Details

analyze2.7s (9.8%)

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)

sample382.0ms (1.4%)

Algorithm

1×

intervals

Results

91.0ms	27×	body	4096	invalid
86.0ms	120×	body	1024	valid
53.0ms	22×	body	2048	invalid
41.0ms	14×	body	4096	valid
40.0ms	34×	body	2048	valid
20.0ms	46×	body	512	valid
15.0ms	24×	body	1024	invalid
5.0ms	13×	body	512	invalid
5.0ms	17×	body	256	valid
4.0ms	30×	body	128	invalid
4.0ms	25×	body	128	valid
2.0ms	7×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify183.0ms (0.7%)

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

Merged error: 40.6b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
1.3b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
16.9b	(/.f64 (pow.f64 t 3) (*.f64 l l))
27.8b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite83.0ms (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:

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))
14.0ms	(.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))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.1s (4.1%)

Counts

4 → 12

Calls

4 calls:

629.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
328.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
113.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
51.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5170	4255

prune301.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	185	14	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	14	200

Merged error: 17.1b

Counts

200 → 14

Compiler

Compiled 5386 to 2765 computations (48.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
2.0b	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.3b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
22.6b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite81.0ms (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:

17.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
16.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
10.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

series999.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

518.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
296.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
107.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
77.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify129.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4957	5209
1	4957	5209

prune258.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	185	11	196
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	188	22	210

Merged error: 10.9b

Counts

210 → 22

Compiler

Compiled 5121 to 2438 computations (52.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
2.0b	(*.f64 t (pow.f64 (sin.f64 k) 2))
8.4b	(.f64 (/.f64 (.f64 l l) (.f64 k k)) (/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))
17.7b	(/.f64 (.f64 l l) (.f64 k k))

rewrite64.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`add-exp-log_binary64_457`
120×	`add-cbrt-cube_binary64_455`
76×	`prod-exp_binary64_468`
73×	`div-exp_binary64_470`
46×	`cbrt-unprod_binary64_452`
45×	`cbrt-undiv_binary64_453`
38×	`add-sqr-sqrt_binary64_441`
36×	`times-frac_binary64_425`
34×	`associate-r_binary64_359`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`unswap-sqr_binary64_387` `associate-l_binary64_360`
7×	`unpow-prod-down_binary64_498` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `pow1_binary64_480`
6×	`div-inv_binary64_416`
4×	`add-log-exp_binary64_458`
3×	`sqr-pow_binary64_391` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`*-commutative_binary64_350`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `clear-num_binary64_418` `frac-times_binary64_429` `associate-r/_binary64_361` `associate-/r/_binary64_365` `frac-2neg_binary64_430` `pow-pow_binary64_491` `associate-/r_binary64_363` `associate-/l_binary64_364`

Counts

4 → 163

Calls

4 calls:

22.0ms	(.f64 (/.f64 (.f64 l l) (.f64 k k)) (/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))
7.0ms	(/.f64 (.f64 l l) (.f64 k k))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series482.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(.f64 (/.f64 (.f64 l l) (.f64 k k)) (/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))
74.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
38.0ms	(/.f64 (.f64 l l) (.f64 k k))
27.0ms	(pow.f64 (sin.f64 k) 2)

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5006	3702

prune228.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	167	8	175
Fresh	12	9	21
Picked	1	0	1
Done	0	0	0
Total	180	17	197

Merged error: 3.5b

Counts

197 → 17

Compiler

Compiled 4433 to 2185 computations (50.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.9b	(.f64 (/.f64 l k) (.f64 (/.f64 l k) (/.f64 2 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))))
2.0b	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.7b	(.f64 (/.f64 l k) (/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))

rewrite82.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

207×	`add-exp-log_binary64_457`
131×	`add-cbrt-cube_binary64_455`
85×	`div-exp_binary64_470`
83×	`prod-exp_binary64_468`
55×	`add-sqr-sqrt_binary64_441`
52×	`times-frac_binary64_425`
51×	`cbrt-undiv_binary64_453`
49×	`cbrt-unprod_binary64_452`
37×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
35×	`associate-r_binary64_359`
29×	`associate-l_binary64_360`
12×	`pow1_binary64_480`
8×	`unswap-sqr_binary64_387` `pow-exp_binary64_487` `pow-to-exp_binary64_488`
7×	`unpow-prod-down_binary64_498`
6×	`div-inv_binary64_416` `frac-times_binary64_429` `associate-*r/_binary64_361`
4×	`associate-*l/_binary64_362` `pow-prod-down_binary64_490` `add-log-exp_binary64_458`
3×	`sqr-pow_binary64_391` `*-commutative_binary64_350` `pow-unpow_binary64_496` `unpow2_binary64_484`
1×	`associate-/r/_binary64_365` `pow-pow_binary64_491`

Counts

4 → 195

Calls

4 calls:

22.0ms	(.f64 (/.f64 l k) (/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))
20.0ms	(.f64 (/.f64 l k) (.f64 (/.f64 l k) (/.f64 2 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series791.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

355.0ms	(.f64 (/.f64 l k) (/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))
334.0ms	(.f64 (/.f64 l k) (.f64 (/.f64 l k) (/.f64 2 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))))
75.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
28.0ms	(pow.f64 (sin.f64 k) 2)

simplify93.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4990	4747
1	4990	4747

prune272.0ms (1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	196	11	207
Fresh	10	6	16
Picked	1	0	1
Done	0	0	0
Total	207	17	224

Merged error: 1.3b

Counts

224 → 17

Compiler

Compiled 4913 to 2356 computations (52% saved)

regimes1.8s (6.8%)

Compiler: Compiled 22545 to 16326 computations (27.6% saved)

bsearch405.0ms (1.5%)

Steps

Iters	Range		Point
8	3.0989778997745003e-219	1.0224023517246378e-214	8.801038254637086e-215
8	-1.0383993364890671e+60	-8.112085106247931e+55	-1.1380067627110802e+56

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	74
1	36	74

end0.0ms (0%)

sample16.5s (60.7%)

Algorithm

1×

intervals

Results

4.1s	1176×	body	4096	invalid
2.7s	3822×	body	1024	valid
2.2s	1029×	body	2048	invalid
1.2s	488×	body	4096	valid
1.2s	1011×	body	2048	valid
603.0ms	1375×	body	512	valid
382.0ms	649×	body	1024	invalid
210.0ms	521×	body	512	invalid
149.0ms	1029×	body	128	invalid
134.0ms	474×	body	256	valid
125.0ms	830×	body	128	valid
75.0ms	291×	body	256	invalid

Compiler

Compiled 3531 to 2553 computations (27.7% saved)

Details

analyze2.7s (9.8%)

sample382.0ms (1.4%)

simplify183.0ms (0.7%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite83.0ms (0.3%)

series1.1s (4.1%)

simplify76.0ms (0.3%)

prune301.0ms (1.1%)

localize16.0ms (0.1%)

rewrite81.0ms (0.3%)

series999.0ms (3.7%)

simplify129.0ms (0.5%)

prune258.0ms (1%)

localize16.0ms (0.1%)

rewrite64.0ms (0.2%)

series482.0ms (1.8%)

simplify80.0ms (0.3%)

prune228.0ms (0.8%)

localize15.0ms (0.1%)

rewrite82.0ms (0.3%)

series791.0ms (2.9%)

simplify93.0ms (0.3%)

prune272.0ms (1%)

regimes1.8s (6.8%)

bsearch405.0ms (1.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample16.5s (60.7%)

Profiling