Details

analyze2.8s (16.2%)

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)

sample5.0s (28.9%)

Results

2.4s	2708×	body	1024	valid
845.0ms	3690×	body	128	valid
821.0ms	1304×	body	512	valid
340.0ms	1491×	body	128	invalid
236.0ms	550×	body	256	valid
83.0ms	141×	body	512	invalid
53.0ms	118×	body	256	invalid
46.0ms	51×	body	1024	invalid
9.0ms	4×	body	2048	valid

Compiler

Compiled 86 to 65 computations (24.4% 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

29.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.4b	(/.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)

localize15.0ms (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))
✓	3.4b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
✓	11.5b	(.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)))
✓	15.3b	(/.f64 (pow.f64 t 3) (*.f64 l l))

series451.0ms (2.6%)

Counts

4 → 132

Calls

4 calls:

193.0ms	(.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)))
151.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
74.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
32.0ms	(/.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:

18.0ms	(.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 (1.2%)

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

prune349.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	224	11	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	11	236

Error

12.1b

Counts

236 → 11

Alt Table

Status	Error	Program
	28.9b	(/.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))))
	23.2b	(/.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))))
	37.4b	(/.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))))))))
▶	20.3b	(/.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))))
	43.6b	(/.f64 2 (.f64 (.f64 (*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) (/.f64 l (/.f64 (pow.f64 t 3/2) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	31.6b	(/.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) 3)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	26.7b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 (.f64 l l) (*.f64 t t))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	34.1b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	56.5b	(/.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))))
	41.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	59.9b	(/.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))))))

Compiler

Compiled 8471 to 4768 computations (43.7% 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))
✓	3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	7.2b	(/.f64 (*.f64 t t) l)
✓	11.5b	(.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)))

series332.0ms (1.9%)

Counts

4 → 132

Calls

4 calls:

186.0ms	(.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)))
115.0ms	(.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))
10.0ms	(/.f64 (*.f64 t t) l)

rewrite70.0ms (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:

23.0ms	(.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)))
10.0ms	(.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)

simplify221.0ms (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

prune442.0ms (2.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	258	8	266
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	263	14	277

Error

8.8b

Counts

277 → 14

Alt Table

Status	Error	Program
	21.3b	(/.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))
	21.1b	(/.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))))
▶	14.8b	(/.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))))
	21.6b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) l))
	26.7b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 (.f64 l l) (*.f64 t t))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	34.1b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	42.2b	(/.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))))
	27.9b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l l)))
	37.4b	(/.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))))))))
	14.8b	(/.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))))
	56.5b	(/.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))))
	41.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	29.2b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 t (sin.f64 k))) (sin.f64 k)) (-.f64 (.f64 2 2) (.f64 (pow.f64 (/.f64 k t) 2) (pow.f64 (/.f64 k t) 2)))) (.f64 (*.f64 l (cos.f64 k)) (-.f64 2 (pow.f64 (/.f64 k t) 2)))))
	43.6b	(/.f64 2 (.f64 (.f64 (*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) (/.f64 l (/.f64 (pow.f64 t 3/2) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 10510 to 4499 computations (57.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.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))
	3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	11.5b	(.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)))

series606.0ms (3.5%)

Counts

3 → 108

Calls

3 calls:

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))))

185.0ms

(*.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)))

126.0ms

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

rewrite98.0ms (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:

25.0ms

(/.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))))

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)))

12.0ms

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

simplify223.0ms (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

prune709.0ms (4.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	379	11	390
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	391	13	404

Error

6.9b

Counts

404 → 13

Alt Table

Status	Error	Program
	36.7b	(/.f64 2 (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 2 (/.f64 (.f64 (.f64 k k) (pow.f64 t 3)) (.f64 l l)) (.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l))))))
	25.8b	(cbrt.f64 (.f64 (.f64 (/.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)))) (/.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))))) (/.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))))))
	27.9b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l l)))
▶	12.0b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)))
	33.9b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	15.6b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 (sqrt.f64 2) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	14.9b	(/.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)))))
	16.7b	(/.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))))
	18.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) l))
	51.1b	(-.f64 (fma.f64 (/.f64 l (.f64 k k)) (/.f64 l (pow.f64 t 3)) (fma.f64 1/4 (/.f64 (.f64 (.f64 k k) (.f64 l l)) (pow.f64 t 7)) (fma.f64 1/12 (/.f64 (.f64 (.f64 k k) (.f64 l l)) (pow.f64 t 5)) (.f64 7/240 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 5)))))) (fma.f64 7/120 (/.f64 (.f64 (.f64 k k) (.f64 l l)) (pow.f64 t 3)) (fma.f64 1/24 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 7)) (fma.f64 1/8 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 9)) (fma.f64 31/3024 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 3)) (fma.f64 1/6 (/.f64 (.f64 l l) (pow.f64 t 3)) (.f64 1/2 (/.f64 (.f64 l l) (pow.f64 t 5)))))))))
	41.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	15.5b	(/.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)))
	21.1b	(.f64 (/.f64 2 (.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))

Compiler

Compiled 16229 to 7100 computations (56.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	4.0b	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
✓	6.5b	(/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t))
✓	8.7b	(.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series434.0ms (2.5%)

