Details

analyze2.7s (15.3%)

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 29 to 22 computations (24.1% saved)

sample178.0ms (1%)

Algorithm

1×

intervals

Results

59.0ms	81×	body	1024	valid
21.0ms	126×	body	128	valid
18.0ms	34×	body	512	valid
6.0ms	40×	body	128	invalid
4.0ms	14×	body	256	valid
1.0ms	1×	body	2048	valid
1.0ms	3×	body	256	invalid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 60 to 46 computations (23.3% saved)

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

627×	`distribute-rgt-in_binary64`
623×	`distribute-lft-in_binary64`
431×	`associate-/r/_binary64`
404×	`associate-/r*_binary64`
395×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	54	35
2	181	35
3	898	35
4	3262	35
5	4861	35
6	4933	35
7	5155	35

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

33.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	33.5b	(/.f64 2 (.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))))

Compiler

Compiled 103 to 71 computations (31.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
✓	4.1b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
✓	10.9b	(.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)))
✓	16.2b	(/.f64 (pow.f64 t 3) (*.f64 l l))

series479.0ms (2.7%)

Counts

4 → 132

Calls

4 calls:

202.0ms	(.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)))
131.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
111.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
35.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-exp-log_binary64`
58×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
28×	`times-frac_binary64`
26×	`add-sqr-sqrt_binary64`

Counts

4 → 167

Calls

4 calls:

17.0ms	(.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)))
11.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
8.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
5.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify188.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
569×	`associate-l_binary64`
436×	`associate-r_binary64`
248×	`*-commutative_binary64`
210×	`log-prod_binary64`

Counts

299 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	7807
1	869	7006
2	3862	6945
3	4830	6945
4	5036	6945

prune365.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	223	12	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	224	12	236

Error

12.8b

Counts

236 → 12

Alt Table

Status	Error	Program
	40.2b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l)) (fma.f64 31/180 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 6)) (.f64 l l)) (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (.f64 k k)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (.f64 l l))))))))))
▶	21.7b	(/.f64 2 (.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))))
	26.6b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 3) (/.f64 l (/.f64 t l))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	21.7b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	58.4b	(/.f64 2 (.f64 (exp.f64 (+.f64 (+.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (*.f64 l l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	24.4b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 (*.f64 t t) l) (/.f64 t l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	61.0b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (*.f64 (log.f64 t) 3) (+.f64 (log.f64 l) (log.f64 l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	34.8b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	45.3b	(/.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)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	43.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	53.7b	(/.f64 2 (.f64 (.f64 (.f64 (exp.f64 (-.f64 (.f64 (log.f64 t) 3) (+.f64 (log.f64 l) (log.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	33.3b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (*.f64 l l) (cos.f64 k))))

Compiler

Compiled 8585 to 4838 computations (43.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
✓	2.8b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	8.1b	(/.f64 (*.f64 t t) l)
✓	10.9b	(.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)))

series390.0ms (2.2%)

Counts

4 → 132

Calls

4 calls:

224.0ms	(.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)))
131.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
21.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
13.0ms	(/.f64 (*.f64 t t) l)

rewrite71.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`add-cbrt-cube_binary64`
120×	`add-exp-log_binary64`
70×	`cbrt-unprod_binary64`
70×	`prod-exp_binary64`
44×	`associate-*l/_binary64`

Counts

4 → 167

Calls

4 calls:

22.0ms	(.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)))
12.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
5.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)

simplify234.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
668×	`associate-r_binary64`
357×	`*-commutative_binary64`
255×	`associate-*l/_binary64`
183×	`distribute-rgt-in_binary64`

Counts

299 → 266

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	366	8901
1	1100	7091
2	3652	7057
3	4718	7057
4	4971	7057
5	4931	7057

prune426.0ms (2.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	257	9	266
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	264	14	278

