Details

analyze2.0s (13.7%)

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)

sample106.0ms (0.7%)

Algorithm

1×

intervals

Results

45.0ms	93×	body	1024	valid
15.0ms	42×	body	512	valid
12.0ms	99×	body	128	valid
12.0ms	64×	body	128	invalid
5.0ms	22×	body	256	valid
2.0ms	4×	body	1024	invalid
1.0ms	3×	body	512	invalid
1.0ms	3×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify154.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4931	35
1	4931	35

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: 36.1b

Counts

2 → 1

Compiler

Compiled 46 to 38 computations (17.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
2.2b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
15.9b	(.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)))
19.8b	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite70.0ms (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:

22.0ms	(.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)))
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))

series666.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

392.0ms	(.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)))
177.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
72.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
24.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5555	3677

prune267.0ms (1.8%)

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: 16.3b

Counts

172 → 8

Compiler

Compiled 4976 to 2728 computations (45.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.1b	(*.f64 (/.f64 t l) (sin.f64 k))
10.7b	(/.f64 (*.f64 t t) l)
15.9b	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite76.0ms (0.5%)

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`
44×	`associate-*l/_binary64_362`
34×	`frac-times_binary64_429`
29×	`pow1_binary64_480`
21×	`add-sqr-sqrt_binary64_441` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
18×	`*-un-lft-identity_binary64_419`
17×	`pow-prod-down_binary64_490`
16×	`add-cube-cbrt_binary64_454` `tan-quot_binary64_578`
15×	`associate-l_binary64_360`
14×	`associate-*r/_binary64_361`
13×	`times-frac_binary64_425`
10×	`associate-r_binary64_359`
8×	`flip3-+_binary64_422` `flip-+_binary64_393`
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:

30.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
14.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)

series664.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

405.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
189.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
57.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
14.0ms	(/.f64 (*.f64 t t) l)

simplify102.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4981	4094
1	4981	4094

prune237.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	169	10	179

Merged error: 10.3b

Counts

179 → 10

Compiler

Compiled 5193 to 2586 computations (50.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
1.0b	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.1b	(*.f64 (/.f64 t l) (sin.f64 k))
15.9b	(.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite116.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

187×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
99×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
78×	`associate-*l/_binary64_362`
63×	`frac-times_binary64_429`
49×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
29×	`pow1_binary64_480`
28×	`tan-quot_binary64_578`
25×	`associate-*r/_binary64_361`
23×	`associate-/r/_binary64_365`
21×	`add-sqr-sqrt_binary64_441`
18×	`*-un-lft-identity_binary64_419`
17×	`pow-prod-down_binary64_490`
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 → 202

Calls

4 calls:

34.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
29.0ms	(.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.0ms	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

series921.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
294.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
178.0ms	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
56.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5041	6236

prune308.0ms (2.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	205	9	214
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	209	15	224

Merged error: 9.0b

Counts

224 → 15

Compiler

Compiled 6680 to 3443 computations (48.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(.f64 (tan.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
3.1b	(*.f64 (/.f64 t l) (sin.f64 k))
7.3b	(.f64 (/.f64 2 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))) (/.f64 l t))
10.9b	(.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k)))))

rewrite99.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
67×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
38×	`associate-l_binary64_360`
33×	`add-sqr-sqrt_binary64_441`
31×	`pow1_binary64_480`
28×	`associate-*r/_binary64_361`
27×	`associate-*l/_binary64_362`
25×	`*-un-lft-identity_binary64_419`
24×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
23×	`times-frac_binary64_425` `add-cube-cbrt_binary64_454`
20×	`frac-times_binary64_429`
18×	`pow-prod-down_binary64_490` `associate-r_binary64_359`
14×	`tan-quot_binary64_578`
11×	`associate-/r/_binary64_365`
8×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `*-commutative_binary64_350`
3×	`div-inv_binary64_416`
1×	`distribute-lft-out_binary64_370`

Counts

4 → 169

Calls

4 calls:

32.0ms	(.f64 (/.f64 2 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))) (/.f64 l t))
21.0ms	(.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k)))))
11.0ms	(.f64 (tan.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

series1.3s (8.9%)

Counts

4 → 12

Calls

4 calls:

769.0ms	(.f64 (/.f64 2 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))) (/.f64 l t))
303.0ms	(.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (.f64 (/.f64 t l) (sin.f64 k)))))
163.0ms	(.f64 (tan.f64 k) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
54.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5304	5051

prune233.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	173	8	181
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	181	15	196

Merged error: 7.6b

Counts

196 → 15

Compiler

Compiled 5587 to 2196 computations (60.7% saved)

regimes1.6s (11.3%)

Compiler: Compiled 15160 to 11263 computations (25.7% saved)

bsearch161.0ms (1.1%)

Steps

Iters	Range		Point
10	1.9559842241796614e-41	1.1919469537575551e-27	4.210309937890153e-37
9	-3.3077764745403715e+55	-6.333080407210493e+49	-7.807885226879273e+49

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	54	141
1	54	141

end0.0ms (0%)

sample5.0s (34.9%)

Algorithm

1×

intervals

Results

1.4s	2659×	body	1024	valid
458.0ms	1245×	body	512	valid
447.0ms	3482×	body	128	valid
183.0ms	1471×	body	128	invalid
153.0ms	603×	body	256	valid
65.0ms	176×	body	512	invalid
38.0ms	75×	body	1024	invalid
28.0ms	116×	body	256	invalid
8.0ms	11×	body	2048	valid

Compiler

Compiled 2561 to 1883 computations (26.5% saved)

Details

analyze2.0s (13.7%)

sample106.0ms (0.7%)

simplify154.0ms (1.1%)

prune5.0ms (0%)

localize21.0ms (0.1%)

rewrite70.0ms (0.5%)

series666.0ms (4.6%)

simplify73.0ms (0.5%)

prune267.0ms (1.8%)

localize17.0ms (0.1%)

rewrite76.0ms (0.5%)

series664.0ms (4.6%)

simplify102.0ms (0.7%)

prune237.0ms (1.6%)

localize18.0ms (0.1%)

rewrite116.0ms (0.8%)

series921.0ms (6.4%)

simplify98.0ms (0.7%)

prune308.0ms (2.1%)

localize20.0ms (0.1%)

rewrite99.0ms (0.7%)

series1.3s (8.9%)

simplify83.0ms (0.6%)

prune233.0ms (1.6%)

regimes1.6s (11.3%)

bsearch161.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.0s (34.9%)

Profiling