Details

analyze3.4s (12.6%)

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)

sample17.2s (64%)

Results

5.0s	1242×	body	4096	invalid
3.7s	3898×	body	1024	valid
2.8s	1109×	body	2048	invalid
1.6s	1089×	body	2048	valid
1.3s	517×	body	4096	valid
1.0s	1478×	body	512	valid
639.0ms	722×	body	1024	invalid
363.0ms	553×	body	512	invalid
269.0ms	1097×	body	128	invalid
232.0ms	483×	body	256	valid
214.0ms	791×	body	128	valid
139.0ms	318×	body	256	invalid

Compiler

Compiled 58 to 44 computations (24.1% saved)

preprocess37.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

872×	`times-frac_binary64`
333×	`associate-l_binary64`
321×	`associate-*l/_binary64`
300×	`associate-r_binary64`
224×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	152
1	153	140
2	625	128
3	4028	128
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 28 to 21 computations (25% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

845×	`associate-*l/_binary64`
417×	`associate-/r/_binary64`
388×	`associate-/r*_binary64`
347×	`distribute-rgt-in_binary64`
317×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	52	35
2	180	32
3	1056	32

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

43.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	43.4b	(.f64 (/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))) (*.f64 l l))
	50.8b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))

Status

Error

Program

▶

43.4b

(*.f64 (/.f64 2 (*.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))) (*.f64 l l))

50.8b

(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))

Compiler

Compiled 153 to 107 computations (30.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2))))
✓	1.5b	(*.f64 (pow.f64 t 3) (sin.f64 k))
✓	22.2b	(.f64 (/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))) (*.f64 l l))
✓	33.2b	(.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))

series358.0ms (1.3%)

Counts

4 → 88

Calls

27 calls:

28.0ms	(.f64 (/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))) (*.f64 l l))	l	-inf
26.0ms	(.f64 (/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))) (*.f64 l l))	t	inf
25.0ms	(.f64 (/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))) (*.f64 l l))	l	inf
25.0ms	(.f64 (/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))) (*.f64 l l))	t	-inf
25.0ms	(/.f64 2 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2))))	t	-inf

rewrite69.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

309×	`log1p-udef_binary64`
176×	`add-sqr-sqrt_binary64`
167×	`associate-r_binary64`
167×	`log1p-expm1-u_binary64`
167×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	90
1	366	90
2	4690	90

Stop Event

1×	node limit

Counts

4 → 84

simplify46.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-l_binary64`
420×	`associate-r_binary64`
393×	`times-frac_binary64`
331×	`fma-def_binary64`
253×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	2240
1	301	2215
2	1039	2167

Stop Event

1×	node limit

Counts

172 → 121

prune133.0ms (0.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	108	13	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Error

8.3b

Counts

123 → 13

Alt Table

Status	Error	Program
	49.5b	(pow.f64 (.f64 l (/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))) (/.f64 k t)))) 2)
	25.4b	(.f64 (/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))) (.f64 l l))
	25.4b	(.f64 (/.f64 2 (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 k (/.f64 (cos.f64 k) k)))) (.f64 l l))
	37.3b	(pow.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 l l))) (.f64 t (cbrt.f64 (.f64 (sin.f64 k) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))))) 3)
	51.1b	(/.f64 (/.f64 (.f64 2 (.f64 l l)) (.f64 (sqrt.f64 (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))) (/.f64 k t))) (.f64 (sqrt.f64 (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))) (/.f64 k t)))
	43.9b	(/.f64 (/.f64 (.f64 2 (.f64 l l)) (pow.f64 t 3)) (.f64 (sin.f64 k) (.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2))))
	25.4b	(.f64 (/.f64 (.f64 (/.f64 (/.f64 2 t) (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (.f64 k k)) (.f64 l l))
	41.5b	(+.f64 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) -1/3) (.f64 (/.f64 l (/.f64 t l)) (-.f64 (/.f64 2 (pow.f64 k 4)) 7/60)))
	32.4b	(.f64 (/.f64 l (/.f64 t l)) (-.f64 (/.f64 2 (pow.f64 k 4)) (/.f64 1/3 (.f64 k k))))
	32.7b	(*.f64 2 (/.f64 (/.f64 l (/.f64 t l)) (pow.f64 k 4)))
▶	9.9b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	25.2b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	37.5b	(log.f64 (pow.f64 (pow.f64 (exp.f64 l) l) (/.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))))

Compiler

Compiled 3563 to 2066 computations (42% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))
✓	0.4b	(pow.f64 (sin.f64 k) 2)
✓	4.8b	(.f64 (.f64 (/.f64 l k) (/.f64 l (*.f64 k t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))
✓	5.8b	(/.f64 l (*.f64 k t))

series174.0ms (0.6%)

