Details

analyze865.0ms (9.7%)

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)

sample124.0ms (1.4%)

Algorithm

1×

intervals

Results

73.0ms	38×	body	2048	valid
24.0ms	63×	body	1024	valid
10.0ms	120×	body	128	valid
5.0ms	26×	body	512	valid
1.0ms	9×	body	256	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify196.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	287	20
1	287	20

prune14.0ms (0.2%)

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: 17.4b

Counts

2 → 2

Compiler

Compiled 64 to 44 computations (31.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 l)
0.3b	(*.f64 PI.f64 l)
3.6b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
32.2b	(tan.f64 (*.f64 PI.f64 l))

rewrite23.0ms (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)
3.0ms	(tan.f64 (*.f64 PI.f64 l))

series314.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
88.0ms	(tan.f64 (*.f64 PI.f64 l))
34.0ms	(*.f64 PI.f64 l)
31.0ms	(*.f64 PI.f64 l)

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4967	914
1	4967	914

prune436.0ms (4.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	58	20	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	21	80

Merged error: 13.8b

Counts

80 → 21

Compiler

Compiled 7842 to 4094 computations (47.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
0.3b	(*.f64 PI.f64 l)
0.3b	(*.f64 PI.f64 l)
32.2b	(tan.f64 (*.f64 PI.f64 l))

rewrite20.0ms (0.2%)

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

series254.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
65.0ms	(tan.f64 (*.f64 PI.f64 l))
29.0ms	(*.f64 PI.f64 l)
28.0ms	(*.f64 PI.f64 l)

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4878	1019
1	4878	1019

prune323.0ms (3.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	6	14	20
Picked	0	1	1
Done	0	0	0
Total	84	21	105

Merged error: 13.8b

Counts

105 → 21

Compiler

Compiled 6133 to 3293 computations (46.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 l)
0.3b	(*.f64 PI.f64 l)
0.6b	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
32.2b	(tan.f64 (*.f64 PI.f64 l))

rewrite64.0ms (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:

14.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
4.0ms	(*.f64 PI.f64 l)
4.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series320.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
66.0ms	(tan.f64 (*.f64 PI.f64 l))
30.0ms	(*.f64 PI.f64 l)
28.0ms	(*.f64 PI.f64 l)

simplify148.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5127	6495

prune666.0ms (7.5%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	252	8	260
Fresh	4	15	19
Picked	1	0	1
Done	0	1	1
Total	257	24	281

Merged error: 13.8b

Counts

281 → 24

Compiler

Compiled 14579 to 6447 computations (55.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))) F)))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
32.1b	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))

rewrite62.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

396×	`times-frac_binary64`
193×	`add-sqr-sqrt_binary64`
191×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
44×	`associate-/r*_binary64`
25×	`add-exp-log_binary64`
17×	`div-inv_binary64`
15×	`div-exp_binary64`
13×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`cbrt-undiv_binary64` `sqrt-prod_binary64`
5×	`associate-/r/_binary64`
4×	`add-log-exp_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `tan-quot_binary64`

Counts

4 → 238

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))) F)))
3.0ms	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series250.0ms (2.8%)

Counts

4 → 8

Calls

4 calls:

187.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))) F)))
62.0ms	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify141.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5086	6429

prune247.0ms (2.8%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	0	22	22
Picked	1	0	1
Done	0	1	1
Total	246	24	270

Merged error: 13.8b

Counts

270 → 24

Compiler

Compiled 6623 to 1722 computations (74% saved)

regimes291.0ms (3.3%)

Compiler: Compiled 3437 to 2052 computations (40.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	23
1	69	23

end0.0ms (0%)

sample4.0s (44.6%)

Algorithm

1×

intervals

Results

1.9s	990×	body	2048	valid
699.0ms	1837×	body	1024	valid
354.0ms	47×	body	4096	valid
213.0ms	4128×	body	128	valid
157.0ms	727×	body	512	valid
35.0ms	271×	body	256	valid
11.0ms	188×	body	128	invalid
6.0ms	7×	body	2048	invalid
2.0ms	4×	body	8192	exit

Compiler

Compiled 557 to 335 computations (39.9% saved)

Details

analyze865.0ms (9.7%)

sample124.0ms (1.4%)

simplify196.0ms (2.2%)

prune14.0ms (0.2%)

localize10.0ms (0.1%)

rewrite23.0ms (0.3%)

series314.0ms (3.5%)

simplify68.0ms (0.8%)

prune436.0ms (4.9%)

localize12.0ms (0.1%)

rewrite20.0ms (0.2%)

series254.0ms (2.8%)

simplify71.0ms (0.8%)

prune323.0ms (3.6%)

localize10.0ms (0.1%)

rewrite64.0ms (0.7%)

series320.0ms (3.6%)

simplify148.0ms (1.7%)

prune666.0ms (7.5%)

localize13.0ms (0.2%)

rewrite62.0ms (0.7%)

series250.0ms (2.8%)

simplify141.0ms (1.6%)

prune247.0ms (2.8%)

regimes291.0ms (3.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.0s (44.6%)

Profiling