Counts

3 → 108

Calls

3 calls:

190.0ms

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

161.0ms

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

82.0ms

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

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-cbrt-cube_binary64`
97×	`add-exp-log_binary64`
51×	`cbrt-unprod_binary64`
51×	`prod-exp_binary64`
31×	`times-frac_binary64`

Counts

3 → 145

Calls

3 calls:

19.0ms

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

16.0ms

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

8.0ms

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

simplify182.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

650×	`associate-l_binary64`
568×	`associate-/l*_binary64`
544×	`fma-def_binary64`
310×	`times-frac_binary64`
205×	`associate-*l/_binary64`

Counts

253 → 277

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	376	9901
1	1170	8597
2	4943	8586
3	5331	8586

prune734.0ms (4.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	330	9	339
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	337	15	352

Error

5.9b

Counts

352 → 15

Alt Table

Status	Error	Program
	29.5b	(/.f64 2 (/.f64 (fma.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t t)) l) (fma.f64 1/3 (/.f64 (.f64 (*.f64 t t) (pow.f64 k 4)) l) (/.f64 (pow.f64 k 4) l))) (/.f64 l t)))
	12.7b	(/.f64 2 (/.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (/.f64 l (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) t))))
	12.3b	(/.f64 2 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t))) (cbrt.f64 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)))) (cbrt.f64 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)))))
	33.9b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	15.6b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 (sqrt.f64 2) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	24.2b	(/.f64 2 (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)) (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t))) (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)))))
	12.8b	(/.f64 2 (/.f64 (.f64 t (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 t l)) (tan.f64 k)) (fma.f64 -1 (pow.f64 (/.f64 k t) 2) -2))) (neg.f64 (/.f64 l t))))
	51.1b	(-.f64 (fma.f64 (/.f64 l (.f64 k k)) (/.f64 l (pow.f64 t 3)) (fma.f64 1/4 (/.f64 (.f64 (.f64 k k) (.f64 l l)) (pow.f64 t 7)) (fma.f64 1/12 (/.f64 (.f64 (.f64 k k) (.f64 l l)) (pow.f64 t 5)) (.f64 7/240 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 5)))))) (fma.f64 7/120 (/.f64 (.f64 (.f64 k k) (.f64 l l)) (pow.f64 t 3)) (fma.f64 1/24 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 7)) (fma.f64 1/8 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 9)) (fma.f64 31/3024 (/.f64 (.f64 (.f64 l l) (pow.f64 k 4)) (pow.f64 t 3)) (fma.f64 1/6 (/.f64 (.f64 l l) (pow.f64 t 3)) (.f64 1/2 (/.f64 (.f64 l l) (pow.f64 t 5)))))))))
	12.0b	(/.f64 2 (/.f64 1 (/.f64 (/.f64 l t) (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	21.1b	(.f64 (/.f64 2 (.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))
	12.4b	(/.f64 2 (/.f64 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 (cbrt.f64 l) (cbrt.f64 t))))
	25.8b	(cbrt.f64 (.f64 (.f64 (/.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)))) (/.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))))) (/.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))))))
	21.2b	(/.f64 2 (/.f64 (/.f64 (fma.f64 2 (/.f64 (.f64 (pow.f64 (sin.f64 k) 2) (.f64 t t)) (cos.f64 k)) (/.f64 (.f64 (.f64 k k) (pow.f64 (sin.f64 k) 2)) (cos.f64 k))) l) (/.f64 l t)))
	15.5b	(/.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)))
	12.3b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (.f64 (cbrt.f64 (tan.f64 k)) (cbrt.f64 (tan.f64 k)))) (cbrt.f64 (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)))

Compiler

Compiled 13014 to 5289 computations (59.4% saved)

regimes3.5s (20.2%)

Accuracy

Total 3.2b remaining (32%)

Threshold costs 0b (0%)

Counts

307 → 3

Compiler

Compiled 66315 to 44272 computations (33.2% saved)

bsearch221.0ms (1.3%)

Steps

Iters	Range		Point
10	4.103169418876562e-72	1.0583857677967169e-60	4.33929589454827e-71
8	-3.7769946996647616e-6	-1.4628124609259599e-8	-2.503593351605439e-7

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	142
1	52	142
2	52	142

end430.0ms (2.5%)

Compiler: Compiled 901 to 509 computations (43.5% saved)

Details

analyze2.8s (16.2%)

sample5.0s (28.9%)

simplify53.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series451.0ms (2.6%)

rewrite57.0ms (0.3%)

simplify208.0ms (1.2%)

prune349.0ms (2%)

localize18.0ms (0.1%)

series332.0ms (1.9%)

rewrite70.0ms (0.4%)

simplify221.0ms (1.3%)

prune442.0ms (2.6%)

localize18.0ms (0.1%)

series606.0ms (3.5%)

rewrite98.0ms (0.6%)

simplify223.0ms (1.3%)

prune709.0ms (4.1%)

localize18.0ms (0.1%)

series434.0ms (2.5%)

rewrite65.0ms (0.4%)

simplify182.0ms (1.1%)

prune734.0ms (4.3%)

regimes3.5s (20.2%)

bsearch221.0ms (1.3%)

simplify3.0ms (0%)

end430.0ms (2.5%)

Profiling