Counts

4 → 44

Calls

24 calls:

20.0ms	(.f64 (.f64 (/.f64 l k) (/.f64 l (*.f64 k t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))	t	-inf
18.0ms	(.f64 (.f64 (/.f64 l k) (/.f64 l (*.f64 k t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))	l	-inf
18.0ms	(.f64 (.f64 (/.f64 l k) (/.f64 l (*.f64 k t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))	t	0
17.0ms	(.f64 (.f64 (/.f64 l k) (/.f64 l (*.f64 k t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))	l	0
17.0ms	(.f64 (.f64 (/.f64 l k) (/.f64 l (*.f64 k t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))	l	inf

rewrite80.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`log1p-udef_binary64`
155×	`egg-rr`
153×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	306	47
2	4502	47

Stop Event

1×	node limit

Counts

4 → 155

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
561×	`cancel-sign-sub-inv_binary64`
364×	`fma-neg_binary64`
191×	`distribute-rgt-neg-in_binary64`
187×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1104
1	164	1094
2	534	1074
3	2488	1066

Stop Event

1×	node limit

Counts

199 → 181

prune327.0ms (1.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	165	16	181
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	177	17	194

Error

1.5b

Counts

194 → 17

Alt Table

Status	Error	Program
	9.9b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (pow.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (cos.f64 k)) -1)))
	15.4b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (/.f64 (cos.f64 k) (cbrt.f64 (pow.f64 (pow.f64 (sin.f64 k) 2) 3)))))
	7.7b	(.f64 2 (/.f64 (.f64 l (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) k))
	9.9b	(.f64 2 (/.f64 (/.f64 (.f64 (/.f64 (pow.f64 (/.f64 l k) 2) t) (cos.f64 k)) (sin.f64 k)) (sin.f64 k)))
	5.6b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 l k)) 2) 1) (/.f64 (cbrt.f64 (/.f64 l k)) t))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	5.6b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (cbrt.f64 (/.f64 (/.f64 l k) t)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 l k) t)) 2))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	30.4b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (.f64 (sqrt.f64 (cos.f64 k)) (.f64 (sqrt.f64 (cos.f64 k)) (pow.f64 (sin.f64 k) -2)))))
	11.1b	(.f64 2 (/.f64 (.f64 (.f64 l (/.f64 (/.f64 l k) t)) (cos.f64 k)) (.f64 k (pow.f64 (sin.f64 k) 2))))
	10.0b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (.f64 (pow.f64 (cbrt.f64 (cos.f64 k)) 2) (.f64 (cbrt.f64 (cos.f64 k)) (pow.f64 (sin.f64 k) -2)))))
▶	4.8b	(.f64 2 (/.f64 (.f64 (/.f64 (/.f64 l k) t) (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))) (/.f64 k l)))
	7.3b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (/.f64 (pow.f64 (cbrt.f64 l) 2) t) (/.f64 (cbrt.f64 l) k))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	14.9b	(.f64 2 (/.f64 (.f64 l (/.f64 l k)) (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (cos.f64 k)) (.f64 k t))))
	24.1b	(.f64 2 (pow.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 (/.f64 l k) 2) t) (cos.f64 k))) (sin.f64 k)) 2))
	37.3b	(pow.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 l l))) (.f64 t (cbrt.f64 (.f64 (sin.f64 k) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))))) 3)
	5.6b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (/.f64 l k) (cbrt.f64 t)))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	23.0b	(.f64 2 (.f64 (.f64 l l) (/.f64 (cos.f64 k) (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	9.9b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (*.f64 (/.f64 1 (sin.f64 k)) (/.f64 (cos.f64 k) (sin.f64 k)))))

Compiler

Compiled 4996 to 2435 computations (51.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 k) -2)
✓	0.5b	(/.f64 (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))) (/.f64 k l))
✓	2.4b	(/.f64 (/.f64 l k) t)
✓	4.9b	(.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))

series272.0ms (1%)

Counts

4 → 120

Calls

30 calls:

22.0ms	(/.f64 (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))) (/.f64 k l))	t	-inf
19.0ms	(/.f64 (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))) (/.f64 k l))	l	-inf
19.0ms	(/.f64 (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))) (/.f64 k l))	l	0
19.0ms	(/.f64 (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))) (/.f64 k l))	t	inf
17.0ms	(/.f64 (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))) (/.f64 k l))	l	inf

rewrite80.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

284×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
147×	`egg-rr`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	311	59
2	4643	59

Stop Event

1×	node limit

Counts

4 → 147

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
613×	`associate-/l/_binary64`
375×	`cancel-sign-sub-inv_binary64`
345×	`fma-neg_binary64`
259×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	2109
1	201	2105
2	636	2087
3	2722	2076

