Details

analyze2.4s (11.1%)

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)

sample414.0ms (1.9%)

Algorithm

1×

intervals

Results

146.0ms	35×	body	4096	invalid
69.0ms	125×	body	1024	valid
63.0ms	32×	body	2048	invalid
43.0ms	34×	body	2048	valid
19.0ms	14×	body	4096	valid
15.0ms	39×	body	512	valid
13.0ms	20×	body	512	invalid
11.0ms	20×	body	1024	invalid
4.0ms	16×	body	256	valid
4.0ms	28×	body	128	valid
4.0ms	16×	body	256	invalid
4.0ms	27×	body	128	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify115.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

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

Error

39.5b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
1.7b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
16.6b	(/.f64 (pow.f64 t 3) (*.f64 l l))
25.9b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite76.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-exp-log_binary64_457`
139×	`prod-exp_binary64_468`
52×	`add-cbrt-cube_binary64_455`
51×	`div-exp_binary64_470`
37×	`times-frac_binary64_425`
33×	`add-sqr-sqrt_binary64_441`
32×	`pow-exp_binary64_487`
26×	`cbrt-unprod_binary64_452`
24×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
23×	`unpow-prod-down_binary64_498` `pow-to-exp_binary64_488`
18×	`associate-l_binary64_360`
12×	`associate-/l*_binary64_364`
11×	`pow1_binary64_480`
10×	`associate-*l/_binary64_362` `cube-prod_binary64_447`
8×	`cbrt-undiv_binary64_453`
5×	`unswap-sqr_binary64_387` `sqr-pow_binary64_391`
4×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458` `tan-quot_binary64_578`
3×	`unpow3_binary64_485` `cube-mult_binary64_449` `div-inv_binary64_416` `*-commutative_binary64_350`
2×	`frac-times_binary64_429` `associate-*r/_binary64_361`
1×	`clear-num_binary64_418` `frac-2neg_binary64_430` `unpow2_binary64_484` `associate-/r*_binary64_363`

Counts

4 → 187

Calls

4 calls:

20.0ms	(.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))
11.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series613.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

351.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
168.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
67.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
26.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5178	4255

prune287.0ms (1.3%)

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

Error

14.1b

Counts

200 → 12

Compiler

Compiled 5317 to 2717 computations (48.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(/.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))
5.1b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
19.8b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite74.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`add-exp-log_binary64_457`
183×	`prod-exp_binary64_468`
173×	`add-cbrt-cube_binary64_455`
87×	`cbrt-unprod_binary64_452`
82×	`div-exp_binary64_470`
46×	`cbrt-undiv_binary64_453`
23×	`add-sqr-sqrt_binary64_441`
20×	`times-frac_binary64_425`
17×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
15×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
9×	`associate-r_binary64_359` `pow1_binary64_480`
6×	`div-inv_binary64_416` `associate-/r*_binary64_363`
4×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `unswap-sqr_binary64_387` `associate-l_binary64_360` `associate-/l*_binary64_364`
3×	`pow-prod-down_binary64_490`
2×	`clear-num_binary64_418` `sqr-pow_binary64_391` `*-commutative_binary64_350` `frac-2neg_binary64_430` `unpow2_binary64_484`
1×	`associate-/r/_binary64_365`

Counts

4 → 184

Calls

4 calls:

20.0ms	(/.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))

series529.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

277.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
151.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
59.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
42.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify122.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4978	5209
1	4978	5209

prune252.0ms (1.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	186	10	196
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	188	20	208

Error

10.0b

Counts

208 → 20

Compiler

Compiled 5139 to 2422 computations (52.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.6b	(/.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))
19.8b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-exp-log_binary64_457`
128×	`add-cbrt-cube_binary64_455`
111×	`prod-exp_binary64_468`
61×	`cbrt-unprod_binary64_452`
55×	`div-exp_binary64_470`
37×	`cbrt-undiv_binary64_453`
25×	`add-sqr-sqrt_binary64_441`
20×	`times-frac_binary64_425`
19×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`associate-r_binary64_359` `pow-exp_binary64_487` `pow-to-exp_binary64_488`
7×	`unpow-prod-down_binary64_498`
6×	`div-inv_binary64_416` `associate-/r*_binary64_363`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `associate-/l*_binary64_364`
3×	`sqr-pow_binary64_391` `associate-l_binary64_360` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`associate-/r/_binary64_365` `*-commutative_binary64_350` `pow-pow_binary64_491`

