Details

analyze743.0ms (17%)

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

sample66.0ms (1.5%)

Algorithm

1×

intervals

Results

22.0ms	48×	body	1280	valid
12.0ms	124×	body	80	valid
12.0ms	43×	body	640	valid
6.0ms	28×	body	320	valid
2.0ms	13×	body	160	valid
0.0ms	5×	body	80	invalid

simplify438.0ms (10%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	382	11
1	382	11

prune10.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1.0 (sin.f64 B)) (*.f64 x (/.f64 1.0 (tan.f64 B))))
0.1b	(/.f64 1.0 (sin.f64 B))
0.1b	(/.f64 1.0 (tan.f64 B))
0.2b	(*.f64 x (/.f64 1.0 (tan.f64 B)))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
14×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/l_binary64`
3×	`cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

11.0ms	(/.f64 1.0 (tan.f64 B))
10.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
7.0ms	(-.f64 (/.f64 1.0 (sin.f64 B)) (*.f64 x (/.f64 1.0 (tan.f64 B))))
4.0ms	(/.f64 1.0 (sin.f64 B))

series102.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
39.0ms	(-.f64 (/.f64 1.0 (sin.f64 B)) (*.f64 x (/.f64 1.0 (tan.f64 B))))
14.0ms	(/.f64 1.0 (tan.f64 B))
6.0ms	(/.f64 1.0 (sin.f64 B))

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5054	989

prune176.0ms (4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1.0 (sin.f64 B)) (.f64 1.0 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B))))
0.1b	(*.f64 x (cos.f64 B))
0.1b	(/.f64 1.0 (sin.f64 B))
0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`times-frac_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64`
4×	`associate-/l*_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`cbrt-unprod_binary64` `associate-*r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(-.f64 (/.f64 1.0 (sin.f64 B)) (.f64 1.0 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B))))
7.0ms	(/.f64 1.0 (sin.f64 B))
6.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
4.0ms	(*.f64 x (cos.f64 B))

series64.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(-.f64 (/.f64 1.0 (sin.f64 B)) (.f64 1.0 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B))))
21.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))
6.0ms	(/.f64 1.0 (sin.f64 B))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5003	853

prune128.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 0.0b

Counts

103 → 10

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 x (cos.f64 B))
0.2b	(/.f64 (-.f64 1.0 (.f64 (.f64 x (cos.f64 B)) 1.0)) (sin.f64 B))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1.0 (.f64 (.f64 x (cos.f64 B)) 1.0)) (sin.f64 B))
4.0ms	(*.f64 x (cos.f64 B))

series28.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

20.0ms	(/.f64 (-.f64 1.0 (.f64 (.f64 x (cos.f64 B)) 1.0)) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))

simplify51.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4968	691
1	4968	691

prune87.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	59	9	68

Merged error: 0.0b

Counts

68 → 9

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1.0 (sin.f64 B))
0.1b	(/.f64 1.0 (sin.f64 B))
0.2b	(.f64 (.f64 x (/.f64 1.0 (sin.f64 B))) (cos.f64 B))
0.3b	(*.f64 x (/.f64 1.0 (sin.f64 B)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
28×	`times-frac_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-r_binary64`
11×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
3×	`div-inv_binary64`
2×	`associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`
1×	`associate-*l/_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(.f64 (.f64 x (/.f64 1.0 (sin.f64 B))) (cos.f64 B))
7.0ms	(*.f64 x (/.f64 1.0 (sin.f64 B)))
4.0ms	(/.f64 1.0 (sin.f64 B))
4.0ms	(/.f64 1.0 (sin.f64 B))

series51.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (.f64 x (/.f64 1.0 (sin.f64 B))) (cos.f64 B))
17.0ms	(*.f64 x (/.f64 1.0 (sin.f64 B)))
6.0ms	(/.f64 1.0 (sin.f64 B))
6.0ms	(/.f64 1.0 (sin.f64 B))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4986	949
1	4986	949

prune131.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Merged error: 0.0b

Counts

128 → 9

regimes113.0ms (2.6%)

Accuracy

Total 0.2b remaining (85.3%)

Threshold costs 0.2b (85.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	11
1	53	11

end0.0ms (0%)

sample1.9s (42.4%)

Algorithm

1×

intervals

Results

742.0ms	1642×	body	1280	valid
428.0ms	1497×	body	640	valid
285.0ms	3812×	body	80	valid
139.0ms	693×	body	320	valid
53.0ms	356×	body	160	valid
12.0ms	177×	body	80	invalid
1.0ms	3×	body	640	invalid
0.0ms	1×	body	1280	invalid

Details

analyze743.0ms (17%)

sample66.0ms (1.5%)

simplify438.0ms (10%)

prune10.0ms (0.2%)

localize12.0ms (0.3%)

rewrite36.0ms (0.8%)

series102.0ms (2.3%)

simplify55.0ms (1.3%)

prune176.0ms (4%)

localize11.0ms (0.3%)

rewrite26.0ms (0.6%)

series64.0ms (1.5%)

simplify59.0ms (1.3%)

prune128.0ms (2.9%)

localize10.0ms (0.2%)

rewrite12.0ms (0.3%)

series28.0ms (0.6%)

simplify51.0ms (1.2%)

prune87.0ms (2%)

localize11.0ms (0.2%)

rewrite26.0ms (0.6%)

series51.0ms (1.2%)

simplify63.0ms (1.4%)

prune131.0ms (3%)

regimes113.0ms (2.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (42.4%)

Profiling