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)

sample99.0ms (1.5%)

Algorithm

1×

intervals

Results

45.0ms	62×	body	2048	valid
38.0ms	130×	body	1024	valid
7.0ms	40×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	10×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify172.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (0%)

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: 39.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.2b	(cos.f64 (+.f64 x eps))

rewrite14.0ms (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))
5.0ms	(cos.f64 (+.f64 x eps))

series103.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

76.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
27.0ms	(cos.f64 (+.f64 x eps))

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5098	444

prune82.0ms (1.2%)

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: 0.3b

Counts

33 → 6

Compiler

Compiled 1139 to 649 computations (43% 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))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite45.0ms (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))

series284.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
91.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
44.0ms	(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 (44.0ms)

Iter	Nodes	Cost
0	4950	1369
1	4950	1369

prune275.0ms (4.1%)

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: 0.2b

Counts

78 → 13

Compiler

Compiled 4724 to 3386 computations (28.3% 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)))))
0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
2.0b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite28.0ms (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))))
5.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

series225.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

105.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
85.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
35.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify101.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4857	1328
1	4857	1328

prune384.0ms (5.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	60	14	74

Merged error: 0.1b

Counts

74 → 14

Compiler

Compiled 6576 to 5210 computations (20.8% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite37.0ms (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)))
9.0ms	(.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)))

series402.0ms (6%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(.f64 (.f64 (sin.f64 x) (cos.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))
92.0ms	(.f64 (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2))) (sin.f64 (/.f64 eps 2)))
82.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
73.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5242	1480

prune453.0ms (6.8%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	82	18	100

Merged error: 0.0b

Counts

100 → 18

Compiler

Compiled 8043 to 6379 computations (20.7% saved)

regimes136.0ms (2%)

Compiler: Compiled 1452 to 1214 computations (16.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	43
1	26	43

end0.0ms (0%)

sample3.6s (53.5%)

Algorithm

1×

intervals

Results

1.4s	2079×	body	2048	valid
1.2s	3810×	body	1024	valid
234.0ms	1295×	body	512	valid
67.0ms	559×	body	256	valid
16.0ms	253×	body	128	valid
7.0ms	4×	body	4096	valid

Compiler

Compiled 513 to 430 computations (16.2% saved)

Details

analyze2.0ms (0%)

sample99.0ms (1.5%)

simplify172.0ms (2.6%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite14.0ms (0.2%)

series103.0ms (1.6%)

simplify59.0ms (0.9%)

prune82.0ms (1.2%)

localize13.0ms (0.2%)

rewrite45.0ms (0.7%)

series284.0ms (4.3%)

simplify60.0ms (0.9%)

prune275.0ms (4.1%)

localize12.0ms (0.2%)

rewrite28.0ms (0.4%)

series225.0ms (3.4%)

simplify101.0ms (1.5%)

prune384.0ms (5.8%)

localize23.0ms (0.3%)

rewrite37.0ms (0.6%)

series402.0ms (6%)

simplify70.0ms (1%)

prune453.0ms (6.8%)

regimes136.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.6s (53.5%)

Profiling