Details

analyze2.5s (10.9%)

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)

sample346.0ms (1.5%)

Algorithm

1×

intervals

Results

86.0ms	28×	body	4096	invalid
68.0ms	36×	body	2048	invalid
62.0ms	120×	body	1024	valid
29.0ms	34×	body	2048	valid
26.0ms	12×	body	4096	valid
17.0ms	26×	body	1024	invalid
16.0ms	43×	body	512	valid
8.0ms	23×	body	512	invalid
5.0ms	10×	body	256	invalid
5.0ms	20×	body	256	valid
3.0ms	27×	body	128	valid
3.0ms	28×	body	128	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify114.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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: 42.2b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
1.0b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
15.4b	(/.f64 (pow.f64 t 3) (*.f64 l l))
31.4b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite77.0ms (0.3%)

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))
12.0ms	(.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 (2.7%)

Counts

4 → 12

Calls

4 calls:

344.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
174.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
68.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
26.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5178	4255

prune281.0ms (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

Merged error: 15.9b

Counts

200 → 12

Compiler

Compiled 5274 to 2697 computations (48.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.8b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
20.5b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite51.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`add-exp-log_binary64_457`
102×	`prod-exp_binary64_468`
87×	`add-cbrt-cube_binary64_455`
48×	`cbrt-unprod_binary64_452`
27×	`div-exp_binary64_470`
15×	`add-sqr-sqrt_binary64_441` `cbrt-undiv_binary64_453`
10×	`pow-exp_binary64_487` `pow-to-exp_binary64_488` `pow1_binary64_480`
9×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
7×	`unpow-prod-down_binary64_498`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `associate-l_binary64_360`
3×	`pow-prod-down_binary64_490` `sqr-pow_binary64_391` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`*-commutative_binary64_350`
1×	`clear-num_binary64_418` `times-frac_binary64_425` `div-inv_binary64_416` `frac-2neg_binary64_430` `pow-pow_binary64_491` `associate-/r_binary64_363` `associate-/l_binary64_364`

Counts

4 → 124

Calls

4 calls:

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

series284.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
61.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
41.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
15.0ms	(pow.f64 (sin.f64 k) 2)

simplify65.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5481	2583

prune170.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	127	9	136
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	130	18	148

Merged error: 12.0b

Counts

148 → 18

Compiler

Compiled 3515 to 1602 computations (54.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.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)
0.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
20.5b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite57.0ms (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:

14.0ms	(/.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)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series499.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

276.0ms	(/.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))
14.0ms	(pow.f64 (sin.f64 k) 2)

simplify115.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4983	4252
1	4983	4252

prune230.0ms (1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	154	12	166
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	161	23	184

Merged error: 11.4b

Counts

184 → 23

Compiler

Compiled 4606 to 2338 computations (49.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.6b	(/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
15.8b	(/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-exp-log_binary64_457`
89×	`times-frac_binary64_425`
80×	`add-cbrt-cube_binary64_455`
57×	`div-exp_binary64_470`
44×	`add-sqr-sqrt_binary64_441`
43×	`prod-exp_binary64_468`
38×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
37×	`cbrt-undiv_binary64_453`
21×	`cbrt-unprod_binary64_452`
19×	`associate-/r*_binary64_363`
12×	`div-inv_binary64_416`
8×	`associate-r_binary64_359`
7×	`unpow-prod-down_binary64_498`
6×	`pow-exp_binary64_487` `associate-/r/_binary64_365` `pow-to-exp_binary64_488`
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×	`*-commutative_binary64_350` `pow-pow_binary64_491`

Counts

4 → 175

Calls

4 calls:

16.0ms	(/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
11.0ms	(/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series394.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 k (/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
165.0ms	(/.f64 (.f64 l l) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
38.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
15.0ms	(pow.f64 (sin.f64 k) 2)

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4996	4733
1	4996	4733

prune249.0ms (1.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	174	13	187
Fresh	13	9	22
Picked	1	0	1
Done	0	0	0
Total	188	22	210

Merged error: 1.8b

Counts

210 → 22

Compiler

Compiled 4686 to 2290 computations (51.1% saved)

regimes1.5s (6.5%)

Compiler: Compiled 20943 to 15217 computations (27.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	29
1	19	29

end0.0ms (0%)

sample14.7s (65.4%)

Algorithm

1×

intervals

Results

3.9s	1213×	body	4096	invalid
2.1s	1080×	body	2048	invalid
2.1s	3858×	body	1024	valid
937.0ms	1019×	body	2048	valid
917.0ms	483×	body	4096	valid
524.0ms	1376×	body	512	valid
381.0ms	674×	body	1024	invalid
340.0ms	472×	body	512	invalid
136.0ms	1055×	body	128	invalid
121.0ms	465×	body	256	valid
106.0ms	799×	body	128	valid
61.0ms	257×	body	256	invalid

Compiler

Compiled 3204 to 2330 computations (27.3% saved)

Details

analyze2.5s (10.9%)

sample346.0ms (1.5%)

simplify114.0ms (0.5%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite77.0ms (0.3%)

series613.0ms (2.7%)

simplify79.0ms (0.4%)

prune281.0ms (1.3%)

localize15.0ms (0.1%)

rewrite51.0ms (0.2%)

series284.0ms (1.3%)

simplify65.0ms (0.3%)

prune170.0ms (0.8%)

localize16.0ms (0.1%)

rewrite57.0ms (0.3%)

series499.0ms (2.2%)

simplify115.0ms (0.5%)

prune230.0ms (1%)

localize14.0ms (0.1%)

rewrite56.0ms (0.3%)

series394.0ms (1.8%)

simplify112.0ms (0.5%)

prune249.0ms (1.1%)

regimes1.5s (6.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample14.7s (65.4%)

Profiling