Counts

4 → 154

Calls

4 calls:

15.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
14.0ms	(/.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)

series498.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
170.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
38.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
16.0ms	(pow.f64 (sin.f64 k) 2)

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4983	4252
1	4983	4252

prune204.0ms (0.9%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	6	13	19
Picked	0	1	1
Done	0	0	0
Total	166	20	186

Error

9.2b

Counts

186 → 20

Compiler

Compiled 4461 to 2234 computations (49.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 2 (.f64 (/.f64 k (.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))
8.9b	(/.f64 k (*.f64 l l))
10.9b	(.f64 (/.f64 k (.f64 l l)) (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))

rewrite59.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

208×	`add-exp-log_binary64_457`
133×	`add-cbrt-cube_binary64_455`
94×	`prod-exp_binary64_468`
75×	`div-exp_binary64_470`
52×	`cbrt-unprod_binary64_452`
49×	`cbrt-undiv_binary64_453`
25×	`add-sqr-sqrt_binary64_441`
15×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
13×	`times-frac_binary64_425`
10×	`associate-l_binary64_360`
7×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
6×	`unswap-sqr_binary64_387` `pow1_binary64_480` `associate-/l*_binary64_364`
4×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `div-inv_binary64_416`
3×	`associate-/r/_binary64_365`
2×	`associate-l/_binary64_362` `clear-num_binary64_418` `frac-times_binary64_429` `sqr-pow_binary64_391` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430` `unpow2_binary64_484` `associate-/r_binary64_363`
1×	`pow-prod-down_binary64_490`

Counts

4 → 158

Calls

4 calls:

15.0ms	(.f64 (/.f64 k (.f64 l l)) (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
14.0ms	(/.f64 2 (.f64 (/.f64 k (.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))
4.0ms	(/.f64 k (*.f64 l l))

series408.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(.f64 (/.f64 k (.f64 l l)) (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
168.0ms	(/.f64 2 (.f64 (/.f64 k (.f64 l l)) (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
42.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
17.0ms	(/.f64 k (*.f64 l l))

simplify106.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4972	3931
1	4972	3931

prune188.0ms (0.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	6	12	18
Picked	1	0	1
Done	1	0	1
Total	172	18	190

Error

3.8b

Counts

190 → 18

Compiler

Compiled 3881 to 1848 computations (52.4% saved)

regimes1.2s (5.7%)

Accuracy

Total 4.7b remaining (53.1%)

Threshold costs 0b (0%)

Compiler

Compiled 15508 to 11236 computations (27.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	41
1	22	41

end0.0ms (0%)

sample13.9s (63.6%)

Algorithm

1×

intervals

Results

3.9s	1310×	body	4096	invalid
2.0s	1076×	body	2048	invalid
2.0s	3824×	body	1024	valid
973.0ms	1012×	body	2048	valid
955.0ms	494×	body	4096	valid
556.0ms	1384×	body	512	valid
372.0ms	664×	body	1024	invalid
188.0ms	517×	body	512	invalid
140.0ms	1069×	body	128	invalid
121.0ms	452×	body	256	valid
117.0ms	834×	body	128	valid
75.0ms	313×	body	256	invalid

Compiler

Compiled 2326 to 1688 computations (27.4% saved)

Details

analyze2.4s (11.1%)

sample414.0ms (1.9%)

simplify115.0ms (0.5%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite76.0ms (0.4%)

series613.0ms (2.8%)

simplify78.0ms (0.4%)

prune287.0ms (1.3%)

localize15.0ms (0.1%)

rewrite74.0ms (0.3%)

series529.0ms (2.4%)

simplify122.0ms (0.6%)

prune252.0ms (1.2%)

localize17.0ms (0.1%)

rewrite58.0ms (0.3%)

series498.0ms (2.3%)

simplify112.0ms (0.5%)

prune204.0ms (0.9%)

localize15.0ms (0.1%)

rewrite59.0ms (0.3%)

series408.0ms (1.9%)

simplify106.0ms (0.5%)

prune188.0ms (0.9%)

regimes1.2s (5.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample13.9s (63.6%)

Profiling