Details

analyze1.7s (20.2%)

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
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample140.0ms (1.7%)

Algorithm

1×

intervals

Results

63.0ms	68×	body	1280	valid
29.0ms	48×	body	640	valid
17.0ms	119×	body	80	valid
11.0ms	15×	body	320	valid
3.0ms	20×	body	80	invalid
2.0ms	6×	body	160	valid
0.0ms	4×	body	80	nan

simplify480.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4951	26
1	4951	26

prune12.0ms (0.1%)

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: 14.3b

Counts

2 → 1

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(*.f64 x (/.f64 1.0 (tan.f64 B)))
7.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0))))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`pow-unpow_binary64`
25×	`add-exp-log_binary64`
21×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64` `associate-l_binary64`
13×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
8×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
7×	`pow1_binary64`
5×	`div-inv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `pow-neg_binary64`
3×	`pow-to-exp_binary64` `associate-/r_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-sub_binary64` `associate-/l*_binary64` `pow-exp_binary64`
2×	`frac-times_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `neg-mul-1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `tan-quot_binary64` `associate-*l/_binary64`

Counts

4 → 154

Calls

4 calls:

18.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0))))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))
4.0ms	(/.f64 F (sin.f64 B))

series149.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0))))
35.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))
30.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
12.0ms	(/.f64 F (sin.f64 B))

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4935	2393
1	4935	2393

prune336.0ms (4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	153	13	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	13	167

Merged error: 0.0b

Counts

167 → 13

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 x (/.f64 1.0 (tan.f64 B)))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`times-frac_binary64`
30×	`pow-unpow_binary64`
25×	`add-exp-log_binary64`
21×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64`
13×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
8×	`prod-exp_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64`
6×	`associate-l_binary64`
5×	`associate-*r/_binary64` `unswap-sqr_binary64` `pow-neg_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `div-inv_binary64`
3×	`pow-to-exp_binary64` `associate-/l/_binary64` `associate-/r*_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `pow-sub_binary64` `pow-exp_binary64`
2×	`un-div-inv_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `neg-mul-1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `tan-quot_binary64`

Counts

4 → 133

Calls

4 calls:

13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))
13.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
7.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))

series150.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
31.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
28.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
24.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5131	2183

prune280.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	145	13	158

Merged error: 0.0b

Counts

158 → 13

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 x 1.0) (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`pow-unpow_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
24×	`times-frac_binary64`
16×	`add-cbrt-cube_binary64`
13×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
6×	`associate-/r*_binary64` `div-exp_binary64`
5×	`pow1_binary64` `pow-neg_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `div-inv_binary64`
3×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-sub_binary64` `pow-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `un-div-inv_binary64`
1×	`pow-pow_binary64` `neg-mul-1_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

14.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
11.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))
5.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))

series147.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
30.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
27.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
23.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4945	2100
1	4945	2100

prune248.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	129	5	134
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	136	11	147

Merged error: 0.0b

Counts

147 → 11

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 x 1.0) (tan.f64 B))
0.2b	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
0.2b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`times-frac_binary64`
13×	`pow-unpow_binary64`
7×	`associate-l_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
6×	`div-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/r_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l_binary64`
3×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

12.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
11.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))
5.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))

series229.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
83.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
26.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
26.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4974	1776
1	4974	1776

prune167.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	109	11	120

Merged error: 0.0b

Counts

120 → 11

regimes246.0ms (2.9%)

Accuracy

Total 0.2b remaining (74.9%)

Threshold costs 0.2b (74.9%)

bsearch134.0ms (1.6%)

Steps

Iters	Range		Point
8	3040.7324025650373	7712014.360816213	6874909.974872331
9	-2.166553379375817e+30	-4.0218625629144235e+21	-1.1305106783563191e+26

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	75
1	104	75

end0.0ms (0%)

sample3.5s (41.7%)

Algorithm

1×

intervals

Results

1.4s	1604×	body	1280	valid
820.0ms	1400×	body	640	valid
536.0ms	3968×	body	80	valid
283.0ms	686×	body	320	valid
93.0ms	662×	body	80	invalid
93.0ms	342×	body	160	valid
11.0ms	120×	body	80	nan
0.0ms	1×	body	320	invalid

Details

analyze1.7s (20.2%)

sample140.0ms (1.7%)

simplify480.0ms (5.7%)

prune12.0ms (0.1%)

localize24.0ms (0.3%)

rewrite56.0ms (0.7%)

series149.0ms (1.8%)

simplify68.0ms (0.8%)

prune336.0ms (4%)

localize22.0ms (0.3%)

rewrite49.0ms (0.6%)

series150.0ms (1.8%)

simplify38.0ms (0.5%)

prune280.0ms (3.3%)

localize22.0ms (0.3%)

rewrite45.0ms (0.5%)

series147.0ms (1.7%)

simplify54.0ms (0.6%)

prune248.0ms (2.9%)

localize23.0ms (0.3%)

rewrite40.0ms (0.5%)

series229.0ms (2.7%)

simplify48.0ms (0.6%)

prune167.0ms (2%)

regimes246.0ms (2.9%)

bsearch134.0ms (1.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (41.7%)

Profiling