Details

analyze3.0s (19.5%)

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
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)

sample175.0ms (1.1%)

Algorithm

1×

intervals

Results

57.0ms	80×	body	1024	valid
24.0ms	122×	body	128	valid
19.0ms	39×	body	512	valid
6.0ms	37×	body	128	invalid
5.0ms	15×	body	256	valid
3.0ms	4×	body	1024	invalid
1.0ms	2×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 60 to 46 computations (23.3% saved)

simplify47.0ms (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

32.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.2b	(/.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))
✓	2.7b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
✓	12.8b	(.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)))
✓	16.5b	(/.f64 (pow.f64 t 3) (*.f64 l l))

series412.0ms (2.7%)

Counts

4 → 132

Calls

4 calls:

187.0ms	(.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)))
121.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
70.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
33.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite55.0ms (0.4%)

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)))
9.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
7.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
5.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify208.0ms (1.4%)

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

prune357.0ms (2.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	221	14	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	14	236

Error

13.9b

Counts

236 → 14

Alt Table

Status	Error	Program
	44.8b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 (.f64 l l) (pow.f64 (sqrt.f64 t) 3))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	32.7b	(/.f64 2 (.f64 (/.f64 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (sin.f64 k)) (.f64 (*.f64 l l) (cos.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	23.7b	(/.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))))
	40.1b	(/.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))))
	40.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	39.5b	(/.f64 2 (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))))))))
	32.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	25.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l (/.f64 (.f64 t t) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	32.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l l)))
	41.3b	(/.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)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	54.9b	(/.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))))
	57.5b	(/.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))))))
	24.9b	(/.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))))
	51.1b	(/.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))))

Compiler

Compiled 8649 to 4894 computations (43.4% saved)

localize20.0ms (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))
✓	5.1b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	9.1b	(/.f64 (*.f64 t t) l)
✓	12.8b	(.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)))

series356.0ms (2.3%)

Counts

4 → 132

Calls

4 calls:

189.0ms	(.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)))
136.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
20.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
12.0ms	(/.f64 (*.f64 t t) l)

rewrite67.0ms (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:

20.0ms	(.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)))
11.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
6.0ms	(/.f64 (*.f64 t t) l)
5.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

simplify224.0ms (1.5%)

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

prune424.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	259	7	266
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	268	12	280

Error

9.6b

Counts

280 → 12

Alt Table

Status	Error	Program
	26.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (/.f64 (*.f64 k t) l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	17.0b	(/.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))))
	31.5b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 t (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
	39.5b	(/.f64 2 (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))))))))
	32.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	24.4b	(/.f64 2 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 (*.f64 t (sin.f64 k)) l) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	25.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l (cos.f64 k))))
	57.5b	(/.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))))))
	17.2b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 t (cbrt.f64 l))) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	44.8b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 (.f64 l l) (pow.f64 (sqrt.f64 t) 3))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	17.0b	(/.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))))
	54.9b	(/.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))))

Compiler

Compiled 10378 to 4409 computations (57.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.1b	(.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k)))
✓	2.5b	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
	5.1b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	12.8b	(.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)))

series426.0ms (2.8%)

Counts

3 → 108

Calls

3 calls:

214.0ms

(*.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)))

134.0ms

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

77.0ms

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

rewrite83.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-cbrt-cube_binary64`
145×	`add-exp-log_binary64`
76×	`cbrt-unprod_binary64`
76×	`prod-exp_binary64`
66×	`times-frac_binary64`

Counts

3 → 188

Calls

3 calls:

22.0ms

(*.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))

13.0ms

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

simplify181.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
546×	`*-commutative_binary64`
533×	`distribute-rgt-in_binary64`
350×	`associate-*l/_binary64`
220×	`associate-/l*_binary64`

Counts

296 → 325

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	415	10198
1	1359	8093
2	3659	8029
3	5190	8029

prune580.0ms (3.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	379	8	387
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	386	13	399

Error

7.3b

Counts

399 → 13

Alt Table

Status	Error	Program
	39.5b	(/.f64 2 (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))))))))
	32.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	16.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	24.4b	(/.f64 2 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 (*.f64 t (sin.f64 k)) l) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	57.5b	(/.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))))))
	18.4b	(/.f64 2 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (.f64 (/.f64 t l) (sin.f64 k)) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	47.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (sqrt.f64 t) (sqrt.f64 (/.f64 l t))) (.f64 (/.f64 (sqrt.f64 t) (sqrt.f64 (/.f64 l t))) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	44.8b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 (.f64 l l) (pow.f64 (sqrt.f64 t) 3))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	36.9b	(/.f64 2 (.f64 (sqrt.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 (.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))))))
	16.2b	(/.f64 2 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	17.1b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	21.7b	(/.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))))
▶	13.2b	(/.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))))