Error

9.1b

Counts

278 → 14

Alt Table

Status	Error	Program
	33.6b	(/.f64 2 (.f64 (/.f64 (.f64 (tan.f64 k) (.f64 (sin.f64 k) (pow.f64 t 3))) (.f64 l l)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	21.2b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) l))
	21.7b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	21.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 t (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l (cos.f64 k))))
	58.4b	(/.f64 2 (.f64 (exp.f64 (+.f64 (+.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (*.f64 l l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	40.9b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (sqrt.f64 l))) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	34.8b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	42.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (fma.f64 (/.f64 (.f64 t (pow.f64 k 3)) l) -1/6 (fma.f64 1/120 (/.f64 (.f64 t (pow.f64 k 5)) l) (/.f64 (*.f64 k t) l)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	40.2b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l)) (fma.f64 31/180 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 6)) (.f64 l l)) (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (.f64 k k)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (.f64 l l))))))))))
	36.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (fma.f64 (/.f64 (.f64 t (pow.f64 k 3)) l) -1/6 (/.f64 (.f64 k t) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	31.1b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (-.f64 (.f64 2 2) (.f64 (pow.f64 (/.f64 k t) 2) (pow.f64 (/.f64 k t) 2)))) (.f64 l (-.f64 2 (pow.f64 (/.f64 k t) 2)))))
	43.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	16.3b	(/.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))))
	16.3b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 10596 to 4551 computations (57% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(/.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))))
✓	2.5b	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
	2.8b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	10.9b	(.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)))

series679.0ms (3.8%)

Counts

3 → 108

Calls

3 calls:

342.0ms

(/.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))))

209.0ms

(*.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)))

128.0ms

(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))

rewrite100.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`add-cbrt-cube_binary64`
181×	`add-exp-log_binary64`
97×	`cbrt-unprod_binary64`
97×	`prod-exp_binary64`
77×	`associate-*l/_binary64`

Counts

3 → 176

Calls

3 calls:

23.0ms

(/.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))))

21.0ms

(*.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)))

14.0ms

(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))

simplify230.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
478×	`associate-/r*_binary64`
365×	`times-frac_binary64`
326×	`associate-/l*_binary64`
274×	`associate-*l/_binary64`

Counts

284 → 328

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	13414
1	1529	10995
2	4489	10986
3	4965	10986

prune631.0ms (3.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	381	9	390
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	392	12	404

Error

5.7b

Counts

404 → 12

Alt Table

Status	Error	Program
	19.7b	(/.f64 2 (.f64 (/.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 t (sin.f64 k))) (tan.f64 k)) l) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	12.9b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k))))
	25.9b	(.f64 (/.f64 2 (.f64 (-.f64 4 (pow.f64 (/.f64 k t) 4)) (.f64 (tan.f64 k) (.f64 t (.f64 (sin.f64 k) (/.f64 t l)))))) (.f64 (/.f64 l t) (-.f64 2 (pow.f64 (/.f64 k t) 2))))
	25.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) l)))
	43.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	19.3b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (/.f64 (.f64 k t) l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	16.5b	(/.f64 (/.f64 2 (.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)))
	34.6b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	16.5b	(/.f64 (sqrt.f64 2) (/.f64 (.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))) (sqrt.f64 2)))
	16.5b	(.f64 (/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (cos.f64 k))
	40.2b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l)) (fma.f64 31/180 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 6)) (.f64 l l)) (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (.f64 k k)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (.f64 l l))))))))))
	16.3b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 15977 to 6982 computations (56.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k))))
	2.8b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	5.5b	(/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k)))
✓	8.5b	(.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series657.0ms (3.7%)

Counts

3 → 108

Calls

3 calls:

304.0ms

(/.f64 2 (/.f64 (*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k))))

216.0ms

(/.f64 (*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k)))

137.0ms

(*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite109.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

241×	`add-cbrt-cube_binary64`
241×	`add-exp-log_binary64`
122×	`cbrt-unprod_binary64`
122×	`prod-exp_binary64`
74×	`cbrt-undiv_binary64`

Counts

3 → 171

Calls

3 calls:

21.0ms

(/.f64 (*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k)))

20.0ms

(/.f64 2 (/.f64 (*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k))))

16.0ms

(*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify255.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

680×	`associate-/l*_binary64`
536×	`associate-/r*_binary64`
407×	`fma-def_binary64`
250×	`associate-/r/_binary64`
247×	`associate-*l/_binary64`

Counts

279 → 324

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	508	15874
1	1515	12955
2	4715	12931
3	5002	12931

prune704.0ms (4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	380	6	386
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	384	14	398

