Details

analyze7.4s (9.5%)

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 29 to 22 computations (24.1% saved)

sample985.0ms (1.3%)

Algorithm

1×

intervals

Results

338.0ms	34×	body	4096	invalid
186.0ms	124×	body	1024	valid
165.0ms	33×	body	2048	invalid
94.0ms	38×	body	2048	valid
49.0ms	44×	body	512	valid
36.0ms	29×	body	1024	invalid
32.0ms	10×	body	4096	valid
11.0ms	12×	body	512	invalid
10.0ms	30×	body	128	valid
9.0ms	29×	body	128	invalid
6.0ms	10×	body	256	valid
4.0ms	6×	body	256	invalid

Compiler

Compiled 60 to 46 computations (23.3% saved)

simplify39.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

856×	`associate-*l/_binary64`
739×	`associate-*r/_binary64`
417×	`associate-/r/_binary64`
392×	`associate-/r*_binary64`
347×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	52	35
2	172	32
3	806	32
4	5185	32

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

Error

37.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))

Compiler

Compiled 72 to 51 computations (29.2% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(.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))
13.6b	(/.f64 (pow.f64 t 3) (*.f64 l l))
25.5b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite735.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

22.4b

Rules

228×	`add-exp-log_binary64`
139×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
51×	`div-exp_binary64`
37×	`times-frac_binary64`

Counts

4 → 187

Calls

4 calls:

38.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
20.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
18.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
11.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

Compiler

Compiled 4545 to 2196 computations (51.7% saved)

series487.0ms (0.6%)

Error

22.2b

Counts

4 → 42

Calls

4 calls:

152.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
151.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
98.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
41.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

Compiler

Compiled 2443 to 1837 computations (24.8% saved)

simplify311.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

610×	`unswap-sqr_binary64`
534×	`associate-l_binary64`
404×	`associate-r_binary64`
221×	`*-commutative_binary64`
194×	`associate-*l/_binary64`

Counts

229 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	6336
1	813	5646
2	3709	5597
3	5139	5597

prune305.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	193	12	205
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	12	206

Error

16.2b

Counts

206 → 12

Alt Table

Status	Error	Program
	45.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	37.2b	(/.f64 2 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))) (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))) (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))))
	34.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 1 l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	45.6b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3/2) l) (/.f64 (pow.f64 t 3/2) l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
▶	22.7b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (*.f64 l l))))
	34.9b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k)) (pow.f64 (/.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) 2)) (pow.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 t)) 2)))
	37.2b	(/.f64 2 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k))) (cbrt.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k)))) (cbrt.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k)))) (pow.f64 (/.f64 k t) 2)))
	31.6b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l (/.f64 (.f64 t t) l))) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	35.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 t 3)) (cbrt.f64 (pow.f64 t 3))) (/.f64 l (/.f64 t l))) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	30.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	32.7b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l))) (tan.f64 k)) (/.f64 k t)) (/.f64 k t)))
	31.3b	(/.f64 2 (+.f64 (/.f64 (.f64 t (pow.f64 k 4)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (*.f64 l l)))))

Compiler

Compiled 3359 to 1815 computations (46% saved)

localize32.0ms (0%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (*.f64 l l))))
1.2b	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.5b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
20.0b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (*.f64 l l)))

rewrite774.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

Rules

320×	`add-exp-log_binary64`
183×	`prod-exp_binary64`
173×	`add-cbrt-cube_binary64`
87×	`cbrt-unprod_binary64`
82×	`div-exp_binary64`

Counts

4 → 184

Calls

4 calls:

24.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (*.f64 l l))))
23.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (*.f64 l l)))
14.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
10.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

Compiler

Compiled 5538 to 2101 computations (62.1% saved)

series464.0ms (0.6%)

Error

15.9b

Counts

4 → 42

Calls

4 calls:

174.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (*.f64 l l))))
137.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (*.f64 l l)))
53.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
43.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

Compiler

Compiled 2167 to 1558 computations (28.1% saved)

simplify368.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
363×	`associate-/r*_binary64`
334×	`associate-r_binary64`
317×	`associate-/l*_binary64`
289×	`cancel-sign-sub-inv_binary64`

Counts

226 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	8421
1	745	6376
2	3840	6368
3	5128	6368

prune308.0ms (0.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	190	10	200
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	195	17	212

