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)

sample81.0ms (1.4%)

Algorithm

1×

intervals

Results

34.0ms	72×	body	2048	valid
32.0ms	123×	body	1024	valid
6.0ms	37×	body	512	valid
2.0ms	16×	body	256	valid
0.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 42.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.7b	(cos.f64 (+.f64 x eps))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
4×	`add-log-exp_binary64_458`
3×	`add-cube-cbrt_binary64_454` `cancel-sign-sub-inv_binary64_385`
2×	`cos-sum_binary64_553` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
1×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `diff-cos_binary64_570` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `associate--l-_binary64_357` `diff-log_binary64_511` `flip--_binary64_394`

Counts

2 → 26

Calls

2 calls:

6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series54.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

39.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
15.0ms	(cos.f64 (+.f64 x eps))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4855	444
1	4855	444

prune35.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	25	7	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	7	33

Merged error: 0.4b

Counts

33 → 7

Compiler

Compiled 476 to 170 computations (64.3% saved)

localize11.0ms (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)))
3.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_419`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
9×	`add-log-exp_binary64_458` `add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454`
6×	`associate-l_binary64_360`
4×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`sum-log_binary64_510` `distribute-lft-out_binary64_370`
2×	`sin-mult_binary64_574` `*-commutative_binary64_350`
1×	`flip3-+_binary64_422` `associate-+r+_binary64_351` `unswap-sqr_binary64_387` `associate-*r/_binary64_361` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 60

Calls

4 calls:

12.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series144.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
50.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
21.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
15.0ms	(+.f64 x (+.f64 x eps))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4916	1369
1	4916	1369

prune97.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	60	12	72
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	65	14	79

Merged error: 0.4b

Counts

79 → 14

Compiler

Compiled 1786 to 1193 computations (33.2% saved)

localize10.0ms (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))))
3.8b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
8×	`add-sqr-sqrt_binary64_441`
7×	`sin-sum_binary64_552`
6×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-l*_binary64_360`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`add-log-exp_binary64_458`
2×	`sin-mult_binary64_574` `*-commutative_binary64_350`
1×	`unswap-sqr_binary64_387` `associate-*r/_binary64_361`

Counts

3 → 52

Calls

3 calls:

9.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
8.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
4.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

series121.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

53.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
48.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
20.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4813	1328
1	4813	1328

prune88.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	51	10	61
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	62	13	75

Merged error: 0.1b

Counts

75 → 13

Compiler

Compiled 1457 to 1160 computations (20.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_441`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
9×	`associate-r_binary64_359` `associate-l_binary64_360`
6×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `associate-*r/_binary64_361` `flip-+_binary64_393`
1×	`sin-cos-mult_binary64_575` `distribute-rgt-in_binary64_369` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `+-commutative_binary64_349`

Counts

4 → 70

Calls

4 calls:

10.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))
7.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
5.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
5.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))

series288.0ms (5%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))
88.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
39.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
38.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4984	1986
1	4984	1986

prune129.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

Compiler

Compiled 2431 to 1684 computations (30.7% saved)

regimes419.0ms (7.3%)

Compiler: Compiled 3997 to 3256 computations (18.5% 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%)

sample3.7s (64.6%)

Algorithm

1×

intervals

Results

1000.0ms	2018×	body	2048	valid
973.0ms	3945×	body	1024	valid
216.0ms	1334×	body	512	valid
53.0ms	480×	body	256	valid
14.0ms	220×	body	128	valid
5.0ms	3×	body	4096	valid

Compiler

Compiled 1343 to 1095 computations (18.5% saved)

Details

analyze2.0ms (0%)

sample81.0ms (1.4%)

simplify98.0ms (1.7%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite12.0ms (0.2%)

series54.0ms (0.9%)

simplify84.0ms (1.4%)

prune35.0ms (0.6%)

localize11.0ms (0.2%)

rewrite40.0ms (0.7%)

series144.0ms (2.5%)

simplify77.0ms (1.3%)

prune97.0ms (1.7%)

localize10.0ms (0.2%)

rewrite25.0ms (0.4%)

series121.0ms (2.1%)

simplify100.0ms (1.7%)

prune88.0ms (1.5%)

localize17.0ms (0.3%)

rewrite33.0ms (0.6%)

series288.0ms (5%)

simplify61.0ms (1.1%)

prune129.0ms (2.2%)

regimes419.0ms (7.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.7s (64.6%)

Profiling