Stop Event

1×	node limit

Counts

267 → 178

prune313.0ms (1.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	172	6	178
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	180	15	195

Error

0.7b

Counts

195 → 15

Alt Table

Status	Error	Program
	24.1b	(.f64 2 (pow.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 (/.f64 l k) 2) t) (cos.f64 k))) (sin.f64 k)) 2))
▶	4.6b	(.f64 2 (/.f64 (/.f64 (/.f64 l k) (/.f64 t (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) (/.f64 k l)))
	37.3b	(pow.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 l l))) (.f64 t (cbrt.f64 (.f64 (sin.f64 k) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))))) 3)
	4.8b	(.f64 2 (/.f64 (.f64 (/.f64 (/.f64 l k) t) (*.f64 (cos.f64 k) (/.f64 1 (pow.f64 (sin.f64 k) 2)))) (/.f64 k l)))
	9.9b	(.f64 2 (/.f64 (/.f64 (.f64 (/.f64 (pow.f64 (/.f64 l k) 2) t) (cos.f64 k)) (sin.f64 k)) (sin.f64 k)))
	5.6b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (cbrt.f64 (/.f64 (/.f64 l k) t)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 l k) t)) 2))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	10.0b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (.f64 (pow.f64 (cbrt.f64 (cos.f64 k)) 2) (.f64 (cbrt.f64 (cos.f64 k)) (pow.f64 (sin.f64 k) -2)))))
	7.3b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (/.f64 (pow.f64 (cbrt.f64 l) 2) t) (/.f64 (cbrt.f64 l) k))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	4.8b	(.f64 2 (/.f64 (/.f64 (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)) (*.f64 t (/.f64 k l))) (/.f64 k l)))
	5.6b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (/.f64 l k) (cbrt.f64 t)))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	7.7b	(.f64 2 (/.f64 (.f64 l (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) k))
	9.3b	(.f64 2 (/.f64 (.f64 (/.f64 l (*.f64 k t)) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))) (/.f64 k l)))
	29.0b	(.f64 2 (.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 l (.f64 k t)) (cos.f64 k))) (/.f64 1 (sin.f64 k))) (pow.f64 (cbrt.f64 (/.f64 k l)) 2)) (/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 l (.f64 k t)) (cos.f64 k))) (/.f64 1 (sin.f64 k))) (cbrt.f64 (/.f64 k l)))))
	28.8b	(.f64 2 (/.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 l (.f64 k t)) (cos.f64 k))) (/.f64 1 (sin.f64 k))) 2) (/.f64 k l)))
	30.4b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (.f64 (sqrt.f64 (cos.f64 k)) (.f64 (sqrt.f64 (cos.f64 k)) (pow.f64 (sin.f64 k) -2)))))

Compiler

Compiled 5079 to 2431 computations (52.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (sin.f64 k) -2)
✓	0.5b	(/.f64 (/.f64 (/.f64 l k) (/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) (/.f64 k l))
✓	3.2b	(/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))
✓	3.4b	(/.f64 (/.f64 l k) (/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2))))

series268.0ms (1%)

Counts

3 → 96

Calls

24 calls:

18.0ms	(/.f64 (/.f64 (/.f64 l k) (/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) (/.f64 k l))	t	-inf
18.0ms	(/.f64 (/.f64 (/.f64 l k) (/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) (/.f64 k l))	l	-inf
17.0ms	(/.f64 (/.f64 (/.f64 l k) (/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) (/.f64 k l))	l	0
17.0ms	(/.f64 (/.f64 (/.f64 l k) (/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) (/.f64 k l))	t	inf
17.0ms	(/.f64 (/.f64 (/.f64 l k) (/.f64 t (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) (/.f64 k l))	l	inf

rewrite85.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

162×	`add-sqr-sqrt_binary64`
153×	`egg-rr`
153×	`times-frac_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	317	57
2	4978	57

Stop Event

1×	node limit

Counts

3 → 153

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

375×	`cancel-sign-sub-inv_binary64`
345×	`fma-neg_binary64`
259×	`times-frac_binary64`
226×	`associate-/l*_binary64`
223×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	2091
1	221	2088
2	723	2059
3	3206	2049

Stop Event

1×	node limit

Counts

249 → 183

prune365.0ms (1.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	202	6	208
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	208	15	223

