Details

analyze857.0ms (13.5%)

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
18.7%	81.2%	0.1%	7
18.7%	81.2%	0.1%	8
29.7%	69.5%	0.9%	9
30.4%	67.9%	1.7%	10
36.3%	61.1%	2.6%	11
36.9%	59.5%	3.6%	12
39.9%	55.9%	4.2%	13
40.2%	54.9%	4.9%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample88.0ms (1.4%)

Algorithm

1×

intervals

Results

37.0ms	39×	body	2048	valid
14.0ms	4×	body	4096	valid
13.0ms	55×	body	1024	valid
7.0ms	132×	body	128	valid
3.0ms	19×	body	512	valid
1.0ms	7×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify115.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	299	20
1	299	20

prune6.0ms (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: 17.5b

Counts

2 → 2

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
3.7b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
29.0b	(tan.f64 (*.f64 PI.f64 l))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

7.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
4.0ms	(*.f64 PI.f64 l)
4.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series164.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
58.0ms	(tan.f64 (*.f64 PI.f64 l))
13.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5225	914

prune90.0ms (1.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	64	14	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	66	14	80

Merged error: 13.8b

Counts

80 → 14

Compiler

Compiled 1520 to 410 computations (73% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.7b	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
29.0b	(tan.f64 (*.f64 PI.f64 l))

rewrite55.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

396×	`times-frac_binary64`
197×	`add-sqr-sqrt_binary64`
193×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
44×	`associate-/r*_binary64`
29×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64` `div-inv_binary64`
15×	`div-exp_binary64`
9×	`pow1_binary64`
6×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64`
5×	`associate-/r/_binary64`
4×	`add-log-exp_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `tan-quot_binary64`

Counts

4 → 248

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series164.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
33.0ms	(tan.f64 (*.f64 PI.f64 l))
13.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify164.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4906	6379
1	4906	6379

prune254.0ms (4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	254	6	260
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	256	18	274

Merged error: 13.8b

Counts

274 → 18

Compiler

Compiled 6355 to 1814 computations (71.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
29.0b	(tan.f64 (*.f64 PI.f64 l))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `tan-quot_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 72

Calls

4 calls:

4.0ms	(*.f64 PI.f64 l)
4.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series134.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
34.0ms	(tan.f64 (*.f64 PI.f64 l))
15.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5145	1019

prune79.0ms (1.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	84	18	102

Merged error: 13.8b

Counts

102 → 18

Compiler

Compiled 1773 to 545 computations (69.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.6b	(/.f64 1 (/.f64 F (tan.f64 (*.f64 PI.f64 l))))
29.0b	(tan.f64 (*.f64 PI.f64 l))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64`
14×	`associate-/r*_binary64`
13×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`div-exp_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`associate-/r/_binary64` `div-inv_binary64` `tan-quot_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `rec-exp_binary64` `*-commutative_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 124

Calls

4 calls:

7.0ms	(/.f64 1 (/.f64 F (tan.f64 (*.f64 PI.f64 l))))
6.0ms	(*.f64 PI.f64 l)
4.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series156.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(/.f64 1 (/.f64 F (tan.f64 (*.f64 PI.f64 l))))
33.0ms	(tan.f64 (*.f64 PI.f64 l))
16.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4931	2260
1	4931	2260

prune104.0ms (1.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	15	16
Picked	0	1	1
Done	0	1	1
Total	136	18	154

Merged error: 13.8b

Counts

154 → 18

Compiler

Compiled 2718 to 804 computations (70.4% saved)

regimes570.0ms (9%)

Compiler: Compiled 7570 to 4337 computations (42.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	23
1	33	23

end0.0ms (0%)

sample3.0s (46.7%)

Algorithm

1×

intervals

Results

899.0ms	1067×	body	2048	valid
444.0ms	1842×	body	1024	valid
211.0ms	4033×	body	128	valid
176.0ms	52×	body	4096	valid
116.0ms	715×	body	512	valid
33.0ms	291×	body	256	valid
13.0ms	188×	body	128	invalid
6.0ms	9×	body	2048	invalid
2.0ms	5×	body	8192	exit

Compiler

Compiled 1212 to 695 computations (42.7% saved)

Details

analyze857.0ms (13.5%)

sample88.0ms (1.4%)

simplify115.0ms (1.8%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

rewrite22.0ms (0.3%)

series164.0ms (2.6%)

simplify78.0ms (1.2%)

prune90.0ms (1.4%)

localize9.0ms (0.1%)

rewrite55.0ms (0.9%)

series164.0ms (2.6%)

simplify164.0ms (2.6%)

prune254.0ms (4%)

localize8.0ms (0.1%)

rewrite18.0ms (0.3%)

series134.0ms (2.1%)

simplify94.0ms (1.5%)

prune79.0ms (1.2%)

localize9.0ms (0.1%)

rewrite29.0ms (0.5%)

series156.0ms (2.5%)

simplify99.0ms (1.6%)

prune104.0ms (1.6%)

regimes570.0ms (9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.0s (46.7%)

Profiling