Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample103.0ms (1.6%)

Algorithm

1×

intervals

Results

47.0ms	68×	body	2048	valid
39.0ms	131×	body	1024	valid
7.0ms	39×	body	512	valid
1.0ms	12×	body	256	valid
0.0ms	6×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify165.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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: 40.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.9b	(cos.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
4×	`add-log-exp_binary64_118`
3×	`add-cube-cbrt_binary64_114` `cancel-sign-sub-inv_binary64_45`
2×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `cos-sum_binary64_213` `pow1_binary64_140`
1×	`associate--l-_binary64_17` `distribute-lft-out--_binary64_31` `diff-cos_binary64_230` `flip--_binary64_54` `difference-of-squares_binary64_48` `diff-log_binary64_171` `flip3--_binary64_83` `sub-neg_binary64_72`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series101.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

74.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
27.0ms	(cos.f64 (+.f64 x eps))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5098	444

prune80.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	26	6	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	6	33

Merged error: 0.5b

Counts

33 → 6

Compiler

Compiled 1038 to 605 computations (41.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.9b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_79`
11×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
9×	`add-sqr-sqrt_binary64_101` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114`
6×	`associate-l_binary64_20`
4×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150` `associate-r_binary64_19`
3×	`sum-log_binary64_170` `distribute-lft-out_binary64_30`
2×	`sin-mult_binary64_234` `*-commutative_binary64_10`
1×	`flip-+_binary64_53` `+-commutative_binary64_9` `associate-*r/_binary64_21` `unswap-sqr_binary64_47` `associate-+r+_binary64_11` `flip3-+_binary64_82`

Counts

4 → 60

Calls

4 calls:

13.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series293.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
99.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
40.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
33.0ms	(+.f64 x (+.f64 x eps))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4950	1369
1	4950	1369

prune249.0ms (3.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	65	13	78

Merged error: 0.4b

Counts

78 → 13

Compiler

Compiled 3994 to 2993 computations (25.1% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
2.9b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
8×	`add-sqr-sqrt_binary64_101`
7×	`sin-sum_binary64_212`
6×	`associate-l_binary64_20` `add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
5×	`distribute-lft-in_binary64_28` `distribute-rgt-in_binary64_29`
4×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150` `associate-r_binary64_19`
3×	`add-log-exp_binary64_118`
2×	`sin-mult_binary64_234` `*-commutative_binary64_10`
1×	`associate-*r/_binary64_21` `unswap-sqr_binary64_47`

Counts

3 → 52

Calls

3 calls:

10.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
9.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
4.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

series230.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

103.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
89.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
37.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4857	1328
1	4857	1328

prune299.0ms (4.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	51	10	61
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	60	14	74

Merged error: 0.1b

Counts

74 → 14

Compiler

Compiled 4730 to 3854 computations (18.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
0.2b	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
0.2b	(.f64 (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))
0.2b	(.f64 (.f64 (sin.f64 x) (cos.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
14×	`add-sqr-sqrt_binary64_101`
12×	`associate-r_binary64_19`
10×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
8×	`associate-l_binary64_20` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150`
4×	`*-commutative_binary64_10` `add-log-exp_binary64_118`
2×	`sin-cos-mult_binary64_235` `unswap-sqr_binary64_47`
1×	`associate-*l/_binary64_22`

Counts

4 → 74

Calls

4 calls:

9.0ms	(.f64 (.f64 (sin.f64 x) (cos.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))
8.0ms	(.f64 (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))
6.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
5.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))

series386.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(.f64 (.f64 (sin.f64 x) (cos.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))
91.0ms	(.f64 (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))
71.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
69.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5242	1480

prune383.0ms (6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	5	8	13
Picked	0	1	1
Done	0	0	0
Total	86	14	100

Merged error: 0.1b

Counts

100 → 14

Compiler

Compiled 6641 to 5258 computations (20.8% saved)

regimes106.0ms (1.7%)

Compiler: Compiled 1032 to 875 computations (15.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	24	35

end0.0ms (0%)

sample3.5s (54.7%)

Algorithm

1×

intervals

Results

1.4s	2111×	body	2048	valid
1.2s	3844×	body	1024	valid
236.0ms	1300×	body	512	valid
62.0ms	499×	body	256	valid
16.0ms	244×	body	128	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 368 to 313 computations (14.9% saved)

Details

analyze2.0ms (0%)

sample103.0ms (1.6%)

simplify165.0ms (2.6%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series101.0ms (1.6%)

simplify58.0ms (0.9%)

prune80.0ms (1.3%)

localize13.0ms (0.2%)

rewrite44.0ms (0.7%)

series293.0ms (4.6%)

simplify60.0ms (0.9%)

prune249.0ms (3.9%)

localize12.0ms (0.2%)

rewrite27.0ms (0.4%)

series230.0ms (3.6%)

simplify101.0ms (1.6%)

prune299.0ms (4.7%)

localize21.0ms (0.3%)

rewrite36.0ms (0.6%)

series386.0ms (6.1%)

simplify68.0ms (1.1%)

prune383.0ms (6%)

regimes106.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (54.7%)

Profiling