Error

13.7b

Counts

212 → 17

Alt Table

Status	Error	Program
	45.3b	(/.f64 2 (.f64 (/.f64 (.f64 k k) (.f64 (.f64 l l) (cos.f64 k))) (.f64 t (-.f64 (.f64 k k) (*.f64 (pow.f64 k 4) 1/3)))))
	22.7b	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (.f64 l l) (cos.f64 k)))))
	34.9b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (.f64 l l))) (tan.f64 k)) (pow.f64 (/.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) 2)) (pow.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 t)) 2)))
	21.8b	(.f64 (/.f64 (sqrt.f64 2) (/.f64 (.f64 k k) (cos.f64 k))) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))))
	34.6b	(log.f64 (exp.f64 (/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))))
	34.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 1 l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	45.6b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3/2) l) (/.f64 (pow.f64 t 3/2) l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
▶	21.7b	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))))
	22.6b	(.f64 (/.f64 1 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 2 (.f64 (*.f64 l l) (cos.f64 k))))
	44.6b	(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (.f64 l l) (cos.f64 k))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))))
	31.6b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l (/.f64 (.f64 t t) l))) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	42.4b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 (.f64 (sin.f64 k) (sqrt.f64 t)) (.f64 (sin.f64 k) (sqrt.f64 t)))) (.f64 (cos.f64 k) (*.f64 l l))))
	45.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	22.7b	(/.f64 2 (/.f64 (.f64 (.f64 t (.f64 k k)) (pow.f64 (sin.f64 k) 2)) (.f64 (cos.f64 k) (*.f64 l l))))
	30.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	32.7b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l))) (tan.f64 k)) (/.f64 k t)) (/.f64 k t)))
	22.7b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 (.f64 t (sin.f64 k)) (pow.f64 (sin.f64 k) (/.f64 2 2)))) (.f64 (cos.f64 k) (.f64 l l))))

Compiler

Compiled 2867 to 1477 computations (48.5% saved)

localize33.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (cos.f64 k) (*.f64 k k))
4.8b	(/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))
6.5b	(/.f64 (*.f64 l l) t)
13.8b	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))))

rewrite2.2s (2.8%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

567×	`times-frac_binary64`
265×	`add-sqr-sqrt_binary64`
212×	`add-exp-log_binary64`
199×	`*-un-lft-identity_binary64`
199×	`add-cube-cbrt_binary64`

Counts

4 → 411

Calls

4 calls:

124.0ms	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))))
14.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))
9.0ms	(/.f64 (cos.f64 k) (*.f64 k k))
7.0ms	(/.f64 (*.f64 l l) t)

Compiler

Compiled 13144 to 5233 computations (60.2% saved)

series420.0ms (0.5%)

Error

13.7b

Counts

4 → 36

Calls

4 calls:

209.0ms	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))))
103.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))
31.0ms	(/.f64 (*.f64 l l) t)
21.0ms	(/.f64 (cos.f64 k) (*.f64 k k))

Compiler

Compiled 1867 to 1354 computations (27.5% saved)

simplify379.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-/r/_binary64`
684×	`associate-/l*_binary64`
585×	`times-frac_binary64`
573×	`associate-/l/_binary64`
218×	`*-commutative_binary64`

Counts

447 → 376

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	725	14580
1	1925	12639
2	5037	12639

prune559.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	363	13	376
Fresh	14	2	16
Picked	1	0	1
Done	0	0	0
Total	378	15	393

Error

7.1b

Counts

393 → 15

Alt Table

Status	Error	Program
	14.8b	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (/.f64 (/.f64 (pow.f64 (sin.f64 k) 2) l) (/.f64 l t))))
	14.6b	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (.f64 (/.f64 (sin.f64 k) l) (.f64 (/.f64 (sin.f64 k) l) t))))
	13.3b	(.f64 (.f64 l (/.f64 (cos.f64 k) (*.f64 k k))) (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 l t))))
	14.8b	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (*.f64 (/.f64 1 l) (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 l t)))))
	16.3b	(.f64 (.f64 (/.f64 (/.f64 (cos.f64 k) (*.f64 k k)) (/.f64 (sin.f64 k) l)) l) (/.f64 2 (/.f64 (sin.f64 k) (/.f64 1 t))))
	13.4b	(.f64 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (.f64 (sqrt.f64 2) l)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 l t))))
	34.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 1 l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	14.6b	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (cbrt.f64 (pow.f64 (sin.f64 k) 2))) l)) (/.f64 2 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 l t))))
▶	12.9b	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	30.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	19.9b	(.f64 (/.f64 1 k) (.f64 (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))) (/.f64 (cos.f64 k) k)))
	36.0b	(.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (.f64 (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))) (/.f64 (sqrt.f64 (cos.f64 k)) k)))
	13.3b	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (sin.f64 k) l)) (/.f64 2 (/.f64 (sin.f64 k) (/.f64 l t))))
	45.1b	(.f64 (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sin.f64 k) (/.f64 l (sqrt.f64 t)))) (/.f64 (sqrt.f64 (cos.f64 k)) k)) (*.f64 (/.f64 (sqrt.f64 2) (/.f64 (sin.f64 k) (/.f64 l (sqrt.f64 t)))) (/.f64 (sqrt.f64 (cos.f64 k)) k)))
	46.1b	(.f64 (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sin.f64 k) (sqrt.f64 (/.f64 (.f64 l l) t)))) (/.f64 (sqrt.f64 (cos.f64 k)) k)) (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sin.f64 k) (sqrt.f64 (/.f64 (*.f64 l l) t)))) (/.f64 (sqrt.f64 (cos.f64 k)) k)))

