2.0) (pow s 2.0))))
6.7b	(* x (* (pow c 2.0) (pow s 2.0)))
16.5b	(* (pow c 2.0) (pow s 2.0))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log`
88×	`prod-exp`
34×	`add-cbrt-cube`
24×	`add-sqr-sqrt` `pow-to-exp` `pow-exp`
16×	`cbrt-unprod`
13×	`associate-l`
12×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `div-exp`
11×	`pow1`
9×	`associate-r` `unswap-sqr`
8×	`sqr-pow`
5×	`pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 128

Calls

4 calls:

11.0ms	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
9.0ms	(* x (* x (* (pow c 2.0) (pow s 2.0))))
7.0ms	(* (pow c 2.0) (pow s 2.0))
7.0ms	(* x (* (pow c 2.0) (pow s 2.0)))

series260.0ms (4%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
61.0ms	(* x (* x (* (pow c 2.0) (pow s 2.0))))
60.0ms	(* (pow c 2.0) (pow s 2.0))
57.0ms	(* x (* (pow c 2.0) (pow s 2.0)))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4952	1811
1	4952	1811

prune384.0ms (5.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	125	15	140
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	126	16	142

Merged error: 8.7b

Counts

142 → 16

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow (* c s) 2.0)
0.5b	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
4.7b	(* x (* x (pow (* c s) 2.0)))
6.7b	(* x (pow (* c s) 2.0))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log`
26×	`prod-exp`
20×	`add-cbrt-cube`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`pow-exp`
7×	`cbrt-unprod`
6×	`div-exp` `associate-r` `associate-l`
4×	`pow-to-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `times-frac` `associate-/l*` `sqr-pow`
2×	`unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 86

Calls

4 calls:

8.0ms	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
6.0ms	(* x (* x (pow (* c s) 2.0)))
5.0ms	(* x (pow (* c s) 2.0))
4.0ms	(pow (* c s) 2.0)

series194.0ms (3%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
58.0ms	(* x (* x (pow (* c s) 2.0)))
49.0ms	(* x (pow (* c s) 2.0))
16.0ms	(pow (* c s) 2.0)

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	1115
1	4963	1115

prune286.0ms (4.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	10	5	15
Picked	0	1	1
Done	0	0	0
Total	98	16	114

Merged error: 3.6b

Counts

114 → 16

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
0.5b	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
3.0b	(* x (pow (* c s) (* 1/2 2.0)))
4.7b	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

247×	`add-exp-log`
182×	`prod-exp`
56×	`pow-exp`
34×	`add-cbrt-cube`
28×	`pow-to-exp`
22×	`div-exp`
16×	`cbrt-unprod`
13×	`add-sqr-sqrt`
11×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `sqr-pow`
2×	`unpow-prod-down` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 139

Calls

4 calls:

11.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
9.0ms	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))
8.0ms	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
5.0ms	(* x (pow (* c s) (* 1/2 2.0)))

series230.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
59.0ms	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))
49.0ms	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
49.0ms	(* x (pow (* c s) (* 1/2 2.0)))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4918	1843
1	4918	1843

prune378.0ms (5.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	153	14	167

Merged error: 1.0b

Counts

167 → 14

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (* x (* x (pow (* c s) (* 1/2 2.0)))) (pow (* c s) (/ 2.0 2))))
1.3b	(* x (* x (pow (* c s) (* 1/2 2.0))))
3.0b	(* x (pow (* c s) (* 1/2 2.0)))
4.5b	(* (* x (* x (pow (* c s) (* 1/2 2.0)))) (pow (* c s) (/ 2.0 2)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

220×	`add-exp-log`
155×	`prod-exp`
44×	`pow-exp`
34×	`add-cbrt-cube`
25×	`div-exp`
22×	`pow-to-exp`
16×	`cbrt-unprod`
13×	`add-sqr-sqrt`
11×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `sqr-pow`
2×	`unpow-prod-down` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 130

Calls

4 calls:

11.0ms	(/ (cos (* 2.0 x)) (* (* x (* x (pow (* c s) (* 1/2 2.0)))) (pow (* c s) (/ 2.0 2))))
9.0ms	(* (* x (* x (pow (* c s) (* 1/2 2.0)))) (pow (* c s) (/ 2.0 2)))
6.0ms	(* x (* x (pow (* c s) (* 1/2 2.0))))
5.0ms	(* x (pow (* c s) (* 1/2 2.0)))

series238.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (cos (* 2.0 x)) (* (* x (* x (pow (* c s) (* 1/2 2.0)))) (pow (* c s) (/ 2.0 2))))
59.0ms	(* (* x (* x (pow (* c s) (* 1/2 2.0)))) (pow (* c s) (/ 2.0 2)))
58.0ms	(* x (* x (pow (* c s) (* 1/2 2.0))))
49.0ms	(* x (pow (* c s) (* 1/2 2.0)))

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4939	1930
1	4939	1930

prune328.0ms (5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	2	10	12
Picked	1	0	1
Done	1	0	1
Total	140	16	156

Merged error: 0.8b

Counts

156 → 16

regimes582.0ms (8.9%)

Accuracy

Total 3.7b remaining (65.1%)

Threshold costs 0b (0%)

bsearch108.0ms (1.7%)

Steps

Iters	Range		Point
9	1.0569631154164961e-247	8.861296350169727e-239	8.638771279925528e-239
9	-2.559157428029134e-247	-1.7426765548082583e-255	-2.5212314714250252e-247

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	59
1	39	59

end0.0ms (0%)

sample1.9s (29.1%)

Algorithm

1×

intervals

Results

539.0ms	6007×	body	80	valid
342.0ms	698×	body	1280	valid
244.0ms	713×	body	640	valid
161.0ms	1820×	body	80	invalid
96.0ms	385×	body	320	valid
74.0ms	232×	body	640	invalid
64.0ms	142×	body	1280	invalid
45.0ms	192×	body	320	invalid
34.0ms	197×	body	160	valid
17.0ms	107×	body	160	invalid

Details

analyze1.0s (15.8%)

sample63.0ms (1%)

simplify65.0ms (1%)

prune13.0ms (0.2%)

localize14.0ms (0.2%)

rewrite42.0ms (0.6%)

series260.0ms (4%)

simplify70.0ms (1.1%)

prune384.0ms (5.9%)

localize14.0ms (0.2%)

rewrite25.0ms (0.4%)

series194.0ms (3%)

simplify51.0ms (0.8%)

prune286.0ms (4.4%)

localize18.0ms (0.3%)

rewrite43.0ms (0.7%)

series230.0ms (3.5%)

simplify61.0ms (0.9%)

prune378.0ms (5.8%)

localize18.0ms (0.3%)

rewrite38.0ms (0.6%)

series238.0ms (3.7%)

simplify59.0ms (0.9%)

prune328.0ms (5%)

regimes582.0ms (8.9%)

bsearch108.0ms (1.7%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.9s (29.1%)

Profiling