Details

analyze515.0ms (12.1%)

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

sample38.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	48×	body	1280	valid
7.0ms	40×	body	640	valid
5.0ms	132×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid

simplify557.0ms (13.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5284	15

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: 0.3b

Counts

2 → 1

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.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))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`pow1_binary64`
12×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`difference-of-squares_binary64`
4×	`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` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 104

Calls

4 calls:

8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
7.0ms	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))

series99.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
23.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
12.0ms	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
11.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune198.0ms (4.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	13	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Merged error: 0.0b

Counts

117 → 13

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2)))
0.2b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2))))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite55.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64`
239×	`add-sqr-sqrt_binary64`
237×	`*-un-lft-identity_binary64`
113×	`add-cube-cbrt_binary64`
84×	`difference-of-squares_binary64`
46×	`associate-/r*_binary64`
41×	`distribute-lft-out_binary64`
27×	`unpow-prod-down_binary64`
23×	`unpow2_binary64` `sqr-pow_binary64`
21×	`distribute-lft-out--_binary64`
19×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`div-exp_binary64`
7×	`pow1_binary64` `associate-/l*_binary64`
6×	`pow-unpow_binary64` `div-inv_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `1-exp_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 272

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2))))
14.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2)))
4.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series117.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2))))
45.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2)))
11.0ms	(pow.f64 (tan.f64 x) 2)
11.0ms	(pow.f64 (tan.f64 x) 2)

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5170	5486

prune536.0ms (12.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	279	5	284
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	283	14	297

Merged error: 0.0b

Counts

297 → 14

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))))

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
88×	`*-un-lft-identity_binary64`
64×	`times-frac_binary64`
39×	`log-pow_binary64`
38×	`exp-prod_binary64`
36×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
17×	`distribute-lft-out_binary64`
15×	`unpow-prod-down_binary64`
11×	`unpow2_binary64` `sqr-pow_binary64`
9×	`distribute-lft-out--_binary64`
8×	`add-exp-log_binary64` `associate-/l*_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/l/_binary64` `pow-pow_binary64` `div-sub_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 148

Calls

4 calls:

18.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))))
14.0ms	(/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series113.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
45.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))))
11.0ms	(pow.f64 (tan.f64 x) 2)
11.0ms	(pow.f64 (tan.f64 x) 2)

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5018	2243

prune259.0ms (6.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	160	14	174

Merged error: 0.0b

Counts

174 → 14

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 x) (sin.f64 x))
0.2b	(/.f64 (-.f64 1.0 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1.0 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
7.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series97.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(/.f64 (-.f64 1.0 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
19.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
12.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
11.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify48.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5054	1679

prune129.0ms (3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	122	13	135

Merged error: 0.0b

Counts

135 → 13

regimes165.0ms (3.9%)

Accuracy

Total 0.2b remaining (78.7%)

Threshold costs 0.2b (78.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	21
1	45	21

end0.0ms (0%)

sample980.0ms (23.1%)

Algorithm

1×

intervals

Results

387.0ms	1508×	body	1280	valid
196.0ms	1171×	body	640	valid
165.0ms	4377×	body	80	valid
79.0ms	640×	body	320	valid
25.0ms	304×	body	160	valid

Details

analyze515.0ms (12.1%)

sample38.0ms (0.9%)

simplify557.0ms (13.1%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite28.0ms (0.7%)

series99.0ms (2.3%)

simplify56.0ms (1.3%)

prune198.0ms (4.7%)

localize11.0ms (0.3%)

rewrite55.0ms (1.3%)

series117.0ms (2.7%)

simplify76.0ms (1.8%)

prune536.0ms (12.6%)

localize12.0ms (0.3%)

rewrite47.0ms (1.1%)

series113.0ms (2.7%)

simplify42.0ms (1%)

prune259.0ms (6.1%)

localize14.0ms (0.3%)

rewrite31.0ms (0.7%)

series97.0ms (2.3%)

simplify48.0ms (1.1%)

prune129.0ms (3%)

regimes165.0ms (3.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample980.0ms (23.1%)

Profiling