Details

analyze500.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample29.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	60×	body	1024	valid
6.0ms	150×	body	128	valid
4.0ms	31×	body	512	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify200.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune2.0ms (0%)

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

0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_782`
27×	`*-un-lft-identity_binary64_760`
22×	`add-cube-cbrt_binary64_795`
18×	`pow1_binary64_821`
15×	`times-frac_binary64_766`
10×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796`
8×	`tan-quot_binary64_919`
6×	`add-log-exp_binary64_799` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701`
5×	`associate-/l*_binary64_705`
3×	`associate-/r*_binary64_704`
2×	`pow2_binary64_841` `unswap-sqr_binary64_728` `associate-l/_binary64_703` `prod-exp_binary64_809` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `pow-sqr_binary64_733` `pow-plus_binary64_823` `frac-times_binary64_770` `associate-r/_binary64_702` `cbrt-unprod_binary64_793` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757` `flip-+_binary64_734` `div-sub_binary64_765` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 110

Calls

4 calls:

7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series338.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
50.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
46.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
44.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune169.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Error

0.1b

Counts

123 → 14

Compiler

Compiled 2724 to 1598 computations (41.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (cos.f64 x) 2)
0.2b	(pow.f64 (cos.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839` `add-sqr-sqrt_binary64_782`
8×	`add-exp-log_binary64_798` `pow1_binary64_821`
4×	`unpow2_binary64_825` `add-log-exp_binary64_799` `pow-exp_binary64_828` `add-cbrt-cube_binary64_796` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `pow-pow_binary64_832`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)

series56.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow.f64 (sin.f64 x) 2)
14.0ms	(pow.f64 (sin.f64 x) 2)
13.0ms	(pow.f64 (cos.f64 x) 2)
13.0ms	(pow.f64 (cos.f64 x) 2)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4882	660
1	4882	660

prune127.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	85	13	98

Error

0.1b

Counts

98 → 13

Compiler

Compiled 2471 to 1636 computations (33.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (pow.f64 (tan.f64 x) 2))
0.2b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite72.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64_766`
331×	`*-un-lft-identity_binary64_760`
269×	`add-sqr-sqrt_binary64_782`
136×	`difference-of-squares_binary64_729`
133×	`add-cube-cbrt_binary64_795`
54×	`associate-/r*_binary64_704`
48×	`distribute-lft-out_binary64_711`
43×	`unpow-prod-down_binary64_839`
37×	`unpow2_binary64_825` `sqr-pow_binary64_732`
17×	`add-exp-log_binary64_798` `distribute-lft-out--_binary64_712`
9×	`associate-/r/_binary64_706` `add-cbrt-cube_binary64_796`
8×	`cancel-sign-sub-inv_binary64_726`
7×	`div-exp_binary64_811` `pow1_binary64_821`
6×	`add-log-exp_binary64_799` `pow-unpow_binary64_837`
5×	`div-inv_binary64_757` `flip--_binary64_735` `flip3--_binary64_764`
3×	`cbrt-undiv_binary64_794` `associate-/l*_binary64_705`
2×	`pow-exp_binary64_828` `pow-to-exp_binary64_829` `rec-exp_binary64_810` `1-exp_binary64_804` `pow-pow_binary64_832`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `inv-pow_binary64_845` `clear-num_binary64_759` `sub-neg_binary64_753` `pow-flip_binary64_834`

Counts

4 → 304

Calls

4 calls:

20.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
7.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series325.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
46.0ms	(pow.f64 (tan.f64 x) 2)
46.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
38.0ms	(pow.f64 (tan.f64 x) 2)

simplify131.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4976	9047
1	4976	9047

prune510.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	314	2	316
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	317	12	329

Error

0.1b

Counts

329 → 12

Compiler

Compiled 7941 to 5729 computations (27.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
0.2b	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite236.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1992×	`times-frac_binary64_766`
1297×	`*-un-lft-identity_binary64_760`
1161×	`add-sqr-sqrt_binary64_782`
673×	`add-cube-cbrt_binary64_795`
488×	`difference-of-squares_binary64_729`
129×	`distribute-lft-out_binary64_711`
128×	`unpow-prod-down_binary64_839`
127×	`associate-/r/_binary64_706`
124×	`unpow2_binary64_825` `sqr-pow_binary64_732`
64×	`div-inv_binary64_757`
61×	`distribute-lft-out--_binary64_712`
54×	`associate-/r*_binary64_704`
50×	`add-exp-log_binary64_798`
43×	`flip3-+_binary64_763` `flip-+_binary64_734`
34×	`div-exp_binary64_811`
21×	`associate-/l*_binary64_705`
20×	`flip--_binary64_735` `flip3--_binary64_764`
18×	`add-cbrt-cube_binary64_796`
9×	`cbrt-undiv_binary64_794` `rec-exp_binary64_810` `1-exp_binary64_804`
7×	`pow1_binary64_821`
6×	`pow-unpow_binary64_837`
4×	`add-log-exp_binary64_799`
2×	`frac-2neg_binary64_771` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `clear-num_binary64_759` `pow-pow_binary64_832`
1×	`associate-/l/_binary64_707` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 953

Calls

4 calls:

39.0ms	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
9.0ms	(/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series384.0ms (4%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(/.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
106.0ms	(/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
50.0ms	(pow.f64 (tan.f64 x) 2)
38.0ms	(pow.f64 (tan.f64 x) 2)

simplify410.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

965 → 965

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5021	38293

prune2.9s (30.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	961	4	965
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	965	12	977

Error

0.0b

Counts

977 → 12

Compiler

Compiled 27166 to 20109 computations (26% saved)

regimes660.0ms (6.9%)

Accuracy

Total 0.3b remaining (89%)

Threshold costs 0.3b (89%)

Compiler

Compiled 5682 to 4392 computations (22.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms (0%)

sample2.3s (23.9%)

Algorithm

1×

intervals

Results

345.0ms	1968×	body	1024	valid
194.0ms	4524×	body	128	valid
129.0ms	1013×	body	512	valid
43.0ms	491×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 1438 to 1112 computations (22.7% saved)

Details

analyze500.0ms (5.2%)

sample29.0ms (0.3%)

simplify200.0ms (2.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite28.0ms (0.3%)

series338.0ms (3.5%)

simplify80.0ms (0.8%)

prune169.0ms (1.8%)

localize14.0ms (0.1%)

rewrite15.0ms (0.2%)

series56.0ms (0.6%)

simplify93.0ms (1%)

prune127.0ms (1.3%)

localize11.0ms (0.1%)

rewrite72.0ms (0.7%)

series325.0ms (3.4%)

simplify131.0ms (1.4%)

prune510.0ms (5.3%)

localize10.0ms (0.1%)

rewrite236.0ms (2.5%)

series384.0ms (4%)

simplify410.0ms (4.3%)

prune2.9s (30.2%)

regimes660.0ms (6.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (23.9%)

Profiling