Details

analyze1.2s (16.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1027	40
1	1027	40
0	2	2
1	2	2

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)

sample79.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	35×	body	2048	valid
16.0ms	57×	body	1024	valid
8.0ms	130×	body	128	valid
7.0ms	2×	body	4096	valid
4.0ms	23×	body	512	valid
1.0ms	9×	body	256	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

Error

15.8b

Counts

2 → 2

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
3.3b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
31.7b	(tan.f64 (*.f64 PI.f64 l))

rewrite20.0ms (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:

6.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series170.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
57.0ms	(tan.f64 (*.f64 PI.f64 l))
15.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5225	914

prune99.0ms (1.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	60	18	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	19	80

Error

12.4b

Counts

80 → 19

Compiler

Compiled 1608 to 463 computations (71.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.5b	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
31.7b	(tan.f64 (*.f64 PI.f64 l))

rewrite50.0ms (0.7%)

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:

12.0ms	(/.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))

series162.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
35.0ms	(tan.f64 (*.f64 PI.f64 l))
13.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify176.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4906	6379
1	4906	6379

prune266.0ms (3.6%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	250	10	260
Fresh	5	13	18
Picked	0	1	1
Done	0	0	0
Total	255	24	279

Error

12.4b

Counts

279 → 24

Compiler

Compiled 6479 to 1915 computations (70.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.3b	(.f64 (tan.f64 (.f64 PI.f64 l)) (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) F))
31.7b	(tan.f64 (*.f64 PI.f64 l))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64`
15×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`associate-l_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `times-frac_binary64`
3×	`pow-prod-down_binary64` `tan-quot_binary64` `*-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-r/_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(.f64 (tan.f64 (.f64 PI.f64 l)) (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) F))
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series130.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(.f64 (tan.f64 (.f64 PI.f64 l)) (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) F))
36.0ms	(tan.f64 (*.f64 PI.f64 l))
16.0ms	(*.f64 PI.f64 l)
13.0ms	(*.f64 PI.f64 l)

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4933	1182
1	4933	1182

prune134.0ms (1.8%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	2	20	22
Picked	0	1	1
Done	0	1	1
Total	87	23	110

Error

12.4b

Counts

110 → 23

Compiler

Compiled 2655 to 1514 computations (43% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

29.1b	(cbrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
31.7b	(tan.f64 (*.f64 PI.f64 l))
31.7b	(tan.f64 (*.f64 PI.f64 l))
31.7b	(tan.f64 (*.f64 PI.f64 l))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
44×	`cbrt-prod_binary64`
39×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `div-inv_binary64`
3×	`tan-quot_binary64`
1×	`cbrt-div_binary64` `pow1/3_binary64` `associate-/r/_binary64`

Counts

4 → 77

Calls

4 calls:

5.0ms	(cbrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
2.0ms	(tan.f64 (*.f64 PI.f64 l))
2.0ms	(tan.f64 (*.f64 PI.f64 l))
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series314.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
36.0ms	(tan.f64 (*.f64 PI.f64 l))
35.0ms	(tan.f64 (*.f64 PI.f64 l))
32.0ms	(tan.f64 (*.f64 PI.f64 l))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5229	2249

prune148.0ms (2%)

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	2	18	20
Picked	0	1	1
Done	0	2	2
Total	89	23	112

Error

11.5b

Counts

112 → 23

Compiler

Compiled 4544 to 1322 computations (70.9% saved)

regimes687.0ms (9.3%)

Accuracy

Total 1.5b remaining (12.3%)

Threshold costs 0b (0%)

Compiler

Compiled 8465 to 5104 computations (39.7% 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%)

sample3.4s (45.6%)

Algorithm

1×

intervals

Results

878.0ms	1003×	body	2048	valid
516.0ms	1907×	body	1024	valid
234.0ms	4007×	body	128	valid
172.0ms	51×	body	4096	valid
135.0ms	736×	body	512	valid
39.0ms	296×	body	256	valid
15.0ms	208×	body	128	invalid
4.0ms	8×	body	2048	invalid
1.0ms	1×	body	8192	exit

Compiler

Compiled 1349 to 816 computations (39.5% saved)

Details

analyze1.2s (16.2%)

sample79.0ms (1.1%)

simplify22.0ms (0.3%)

prune6.0ms (0.1%)

localize11.0ms (0.1%)

rewrite20.0ms (0.3%)

series170.0ms (2.3%)

simplify83.0ms (1.1%)

prune99.0ms (1.3%)

localize14.0ms (0.2%)

rewrite50.0ms (0.7%)

series162.0ms (2.2%)

simplify176.0ms (2.4%)

prune266.0ms (3.6%)

localize15.0ms (0.2%)

rewrite27.0ms (0.4%)

series130.0ms (1.8%)

simplify83.0ms (1.1%)

prune134.0ms (1.8%)

localize21.0ms (0.3%)

rewrite22.0ms (0.3%)

series314.0ms (4.2%)

simplify81.0ms (1.1%)

prune148.0ms (2%)

regimes687.0ms (9.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (45.6%)

Profiling