Details

analyze2.6s (11.7%)

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)

sample387.0ms (1.8%)

Algorithm

1×

intervals

Results

115.0ms	39×	body	4096	invalid
86.0ms	136×	body	1024	valid
76.0ms	34×	body	2048	invalid
31.0ms	30×	body	2048	valid
17.0ms	40×	body	512	valid
16.0ms	9×	body	4096	valid
11.0ms	20×	body	1024	invalid
5.0ms	37×	body	128	invalid
5.0ms	16×	body	256	valid
4.0ms	25×	body	128	valid
3.0ms	8×	body	512	invalid
1.0ms	5×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify22.0ms (0.1%)

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: 36.5b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
1.5b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
14.9b	(/.f64 (pow.f64 t 3) (*.f64 l l))
25.2b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite82.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-exp-log_binary64`
139×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
51×	`div-exp_binary64`
37×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`pow-exp_binary64`
26×	`cbrt-unprod_binary64`
24×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
23×	`pow-to-exp_binary64` `unpow-prod-down_binary64`
18×	`associate-l_binary64`
12×	`associate-/l*_binary64`
11×	`pow1_binary64`
10×	`cube-prod_binary64` `associate-*l/_binary64`
8×	`cbrt-undiv_binary64`
5×	`sqr-pow_binary64` `unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `tan-quot_binary64`
3×	`div-inv_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
2×	`associate-*r/_binary64` `frac-times_binary64`
1×	`associate-/r*_binary64` `unpow2_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 187

Calls

4 calls:

22.0ms	(.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))
10.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.1s (5.1%)

Counts

4 → 12

Calls

4 calls:

641.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
318.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
121.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
43.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify70.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5158	4265

prune292.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	188	11	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	11	200

Merged error: 15.7b

Counts

200 → 11

Compiler

Compiled 5268 to 2689 computations (49% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.7b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
19.6b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`add-exp-log_binary64`
102×	`prod-exp_binary64`
87×	`add-cbrt-cube_binary64`
48×	`cbrt-unprod_binary64`
27×	`div-exp_binary64`
15×	`cbrt-undiv_binary64` `add-sqr-sqrt_binary64`
10×	`pow-to-exp_binary64` `pow1_binary64` `pow-exp_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64`
2×	`*-commutative_binary64`
1×	`associate-/r_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 124

Calls

4 calls:

16.0ms	(/.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))
3.0ms	(pow.f64 (sin.f64 k) 2)

series504.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

289.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
111.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
75.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
28.0ms	(pow.f64 (sin.f64 k) 2)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5270	2583

prune165.0ms (0.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	130	17	147

Merged error: 11.3b

Counts

147 → 17

Compiler

Compiled 3433 to 1564 computations (54.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
0.4b	(pow.f64 (sin.f64 k) 2)
0.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
19.6b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite68.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-exp-log_binary64`
128×	`add-cbrt-cube_binary64`
111×	`prod-exp_binary64`
61×	`cbrt-unprod_binary64`
55×	`div-exp_binary64`
37×	`cbrt-undiv_binary64`
25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow-to-exp_binary64` `associate-r_binary64` `pow-exp_binary64`
7×	`unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `*-commutative_binary64`

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)

series898.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

513.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
290.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
69.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
25.0ms	(pow.f64 (sin.f64 k) 2)

simplify103.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4962	4249
1	4962	4249

prune215.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	168	15	183

Merged error: 11.0b

Counts

183 → 15

Compiler

Compiled 4292 to 2124 computations (50.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (/.f64 k (*.f64 l l)))
0.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
8.5b	(/.f64 k (*.f64 l l))
9.9b	(/.f64 (/.f64 2 (/.f64 k (.f64 l l))) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))

rewrite104.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

539×	`times-frac_binary64`
197×	`add-sqr-sqrt_binary64`
191×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
151×	`add-exp-log_binary64`
100×	`add-cbrt-cube_binary64`
81×	`div-exp_binary64`
66×	`div-inv_binary64`
55×	`cbrt-undiv_binary64`
39×	`prod-exp_binary64`
32×	`associate-/l*_binary64`
19×	`cbrt-unprod_binary64`
15×	`associate-/r*_binary64`
10×	`associate-/r/_binary64`
8×	`associate-r_binary64`
5×	`pow-to-exp_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64`
1×	`associate-/l/_binary64` `*-commutative_binary64`

Counts

4 → 363

Calls

4 calls:

22.0ms	(/.f64 (/.f64 2 (/.f64 k (.f64 l l))) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
7.0ms	(/.f64 2 (/.f64 k (*.f64 l l)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.0ms	(/.f64 k (*.f64 l l))

series474.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

322.0ms	(/.f64 (/.f64 2 (/.f64 k (.f64 l l))) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
74.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
46.0ms	(/.f64 2 (/.f64 k (*.f64 l l)))
32.0ms	(/.f64 k (*.f64 l l))

simplify131.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5224	14005

prune587.0ms (2.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	360	15	375
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	371	19	390

Merged error: 0.8b

Counts

390 → 19

Compiler

Compiled 11130 to 5138 computations (53.8% saved)

regimes178.0ms (0.8%)

Compiler: Compiled 2054 to 1530 computations (25.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	29
1	17	29

end0.0ms (0%)

sample13.9s (62.9%)

Algorithm

1×

intervals

Results

4.3s	1202×	body	4096	invalid
2.5s	3873×	body	1024	valid
2.3s	1093×	body	2048	invalid
1.1s	491×	body	4096	valid
1.1s	1004×	body	2048	valid
584.0ms	1361×	body	512	valid
391.0ms	669×	body	1024	invalid
190.0ms	465×	body	512	invalid
154.0ms	1099×	body	128	invalid
138.0ms	471×	body	256	valid
126.0ms	800×	body	128	valid
76.0ms	282×	body	256	invalid

Compiler

Compiled 534 to 398 computations (25.5% saved)

Details

analyze2.6s (11.7%)

sample387.0ms (1.8%)

simplify22.0ms (0.1%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite82.0ms (0.4%)

series1.1s (5.1%)

simplify70.0ms (0.3%)

prune292.0ms (1.3%)

localize17.0ms (0.1%)

rewrite56.0ms (0.3%)

series504.0ms (2.3%)

simplify56.0ms (0.3%)

prune165.0ms (0.7%)

localize18.0ms (0.1%)

rewrite68.0ms (0.3%)

series898.0ms (4.1%)

simplify103.0ms (0.5%)

prune215.0ms (1%)

localize17.0ms (0.1%)

rewrite104.0ms (0.5%)

series474.0ms (2.2%)

simplify131.0ms (0.6%)

prune587.0ms (2.7%)

regimes178.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample13.9s (62.9%)

Profiling