Details

analyze4.0s (12.7%)

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
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample210.0ms (0.7%)

Algorithm

1×

intervals

Results

122.0ms	107×	body	1024	valid
31.0ms	46×	body	512	valid
20.0ms	86×	body	128	valid
9.0ms	42×	body	128	invalid
8.0ms	17×	body	256	valid
1.0ms	1×	body	1024	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify325.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4928	35
1	4928	35

prune8.0ms (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: 32.0b

Counts

2 → 1

Compiler

Compiled 46 to 38 computations (17.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
2.9b	(.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))
15.4b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite157.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-exp-log_binary64_457`
58×	`prod-exp_binary64_468`
52×	`add-cbrt-cube_binary64_455`
28×	`times-frac_binary64_425`
26×	`cbrt-unprod_binary64_452` `add-sqr-sqrt_binary64_441`
24×	`div-exp_binary64_470`
20×	`pow1_binary64_480`
19×	`*-un-lft-identity_binary64_419`
18×	`associate-l_binary64_360`
17×	`add-cube-cbrt_binary64_454`
16×	`associate-*l/_binary64_362`
12×	`associate-/l*_binary64_364`
10×	`pow-prod-down_binary64_490` `unpow-prod-down_binary64_498` `associate-r_binary64_359` `frac-times_binary64_429` `cube-prod_binary64_447`
8×	`pow-exp_binary64_487` `pow-to-exp_binary64_488` `tan-quot_binary64_578` `cbrt-undiv_binary64_453`
6×	`associate-*r/_binary64_361`
5×	`unswap-sqr_binary64_387`
4×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `sqr-pow_binary64_391` `flip-+_binary64_393`
3×	`unpow3_binary64_485` `cube-mult_binary64_449` `*-commutative_binary64_350`
2×	`div-inv_binary64_416`
1×	`clear-num_binary64_418` `distribute-rgt-in_binary64_369` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `associate-/r*_binary64_363`

Counts

4 → 159

Calls

4 calls:

50.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
25.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
22.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
15.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series2.5s (7.7%)

Counts

4 → 12

Calls

4 calls:

1.5s	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
623.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
242.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
82.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify131.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5592	3677

prune467.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	8	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	8	172

Merged error: 13.7b

Counts

172 → 8

Compiler

Compiled 4975 to 2725 computations (45.2% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
4.3b	(*.f64 (sin.f64 k) (/.f64 t l))
7.2b	(/.f64 (*.f64 t t) l)
15.4b	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite137.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
70×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
34×	`frac-times_binary64_429`
31×	`associate-*r/_binary64_361`
29×	`pow1_binary64_480`
27×	`associate-*l/_binary64_362`
21×	`add-sqr-sqrt_binary64_441` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
20×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
17×	`pow-prod-down_binary64_490`
16×	`add-cube-cbrt_binary64_454` `tan-quot_binary64_578`
13×	`times-frac_binary64_425`
8×	`flip3-+_binary64_422` `flip-+_binary64_393`
5×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458`
3×	`-commutative_binary64_350` `associate-/r_binary64_363`
2×	`div-inv_binary64_416` `unswap-sqr_binary64_387`
1×	`clear-num_binary64_418` `distribute-rgt-in_binary64_369` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `associate-/l*_binary64_364`

Counts

4 → 159

Calls

4 calls:

57.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
27.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
17.0ms	(*.f64 (sin.f64 k) (/.f64 t l))
10.0ms	(/.f64 (*.f64 t t) l)

series2.1s (6.8%)

Counts

4 → 12

Calls

4 calls:

1.3s	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
614.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
184.0ms	(*.f64 (sin.f64 k) (/.f64 t l))
44.0ms	(/.f64 (*.f64 t t) l)

simplify181.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4956	4106
1	4956	4106

prune447.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	169	10	179

Merged error: 10.3b

Counts

179 → 10

Compiler

Compiled 5191 to 2577 computations (50.4% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(.f64 (.f64 t (/.f64 t l)) (*.f64 (sin.f64 k) (/.f64 t l)))
2.9b	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
4.3b	(*.f64 (sin.f64 k) (/.f64 t l))
15.4b	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite198.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
96×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
61×	`pow1_binary64_480`
52×	`associate-*r/_binary64_361`
41×	`pow-prod-down_binary64_490`
35×	`frac-times_binary64_429`
28×	`associate-*l/_binary64_362`
21×	`associate-r_binary64_359`
19×	`add-sqr-sqrt_binary64_441` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
16×	`*-un-lft-identity_binary64_419` `tan-quot_binary64_578`
14×	`add-cube-cbrt_binary64_454`
10×	`times-frac_binary64_425`
8×	`flip3-+_binary64_422` `flip-+_binary64_393`
6×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `*-commutative_binary64_350`
2×	`unswap-sqr_binary64_387`
1×	`distribute-rgt-in_binary64_369` `div-inv_binary64_416` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368`