Compiler

Compiled 8217 to 3241 computations (60.6% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

1.8b	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))
2.3b	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))
3.7b	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
8.2b	(/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))))

rewrite16.4s (21.1%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

7271×	`times-frac_binary64`
3907×	`add-sqr-sqrt_binary64`
2086×	`*-un-lft-identity_binary64`
2086×	`add-cube-cbrt_binary64`
1946×	`add-exp-log_binary64`

Counts

4 → 2976

Calls

4 calls:

4.1s	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
36.0ms	(/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))))
15.0ms	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))
10.0ms	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))

Compiler

Compiled 157701 to 53343 computations (66.2% saved)

series502.0ms (0.6%)

Error

7.1b

Counts

4 → 40

Calls

4 calls:

143.0ms	(/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))))
115.0ms	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
99.0ms	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))
93.0ms	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))

Compiler

Compiled 3542 to 2512 computations (29.1% saved)

simplify2.4s (3.1%)

Algorithm

1×	egg-herbie

Rules

1574×	`associate-/r/_binary64`
523×	`associate-/l/_binary64`
51×	`sub-neg_binary64`
27×	`remove-double-div_binary64`
27×	`/-rgt-identity_binary64`

Counts

3016 → 1998

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3521	184721
1	5467	184721

prune5.0s (6.5%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	1979	19	1998
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	1987	26	2013

Error

0.6b

Counts

2013 → 26

Alt Table

Status	Error	Program
	54.9b	(.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 (sqrt.f64 l) (cbrt.f64 t)))) (/.f64 (sqrt.f64 2) (/.f64 (cbrt.f64 (sin.f64 k)) (/.f64 (sqrt.f64 l) (sqrt.f64 (cbrt.f64 t)))))) (*.f64 (/.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 (sqrt.f64 l) (cbrt.f64 t)))) (/.f64 (sqrt.f64 2) (/.f64 (cbrt.f64 (sin.f64 k)) (/.f64 (sqrt.f64 l) (sqrt.f64 (cbrt.f64 t)))))))
	6.0b	(.f64 (.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2)) 4) (cbrt.f64 t))) (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 k))) 4) (/.f64 l (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	4.1b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) (/.f64 4 2)) (.f64 (cbrt.f64 (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t))))))) (.f64 (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (cbrt.f64 (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t)))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	2.4b	(.f64 (/.f64 (/.f64 1 k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) (/.f64 4 2)) (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (cbrt.f64 t)))) (*.f64 (/.f64 (/.f64 (cos.f64 k) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 (cbrt.f64 l) (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	14.8b	(.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 2 (/.f64 (/.f64 (pow.f64 (sin.f64 k) 2) l) (/.f64 l t))))
	4.0b	(.f64 (/.f64 (/.f64 1 k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) (/.f64 4 2)) (.f64 (cbrt.f64 (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t))))))) (.f64 (/.f64 (/.f64 (cos.f64 k) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (cbrt.f64 (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	26.4b	(.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (cbrt.f64 t))) (/.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (/.f64 (cbrt.f64 l) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	6.7b	(.f64 (/.f64 (/.f64 1 k) (/.f64 1 l)) (.f64 (/.f64 (/.f64 (cos.f64 k) k) (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	19.9b	(.f64 (/.f64 1 k) (.f64 (/.f64 2 (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 l l) t))) (/.f64 (cos.f64 k) k)))
	5.7b	(.f64 (.f64 (/.f64 (/.f64 1 k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (cbrt.f64 t)))) (/.f64 (/.f64 (cos.f64 k) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 (cbrt.f64 l) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	27.9b	(.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (.f64 (cbrt.f64 (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))))) (/.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 4) (cbrt.f64 (/.f64 l (*.f64 (cbrt.f64 t) (cbrt.f64 t))))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	6.5b	(.f64 (.f64 (.f64 (/.f64 (/.f64 1 k) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2)) 4)) l) (/.f64 (/.f64 (cos.f64 k) k) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 k))) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	35.4b	(.f64 (.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (/.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 k))) 2) 4) (/.f64 (sqrt.f64 l) (cbrt.f64 t)))) (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 k))) 4) (/.f64 (sqrt.f64 l) (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	47.9b	(.f64 (/.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 k))) 4) 1)) (.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 (cos.f64 k)) k) (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 k))) 4)) (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	45.1b	(.f64 (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sin.f64 k) (/.f64 l (sqrt.f64 t)))) (/.f64 (sqrt.f64 (cos.f64 k)) k)) (*.f64 (/.f64 (sqrt.f64 2) (/.f64 (sin.f64 k) (/.f64 l (sqrt.f64 t)))) (/.f64 (sqrt.f64 (cos.f64 k)) k)))
	4.4b	(.f64 (/.f64 (/.f64 1 k) (/.f64 (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 k))) (cbrt.f64 (cbrt.f64 (sin.f64 k)))) 4) l)) (.f64 (/.f64 (/.f64 (cos.f64 k) k) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 k))) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	7.4b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (pow.f64 (cbrt.f64 (sin.f64 k)) 4)) (.f64 (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (.f64 (/.f64 1 l) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	16.3b	(.f64 (.f64 (/.f64 (/.f64 (cos.f64 k) (*.f64 k k)) (/.f64 (sin.f64 k) l)) l) (/.f64 2 (/.f64 (sin.f64 k) (/.f64 1 t))))
	13.4b	(.f64 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (.f64 (sqrt.f64 2) l)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sin.f64 k) 2) (/.f64 l t))))
	14.6b	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (cbrt.f64 (pow.f64 (sin.f64 k) 2))) l)) (/.f64 2 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 l t))))
	37.0b	(.f64 (.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (pow.f64 (cbrt.f64 (sqrt.f64 (sin.f64 k))) 4)) (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sin.f64 k))) 4) (/.f64 l (.f64 (cbrt.f64 t) (cbrt.f64 t)))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	6.0b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) (/.f64 4 2)) (/.f64 1 (cbrt.f64 t)))) (*.f64 (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	35.5b	(.f64 (/.f64 (/.f64 1 k) (/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sin.f64 k))) 4) l)) (.f64 (/.f64 (/.f64 (cos.f64 k) k) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sin.f64 k))) 4) (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))
	13.3b	(.f64 (/.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (sin.f64 k) l)) (/.f64 2 (/.f64 (sin.f64 k) (/.f64 l t))))
	35.9b	(.f64 (.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sin.f64 k))) 4) (cbrt.f64 t))) (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (sin.f64 k))) 4) (/.f64 l (cbrt.f64 t))))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t)))))
	2.5b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 k)) (cbrt.f64 (cos.f64 k))) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) (/.f64 4 2)) (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (cbrt.f64 t)))) (.f64 (/.f64 (/.f64 (cbrt.f64 (cos.f64 k)) k) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 (cbrt.f64 l) (cbrt.f64 t)))) (/.f64 2 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 l (cbrt.f64 t))))))

