Details

analyze2.6s (10.8%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.5%	0.5%	11
0%	99.1%	0.9%	12
0.4%	97.3%	2.3%	13
0.7%	95.8%	3.5%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample444.0ms (1.8%)

Algorithm

1×

intervals

Results

162.0ms	50×	body	4096	invalid
83.0ms	128×	body	1024	valid
64.0ms	31×	body	2048	invalid
36.0ms	31×	body	2048	valid
33.0ms	14×	body	4096	valid
19.0ms	45×	body	512	valid
9.0ms	14×	body	1024	invalid
6.0ms	40×	body	128	invalid
4.0ms	16×	body	256	valid
4.0ms	12×	body	512	invalid
3.0ms	22×	body	128	valid
2.0ms	8×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify180.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5185	32

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 42.9b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
1.1b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
19.0b	(/.f64 (pow.f64 t 3) (*.f64 l l))
27.1b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite81.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-exp-log_binary64_449`
139×	`prod-exp_binary64_460`
52×	`add-cbrt-cube_binary64_447`
51×	`div-exp_binary64_462`
37×	`times-frac_binary64_420`
33×	`add-sqr-sqrt_binary64_435`
32×	`pow-exp_binary64_479`
26×	`cbrt-unprod_binary64_444`
24×	`add-cube-cbrt_binary64_446` `-un-lft-identity_binary64_414` `associate-r*_binary64_356`
23×	`pow-to-exp_binary64_480` `unpow-prod-down_binary64_490`
18×	`associate-l_binary64_357`
12×	`associate-/l*_binary64_361`
11×	`pow1_binary64_472`
10×	`associate-*l/_binary64_359` `cube-prod_binary64_439`
8×	`cbrt-undiv_binary64_445`
5×	`sqr-pow_binary64_386` `unswap-sqr_binary64_382`
4×	`pow-prod-down_binary64_482` `add-log-exp_binary64_450` `tan-quot_binary64_570`
3×	`div-inv_binary64_411` `cube-mult_binary64_441` `*-commutative_binary64_347` `unpow3_binary64_477`
2×	`frac-times_binary64_424` `associate-*r/_binary64_358`
1×	`clear-num_binary64_413` `frac-2neg_binary64_425` `unpow2_binary64_476` `associate-/r*_binary64_360`

Counts

4 → 187

Calls

4 calls:

21.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
13.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
12.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
8.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.2s (4.7%)

Counts

4 → 12

Calls

4 calls:

652.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
333.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
124.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
46.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify74.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5158	4265

prune304.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	187	12	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	12	200

Merged error: 13.2b

Counts

200 → 12

Compiler

Compiled 5296 to 2713 computations (48.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
1.4b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.4b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
20.2b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite78.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`add-exp-log_binary64_449`
183×	`prod-exp_binary64_460`
173×	`add-cbrt-cube_binary64_447`
87×	`cbrt-unprod_binary64_444`
82×	`div-exp_binary64_462`
46×	`cbrt-undiv_binary64_445`
23×	`add-sqr-sqrt_binary64_435`
20×	`times-frac_binary64_420`
17×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
15×	`pow-exp_binary64_479` `pow-to-exp_binary64_480`
9×	`pow1_binary64_472` `associate-r_binary64_356`
6×	`div-inv_binary64_411` `associate-/r*_binary64_360`
4×	`associate-l_binary64_357` `unpow-prod-down_binary64_490` `add-log-exp_binary64_450` `unswap-sqr_binary64_382` `associate-/l*_binary64_361`
3×	`pow-prod-down_binary64_482`
2×	`clear-num_binary64_413` `*-commutative_binary64_347` `sqr-pow_binary64_386` `frac-2neg_binary64_425` `unpow2_binary64_476`
1×	`associate-/r/_binary64_362`

Counts

4 → 184

Calls

4 calls:

17.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
15.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
9.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

series1.0s (4.1%)

Counts

4 → 12

Calls

4 calls:

520.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
311.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
103.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
78.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4985	5216
1	4985	5216

prune252.0ms (1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	184	12	196
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	187	21	208