Error

4.7b

Counts

398 → 14

Alt Table

Status	Error	Program
	19.7b	(/.f64 2 (.f64 (/.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 t (sin.f64 k))) (tan.f64 k)) l) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	52.9b	(/.f64 2 (/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 k 2) (pow.f64 t 2)) l)) (/.f64 (pow.f64 k 4) l)) (.f64 2/3 (/.f64 (.f64 (pow.f64 k 4) (pow.f64 t 2)) l))) (*.f64 (/.f64 l t) (cos.f64 k))))
	25.9b	(.f64 (/.f64 2 (.f64 (-.f64 4 (pow.f64 (/.f64 k t) 4)) (.f64 (tan.f64 k) (.f64 t (.f64 (sin.f64 k) (/.f64 t l)))))) (.f64 (/.f64 l t) (-.f64 2 (pow.f64 (/.f64 k t) 2))))
	43.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	34.6b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	16.5b	(/.f64 (sqrt.f64 2) (/.f64 (.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))) (sqrt.f64 2)))
	12.9b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (.f64 (sin.f64 k) (/.f64 t l))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) (cos.f64 k))))
	14.5b	(/.f64 (.f64 (/.f64 2 (.f64 (.f64 (sin.f64 k) (.f64 t (.f64 (sin.f64 k) (/.f64 t l)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (.f64 l (cos.f64 k))) t)
	40.2b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l)) (fma.f64 31/180 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 6)) (.f64 l l)) (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (.f64 k k)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (.f64 l l))))))))))
	14.5b	(.f64 (/.f64 (sqrt.f64 2) (/.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (/.f64 l t))) (/.f64 (sqrt.f64 2) (/.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (cos.f64 k))))
	19.3b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (/.f64 (.f64 k t) l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	20.5b	(/.f64 2 (/.f64 (/.f64 (.f64 (pow.f64 (sin.f64 k) 2) (fma.f64 k k (.f64 2 (.f64 t t)))) l) (.f64 (/.f64 l t) (cos.f64 k))))
	13.2b	(/.f64 2 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (cbrt.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (cbrt.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (*.f64 (/.f64 l t) (cos.f64 k))))
	16.3b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 17628 to 6861 computations (61.1% saved)

regimes4.2s (23.8%)

Accuracy

Total 5.9b remaining (46.2%)

Threshold costs 0b (0%)

Counts

301 → 6

Compiler

Compiled 65572 to 44219 computations (32.6% saved)

bsearch390.0ms (2.2%)

Steps

Iters	Range		Point
8	9.603363021919364e+148	4.450664799540085e+151	4.4055434024518627e+151
10	3.917977395546506e+19	3.470718608299485e+30	4.375811370949229e+19
6	1.7135334950100707e-246	1.9674172780726993e-245	1.7455086026036075e-246
11	-2.883983939328845e-286	1.0311055014924001e-294	3.8487644440104676e-296
3	-2.1746405634501744e-70	-1.533041149118093e-70	-1.7335409660968685e-70

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	268
1	85	268
2	84	268

end2.0ms (0%)

Compiler: Compiled 180 to 92 computations (48.9% saved)

sample4.5s (25.4%)

Algorithm

1×

intervals

Results

2.0s	2716×	body	1024	valid
591.0ms	1213×	body	512	valid
590.0ms	3514×	body	128	valid
215.0ms	1314×	body	128	invalid
187.0ms	549×	body	256	valid
65.0ms	133×	body	512	invalid
46.0ms	59×	body	1024	invalid
32.0ms	102×	body	256	invalid
10.0ms	8×	body	2048	valid

Compiler

Compiled 744 to 461 computations (38% saved)

Details

analyze2.7s (15.3%)

sample178.0ms (1%)

simplify53.0ms (0.3%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series479.0ms (2.7%)

rewrite57.0ms (0.3%)

simplify188.0ms (1.1%)

prune365.0ms (2.1%)

localize18.0ms (0.1%)

series390.0ms (2.2%)

rewrite71.0ms (0.4%)

simplify234.0ms (1.3%)

prune426.0ms (2.4%)

localize17.0ms (0.1%)

series679.0ms (3.8%)

rewrite100.0ms (0.6%)

simplify230.0ms (1.3%)

prune631.0ms (3.6%)

localize19.0ms (0.1%)

series657.0ms (3.7%)

rewrite109.0ms (0.6%)

simplify255.0ms (1.4%)

prune704.0ms (4%)

regimes4.2s (23.8%)

bsearch390.0ms (2.2%)

simplify6.0ms (0%)

end2.0ms (0%)

sample4.5s (25.4%)

Profiling