Compiler

Compiled 64086 to 21541 computations (66.4% saved)

regimes21.7s (27.9%)

Accuracy

Total 1.5b remaining (56%)

Threshold costs 0b (0%)

Compiler

Compiled 409106 to 248107 computations (39.4% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	78
1	32	78
2	30	78

end1.0ms (0%)

Compiler: Compiled 51 to 30 computations (41.2% saved)

sample15.9s (20.5%)

Algorithm

1×

intervals

Results

4.3s	1146×	body	4096	invalid
3.3s	3883×	body	1024	valid
2.4s	1066×	body	2048	invalid
1.3s	1015×	body	2048	valid
1.1s	452×	body	4096	valid
789.0ms	1404×	body	512	valid
558.0ms	706×	body	1024	invalid
275.0ms	491×	body	512	invalid
192.0ms	1045×	body	128	invalid
174.0ms	484×	body	256	valid
146.0ms	762×	body	128	valid
103.0ms	310×	body	256	invalid

Compiler

Compiled 1307 to 746 computations (42.9% saved)

Details

analyze7.4s (9.5%)

sample985.0ms (1.3%)

simplify39.0ms (0.1%)

prune8.0ms (0%)

localize36.0ms (0%)

rewrite735.0ms (0.9%)

series487.0ms (0.6%)

simplify311.0ms (0.4%)

prune305.0ms (0.4%)

localize32.0ms (0%)

rewrite774.0ms (1%)

series464.0ms (0.6%)

simplify368.0ms (0.5%)

prune308.0ms (0.4%)

localize33.0ms (0%)

rewrite2.2s (2.8%)

series420.0ms (0.5%)

simplify379.0ms (0.5%)

prune559.0ms (0.7%)

localize36.0ms (0%)

rewrite16.4s (21.1%)

series502.0ms (0.6%)

simplify2.4s (3.1%)

prune5.0s (6.5%)

regimes21.7s (27.9%)

simplify6.0ms (0%)

end1.0ms (0%)

sample15.9s (20.5%)

Profiling