Merged error: 9.0b

Counts

208 → 21

Compiler

Compiled 5102 to 2416 computations (52.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.5b	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
1.4b	(*.f64 t (pow.f64 (sin.f64 k) 2))
20.2b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite66.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-exp-log_binary64_449`
128×	`add-cbrt-cube_binary64_447`
111×	`prod-exp_binary64_460`
61×	`cbrt-unprod_binary64_444`
55×	`div-exp_binary64_462`
37×	`cbrt-undiv_binary64_445`
25×	`add-sqr-sqrt_binary64_435`
20×	`times-frac_binary64_420`
19×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
8×	`pow-exp_binary64_479` `pow-to-exp_binary64_480` `associate-r_binary64_356`
7×	`unpow-prod-down_binary64_490`
6×	`div-inv_binary64_411` `associate-/r*_binary64_360`
5×	`pow1_binary64_472`
4×	`add-log-exp_binary64_450` `unswap-sqr_binary64_382` `associate-/l*_binary64_361`
3×	`pow-unpow_binary64_488` `sqr-pow_binary64_386` `associate-l_binary64_357` `unpow2_binary64_476`
2×	`clear-num_binary64_413` `frac-2neg_binary64_425`
1×	`associate-/r/_binary64_362` `*-commutative_binary64_347` `pow-pow_binary64_483`

Counts

4 → 154

Calls

4 calls:

16.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
15.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series943.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

529.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
308.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
74.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
32.0ms	(pow.f64 (sin.f64 k) 2)

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4962	4249
1	4962	4249

prune213.0ms (0.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	167	20	187

Merged error: 8.8b

Counts

187 → 20

Compiler

Compiled 4509 to 2268 computations (49.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))))
1.4b	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.4b	(/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
17.1b	(/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))

rewrite115.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

476×	`times-frac_binary64_420`
208×	`add-exp-log_binary64_449`
172×	`add-sqr-sqrt_binary64_435`
166×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
133×	`add-cbrt-cube_binary64_447`
106×	`div-exp_binary64_462`
70×	`cbrt-undiv_binary64_445`
63×	`prod-exp_binary64_460`
60×	`associate-/r*_binary64_360`
41×	`div-inv_binary64_411`
31×	`cbrt-unprod_binary64_444`
23×	`associate-/r/_binary64_362`
8×	`associate-r_binary64_356`
7×	`pow-exp_binary64_479` `pow-to-exp_binary64_480` `associate-/l*_binary64_361`
4×	`pow1_binary64_472` `unpow-prod-down_binary64_490` `add-log-exp_binary64_450` `unswap-sqr_binary64_382`
3×	`clear-num_binary64_413` `associate-l_binary64_357` `frac-2neg_binary64_425`
2×	`sqr-pow_binary64_386` `unpow2_binary64_476`
1×	`*-commutative_binary64_347`

Counts

4 → 359

Calls

4 calls:

22.0ms	(/.f64 2 (/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))))
15.0ms	(/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
12.0ms	(/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

series1.0s (4.2%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
332.0ms	(/.f64 2 (/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))))
292.0ms	(/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
72.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify136.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4990	13754
1	4990	13754

prune619.0ms (2.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	359	12	371
Fresh	12	7	19
Picked	1	0	1
Done	0	0	0
Total	372	19	391

Merged error: 1.5b

Counts

391 → 19

Compiler

Compiled 10945 to 5407 computations (50.6% saved)

regimes189.0ms (0.8%)

Compiler: Compiled 2076 to 1497 computations (27.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	32
1	22	32

end0.0ms (0%)

sample14.7s (60.1%)

Algorithm

1×

intervals

Results

4.9s	1300×	body	4096	invalid
2.5s	3867×	body	1024	valid
2.3s	1071×	body	2048	invalid
1.2s	492×	body	4096	valid
1.1s	1037×	body	2048	valid
577.0ms	1322×	body	512	valid
424.0ms	714×	body	1024	invalid
195.0ms	504×	body	512	invalid
147.0ms	1031×	body	128	invalid
144.0ms	502×	body	256	valid
114.0ms	780×	body	128	valid
83.0ms	294×	body	256	invalid

Compiler

Compiled 530 to 387 computations (27% saved)

Details

analyze2.6s (10.8%)

sample444.0ms (1.8%)

simplify180.0ms (0.7%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite81.0ms (0.3%)

series1.2s (4.7%)

simplify74.0ms (0.3%)

prune304.0ms (1.2%)

localize16.0ms (0.1%)

rewrite78.0ms (0.3%)

series1.0s (4.1%)

simplify96.0ms (0.4%)

prune252.0ms (1%)

localize16.0ms (0.1%)

rewrite66.0ms (0.3%)

series943.0ms (3.8%)

simplify104.0ms (0.4%)

prune213.0ms (0.9%)

localize16.0ms (0.1%)

rewrite115.0ms (0.5%)

series1.0s (4.2%)

simplify136.0ms (0.6%)

prune619.0ms (2.5%)

regimes189.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample14.7s (60.1%)

Profiling