Details

analyze2.4s (9.6%)

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)

sample424.0ms (1.7%)

Algorithm

1×

intervals

Results

188.0ms	53×	body	4096	invalid
75.0ms	145×	body	1024	valid
55.0ms	29×	body	2048	invalid
24.0ms	51×	body	512	valid
21.0ms	25×	body	2048	valid
15.0ms	7×	body	4096	valid
11.0ms	22×	body	1024	invalid
7.0ms	20×	body	512	invalid
3.0ms	13×	body	256	valid
3.0ms	23×	body	128	invalid
3.0ms	11×	body	256	invalid
2.0ms	15×	body	128	valid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify114.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5185	32

prune7.0ms (0%)

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

Error

39.4b

Counts

2 → 2

Compiler

Compiled 67 to 55 computations (17.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
1.2b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
17.0b	(/.f64 (pow.f64 t 3) (*.f64 l l))
24.3b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite69.0ms (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:

19.0ms	(.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))
10.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
6.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.6s (6.4%)

Counts

4 → 38

Calls

4 calls:

647.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
543.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
296.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
102.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

Compiler

Compiled 1617 to 1402 computations (13.3% saved)

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4966	4857
1	4966	4857

prune331.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	212	13	225
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	214	13	227

Error

13.4b

Counts

227 → 13

Compiler

Compiled 5907 to 3026 computations (48.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
1.2b	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.2b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
18.1b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite48.0ms (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:

14.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
9.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
9.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
3.0ms	(pow.f64 (sin.f64 k) 2)

series862.0ms (3.4%)

Counts

4 → 36

Calls

4 calls:

526.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
178.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
128.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
29.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 1248 to 1042 computations (16.5% saved)

simplify86.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5080	3113

prune200.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	151	9	160
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	156	17	173

Error

9.2b

Counts

173 → 17

Compiler

Compiled 4011 to 1913 computations (52.3% saved)

localize15.0ms (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)
1.2b	(*.f64 t (pow.f64 (sin.f64 k) 2))
18.1b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite58.0ms (0.2%)

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)))
8.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series1.5s (6.1%)

Counts

4 → 39

Calls

4 calls:

737.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
641.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
120.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
35.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 1374 to 1170 computations (14.8% saved)

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5026	5020

prune240.0ms (1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	191	19	210

Error

8.1b

Counts

210 → 19

Compiler

Compiled 5157 to 2579 computations (50% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
1.2b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.8b	(/.f64 (*.f64 l l) k)
10.3b	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))

rewrite61.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`add-exp-log_binary64_457`
100×	`add-cbrt-cube_binary64_455`
73×	`times-frac_binary64_425`
60×	`prod-exp_binary64_468` `div-exp_binary64_470`
57×	`add-sqr-sqrt_binary64_441`
41×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
40×	`cbrt-undiv_binary64_453`
34×	`associate-r_binary64_359` `cbrt-unprod_binary64_452`
11×	`div-inv_binary64_416`
10×	`associate-l_binary64_360` `associate-/r*_binary64_363`
8×	`unswap-sqr_binary64_387`
6×	`pow1_binary64_480`
5×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
4×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `associate-/l*_binary64_364`
2×	`clear-num_binary64_418` `sqr-pow_binary64_391` `associate-/r/_binary64_365` `*-commutative_binary64_350` `frac-2neg_binary64_430` `unpow2_binary64_484`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `frac-times_binary64_429` `associate-r/_binary64_361`

Counts

4 → 185

Calls

4 calls:

22.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
8.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(/.f64 (*.f64 l l) k)

series1.1s (4.5%)

Counts

4 → 36

Calls

4 calls:

634.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
312.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
122.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
63.0ms	(/.f64 (*.f64 l l) k)

Compiler

Compiled 1282 to 1070 computations (16.5% saved)

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4959	5374
1	4959	5374

prune254.0ms (1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	212	9	221
Fresh	9	9	18
Picked	0	1	1
Done	0	0	0
Total	221	19	240

Error

1.4b

Counts

240 → 19

Compiler

Compiled 5489 to 2605 computations (52.5% saved)

regimes1.2s (4.9%)

Accuracy

Total 6.0b remaining (70%)

Threshold costs 0b (0%)

Compiler

Compiled 17018 to 12466 computations (26.7% 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%)

sample14.0s (56%)

Algorithm

1×

intervals

Results

3.9s	1228×	body	4096	invalid
2.1s	1069×	body	2048	invalid
2.1s	3855×	body	1024	valid
939.0ms	491×	body	4096	valid
938.0ms	1004×	body	2048	valid
509.0ms	1408×	body	512	valid
352.0ms	633×	body	1024	invalid
185.0ms	501×	body	512	invalid
127.0ms	1014×	body	128	invalid
118.0ms	467×	body	256	valid
101.0ms	775×	body	128	valid
76.0ms	315×	body	256	invalid

Compiler

Compiled 2583 to 1894 computations (26.7% saved)

Details

analyze2.4s (9.6%)

sample424.0ms (1.7%)

simplify114.0ms (0.5%)

prune7.0ms (0%)

localize21.0ms (0.1%)

rewrite69.0ms (0.3%)

series1.6s (6.4%)

simplify88.0ms (0.4%)

prune331.0ms (1.3%)

localize14.0ms (0.1%)

rewrite48.0ms (0.2%)

series862.0ms (3.4%)

simplify86.0ms (0.3%)

prune200.0ms (0.8%)

localize15.0ms (0.1%)

rewrite58.0ms (0.2%)

series1.5s (6.1%)

simplify107.0ms (0.4%)

prune240.0ms (1%)

localize14.0ms (0.1%)

rewrite61.0ms (0.2%)

series1.1s (4.5%)

simplify104.0ms (0.4%)

prune254.0ms (1%)

regimes1.2s (4.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample14.0s (56%)

Profiling