Details

analyze854.0ms (7.9%)

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)

sample57.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	71×	body	1024	valid
10.0ms	137×	body	128	valid
8.0ms	37×	body	512	valid
2.0ms	11×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify337.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune4.0ms (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

Merged error: 0.4b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series726.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

428.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
100.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
100.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
96.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify157.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4912	2005
1	4912	2005

prune197.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 0.1b

Counts

123 → 13

Compiler

Compiled 2709 to 1581 computations (41.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1 (tan.f64 x))
0.2b	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
0.2b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite151.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`*-un-lft-identity_binary64`
264×	`times-frac_binary64`
183×	`add-sqr-sqrt_binary64`
105×	`add-cube-cbrt_binary64`
68×	`distribute-lft-out_binary64`
52×	`difference-of-squares_binary64`
36×	`associate-/r*_binary64`
26×	`distribute-lft-out--_binary64`
13×	`associate-/r/_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-/l*_binary64`
7×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `cancel-sign-sub-inv_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 256

Calls

4 calls:

43.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
25.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
8.0ms	(-.f64 1 (tan.f64 x))
6.0ms	(pow.f64 (tan.f64 x) 2)

series1.0s (9.5%)

Counts

4 → 12

Calls

4 calls:

546.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
293.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
132.0ms	(pow.f64 (tan.f64 x) 2)
62.0ms	(-.f64 1 (tan.f64 x))

simplify179.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5002	9410

prune728.0ms (6.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	261	7	268
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	266	15	281

Merged error: 0.0b

Counts

281 → 15

Compiler

Compiled 7922 to 5232 computations (34% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.4b	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))

rewrite79.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
70×	`add-sqr-sqrt_binary64`
68×	`times-frac_binary64`
38×	`cancel-sign-sub-inv_binary64`
29×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`
15×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
10×	`unpow2_binary64` `sqr-pow_binary64`
9×	`pow-unpow_binary64`
8×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `distribute-rgt-out--_binary64` `associate-/r/_binary64`
4×	`add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-pow_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 134

Calls

4 calls:

54.0ms	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series1.0s (9.5%)

Counts

4 → 12

Calls

4 calls:

733.0ms	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
108.0ms	(pow.f64 (tan.f64 x) 2)
102.0ms	(pow.f64 (tan.f64 x) 2)
89.0ms	(pow.f64 (tan.f64 x) 2)

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5028	3349

prune293.0ms (2.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	145	16	161

Merged error: 0.0b

Counts

161 → 16

Compiler

Compiled 4237 to 3015 computations (28.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`pow1_binary64`
37×	`pow-prod-up_binary64`
36×	`tan-quot_binary64`
24×	`pow-prod-down_binary64`
23×	`pow-sqr_binary64`
20×	`add-exp-log_binary64`
19×	`pow-plus_binary64`
18×	`add-cbrt-cube_binary64` `frac-times_binary64`
14×	`add-sqr-sqrt_binary64` `pow2_binary64`
12×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `associate-*l/_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`pow-unpow_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

14.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series457.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))
115.0ms	(pow.f64 (tan.f64 x) 2)
95.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
92.0ms	(pow.f64 (tan.f64 x) 2)

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4858	1093
1	4858	1093

prune242.0ms (2.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	3	11	14
Picked	0	1	1
Done	0	1	1
Total	155	15	170

Merged error: 0.0b

Counts

170 → 15

Compiler

Compiled 4380 to 2649 computations (39.5% saved)

regimes712.0ms (6.6%)

Compiler: Compiled 7318 to 5400 computations (26.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample3.3s (30%)

Algorithm

1×

intervals

Results

510.0ms	1996×	body	1024	valid
223.0ms	4426×	body	128	valid
171.0ms	1025×	body	512	valid
60.0ms	549×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 1849 to 1361 computations (26.4% saved)

Details

analyze854.0ms (7.9%)

sample57.0ms (0.5%)

simplify337.0ms (3.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite41.0ms (0.4%)

series726.0ms (6.7%)

simplify157.0ms (1.4%)

prune197.0ms (1.8%)

localize19.0ms (0.2%)

rewrite151.0ms (1.4%)

series1.0s (9.5%)

simplify179.0ms (1.6%)

prune728.0ms (6.7%)

localize10.0ms (0.1%)

rewrite79.0ms (0.7%)

series1.0s (9.5%)

simplify104.0ms (1%)

prune293.0ms (2.7%)

localize13.0ms (0.1%)

rewrite43.0ms (0.4%)

series457.0ms (4.2%)

simplify104.0ms (1%)

prune242.0ms (2.2%)

regimes712.0ms (6.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.3s (30%)

Profiling