Error

0.0b

Counts

223 → 15

Alt Table

Status	Error	Program
	4.8b	(.f64 2 (/.f64 (/.f64 (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)) (*.f64 t (/.f64 k l))) (/.f64 k l)))
	4.9b	(.f64 2 (.f64 (/.f64 (/.f64 (/.f64 l k) t) 1) (/.f64 (*.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)) (/.f64 k l))))
	5.6b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (/.f64 l k) (cbrt.f64 t)))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	10.4b	(.f64 2 (/.f64 (.f64 l (/.f64 1 (.f64 k (/.f64 t (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))))) (/.f64 k l)))
	7.7b	(.f64 2 (/.f64 (.f64 l (.f64 (/.f64 (/.f64 l k) t) (.f64 (cos.f64 k) (pow.f64 (sin.f64 k) -2)))) k))
	32.5b	(.f64 2 (/.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 (/.f64 t (cos.f64 k))) (/.f64 1 (sin.f64 k)))) (/.f64 (/.f64 l k) (/.f64 (sqrt.f64 (/.f64 t (cos.f64 k))) (/.f64 1 (sin.f64 k))))) (/.f64 k l)))
	9.9b	(.f64 2 (/.f64 (/.f64 (.f64 (/.f64 (pow.f64 (/.f64 l k) 2) t) (cos.f64 k)) (sin.f64 k)) (sin.f64 k)))
	23.9b	(.f64 2 (/.f64 (/.f64 (/.f64 l k) (.f64 k (*.f64 k t))) (/.f64 k l)))
	10.0b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (.f64 (pow.f64 (cbrt.f64 (cos.f64 k)) 2) (.f64 (cbrt.f64 (cos.f64 k)) (pow.f64 (sin.f64 k) -2)))))
	7.3b	(.f64 2 (.f64 (.f64 (/.f64 l k) (.f64 (/.f64 (pow.f64 (cbrt.f64 l) 2) t) (/.f64 (cbrt.f64 l) k))) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))
	37.3b	(pow.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 l l))) (.f64 t (cbrt.f64 (.f64 (sin.f64 k) (*.f64 (tan.f64 k) (pow.f64 (/.f64 k t) 2)))))) 3)
	4.8b	(.f64 2 (/.f64 (.f64 (*.f64 (/.f64 (/.f64 l k) t) (cos.f64 k)) (pow.f64 (sin.f64 k) -2)) (/.f64 k l)))
	33.9b	(.f64 2 (/.f64 (.f64 (/.f64 l (/.f64 (sqrt.f64 (/.f64 t (cos.f64 k))) (/.f64 1 (sin.f64 k)))) (/.f64 (/.f64 1 k) (/.f64 (sqrt.f64 (/.f64 t (cos.f64 k))) (/.f64 1 (sin.f64 k))))) (/.f64 k l)))
	28.8b	(.f64 2 (/.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 l (.f64 k t)) (cos.f64 k))) (/.f64 1 (sin.f64 k))) 2) (/.f64 k l)))
	30.4b	(.f64 2 (.f64 (.f64 (/.f64 l k) (/.f64 l (.f64 k t))) (.f64 (sqrt.f64 (cos.f64 k)) (.f64 (sqrt.f64 (cos.f64 k)) (pow.f64 (sin.f64 k) -2)))))

Compiler

Compiled 5527 to 2736 computations (50.5% saved)

regimes2.4s (8.8%)

Accuracy

Total 1.9b remaining (96.8%)

Threshold costs 0b (0%)

Counts

264 → 3

Compiler

Compiled 39766 to 27354 computations (31.2% saved)

bsearch804.0ms (3%)

Algorithm

2×	binary-search

Calls

2 calls:

663.0ms	k
132.0ms	k

Steps

Iters	Point		Range
8.168834379465918e-156	∈ [	1.2368058730276569e-163	,	8.287179254880119e-156	]
-1.5969760918617522e-31	∈ [	-2.33218625274731e-30	,	-1.1483581410334542e-31	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	101
1	49	101

Stop Event

1×

saturated

end255.0ms (0.9%)

Stop Event

1×

fuel

Compiler

Compiled 530 to 341 computations (35.7% saved)

Details

analyze3.4s (12.6%)

sample17.2s (64%)

preprocess37.0ms (0.1%)

simplify21.0ms (0.1%)

prune5.0ms (0%)

localize14.0ms (0.1%)

series358.0ms (1.3%)

rewrite69.0ms (0.3%)

simplify46.0ms (0.2%)

prune133.0ms (0.5%)

localize13.0ms (0%)

series174.0ms (0.6%)

rewrite80.0ms (0.3%)

simplify41.0ms (0.2%)

prune327.0ms (1.2%)

localize14.0ms (0.1%)

series272.0ms (1%)

rewrite80.0ms (0.3%)

simplify61.0ms (0.2%)

prune313.0ms (1.2%)

localize17.0ms (0.1%)

series268.0ms (1%)

rewrite85.0ms (0.3%)

simplify60.0ms (0.2%)

prune365.0ms (1.4%)

regimes2.4s (8.8%)

bsearch804.0ms (3%)

simplify3.0ms (0%)

end255.0ms (0.9%)

Profiling