Counts

4 → 177

Calls

4 calls:

61.0ms	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
33.0ms	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
24.0ms	(.f64 (.f64 t (/.f64 t l)) (*.f64 (sin.f64 k) (/.f64 t l)))
18.0ms	(*.f64 (sin.f64 k) (/.f64 t l))

series2.4s (7.4%)

Counts

4 → 12

Calls

4 calls:

1.3s	(.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
599.0ms	(.f64 (.f64 (.f64 t (/.f64 t l)) (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
233.0ms	(.f64 (.f64 t (/.f64 t l)) (*.f64 (sin.f64 k) (/.f64 t l)))
197.0ms	(*.f64 (sin.f64 k) (/.f64 t l))

simplify164.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5071	4716

prune444.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	184	5	189
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	187	12	199

Merged error: 8.9b

Counts

199 → 12

Compiler

Compiled 5726 to 2904 computations (49.3% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
2.9b	(.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k))
4.3b	(*.f64 (/.f64 t l) (sin.f64 k))
15.4b	(.f64 (.f64 (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite222.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

169×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
103×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
78×	`associate-*l/_binary64_362`
63×	`frac-times_binary64_429`
53×	`associate-*r/_binary64_361`
40×	`pow1_binary64_480`
30×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
28×	`tan-quot_binary64_578`
26×	`pow-prod-down_binary64_490`
23×	`associate-/r/_binary64_365`
21×	`add-sqr-sqrt_binary64_441`
18×	`*-un-lft-identity_binary64_419`
16×	`flip3-+_binary64_422` `add-cube-cbrt_binary64_454` `flip-+_binary64_393`
15×	`associate-l_binary64_360`
13×	`times-frac_binary64_425`
10×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458`
3×	`-commutative_binary64_350` `associate-/l_binary64_364`
2×	`div-inv_binary64_416` `unswap-sqr_binary64_387`
1×	`clear-num_binary64_418` `distribute-rgt-in_binary64_369` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `associate-/r*_binary64_363`

Counts

4 → 198

Calls

4 calls:

61.0ms	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
54.0ms	(.f64 (.f64 (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
29.0ms	(.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k))
15.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

series2.9s (9.2%)

Counts

4 → 12

Calls

4 calls:

1.2s	(.f64 (.f64 (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
921.0ms	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
603.0ms	(.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (/.f64 t l)) (tan.f64 k))
185.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

simplify219.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5002	6036

prune568.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	204	6	210
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	208	14	222

Merged error: 7.8b

Counts

222 → 14

Compiler

Compiled 6110 to 3224 computations (47.2% saved)

regimes2.6s (8.1%)

Compiler: Compiled 13181 to 10190 computations (22.7% saved)

bsearch819.0ms (2.6%)

Steps

Iters	Range		Point
9	2.652433272323878e-17	1.902637499426078e-09	2.6878191797578578e-17
9	2.515142763242519e-130	2.767893164716607e-125	6.055902006289046e-126
7	-3.70473402023751e-188	-3.3572486891367135e-190	-2.335793423968273e-188
7	-1.1292845774171483e-176	-5.4661592509201044e-179	-1.9880298207529304e-177
7	-1.9640534238401676e-67	-5.732788546260007e-69	-1.343344005601436e-68

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	233
1	67	233

end0.0ms (0%)

sample10.5s (32.9%)

Algorithm

1×

intervals

Results

3.2s	2636×	body	1024	valid
1.1s	1300×	body	512	valid
910.0ms	3460×	body	128	valid
363.0ms	1434×	body	128	invalid
318.0ms	599×	body	256	valid
106.0ms	133×	body	512	invalid
76.0ms	55×	body	1024	invalid
66.0ms	114×	body	256	invalid
10.0ms	5×	body	2048	valid

Compiler

Compiled 2188 to 1650 computations (24.6% saved)

Details

analyze4.0s (12.7%)

sample210.0ms (0.7%)

simplify325.0ms (1%)

prune8.0ms (0%)

localize20.0ms (0.1%)

rewrite157.0ms (0.5%)

series2.5s (7.7%)

simplify131.0ms (0.4%)

prune467.0ms (1.5%)

localize44.0ms (0.1%)

rewrite137.0ms (0.4%)

series2.1s (6.8%)

simplify181.0ms (0.6%)

prune447.0ms (1.4%)

localize40.0ms (0.1%)

rewrite198.0ms (0.6%)

series2.4s (7.4%)

simplify164.0ms (0.5%)

prune444.0ms (1.4%)

localize36.0ms (0.1%)

rewrite222.0ms (0.7%)

series2.9s (9.2%)

simplify219.0ms (0.7%)

prune568.0ms (1.8%)

regimes2.6s (8.1%)

bsearch819.0ms (2.6%)

simplify8.0ms (0%)

end0.0ms (0%)

sample10.5s (32.9%)

Profiling