Compiler

Compiled 14976 to 6025 computations (59.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.3b	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k))
	5.1b	(*.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)))
✓	11.2b	(.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series363.0ms (2.4%)

Counts

3 → 108

Calls

3 calls:

187.0ms

(/.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)))

130.0ms

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

46.0ms

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

rewrite77.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-cbrt-cube_binary64`
136×	`add-exp-log_binary64`
77×	`cbrt-unprod_binary64`
77×	`prod-exp_binary64`
29×	`cbrt-undiv_binary64`

Counts

3 → 119

Calls

3 calls:

22.0ms

(/.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)))

17.0ms

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

10.0ms

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

simplify161.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

699×	`times-frac_binary64`
550×	`associate-l_binary64`
497×	`associate-/l*_binary64`
462×	`fma-def_binary64`
262×	`associate-/r*_binary64`

Counts

227 → 218

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	9115
1	1012	7364
2	4621	7337
3	5049	7337

prune424.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	277	3	280
Fresh	7	5	12
Picked	0	1	1
Done	0	0	0
Total	284	9	293

Error

6.8b

Counts

293 → 9

Alt Table

Status	Error	Program
	39.5b	(/.f64 2 (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))))))))
	32.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	13.3b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (sin.f64 k)) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (.f64 (/.f64 l t) (cos.f64 k))))
	24.4b	(/.f64 2 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 (*.f64 t (sin.f64 k)) l) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	16.2b	(/.f64 2 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	19.1b	(/.f64 2 (/.f64 (.f64 t (.f64 (.f64 (/.f64 t l) (pow.f64 (sin.f64 k) 2)) (fma.f64 -1 (pow.f64 (/.f64 k t) 2) -2))) (neg.f64 (.f64 (cos.f64 k) (/.f64 l t)))))
	21.7b	(/.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))))
	21.6b	(/.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 (.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))))

Compiler

Compiled 11610 to 4641 computations (60% saved)

regimes3.2s (20.9%)

Accuracy

Total 3.1b remaining (32%)

Threshold costs 0b (0%)

Counts

250 → 3

Compiler

Compiled 50788 to 34724 computations (31.6% saved)

bsearch120.0ms (0.8%)

Steps

Iters	Range		Point
4	4.472168010199641e-48	7.25852787674901e-48	4.886482039548544e-48
6	-3.24179633777448e-132	-5.1372809285924914e-133	-3.182538400401493e-132

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	137
1	48	137
2	47	137

end1.0ms (0%)

Compiler: Compiled 93 to 47 computations (49.5% saved)

sample4.3s (28.1%)

Algorithm

1×

intervals

Results

2.0s	2677×	body	1024	valid
582.0ms	1227×	body	512	valid
565.0ms	3530×	body	128	valid
226.0ms	1378×	body	128	invalid
184.0ms	555×	body	256	valid
71.0ms	145×	body	512	invalid
48.0ms	64×	body	1024	invalid
38.0ms	120×	body	256	invalid
13.0ms	11×	body	2048	valid

Compiler

Compiled 425 to 273 computations (35.8% saved)

Details

analyze3.0s (19.5%)

sample175.0ms (1.1%)

simplify47.0ms (0.3%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series412.0ms (2.7%)

rewrite55.0ms (0.4%)

simplify208.0ms (1.4%)

prune357.0ms (2.3%)

localize20.0ms (0.1%)

series356.0ms (2.3%)

rewrite67.0ms (0.4%)

simplify224.0ms (1.5%)

prune424.0ms (2.8%)

localize16.0ms (0.1%)

series426.0ms (2.8%)

rewrite83.0ms (0.5%)

simplify181.0ms (1.2%)

prune580.0ms (3.8%)

localize23.0ms (0.1%)

series363.0ms (2.4%)

rewrite77.0ms (0.5%)

simplify161.0ms (1.1%)

prune424.0ms (2.8%)

regimes3.2s (20.9%)

bsearch120.0ms (0.8%)

simplify4.0ms (0%)

end1.0ms (0%)

sample4.3s (28.1%)

Profiling