Details

analyze1.0s (11.5%)

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
18.7%	81.2%	0.1%	7
18.7%	81.2%	0.1%	8
29.7%	69.5%	0.9%	9
30.4%	67.9%	1.7%	10
36.3%	61.1%	2.6%	11
36.9%	59.5%	3.6%	12
39.9%	55.9%	4.2%	13
40.2%	54.9%	4.9%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample3.7s (40.6%)

Results

1.3s	1105×	body	2048	valid
1.0s	1891×	body	1024	valid
529.0ms	4136×	body	128	valid
287.0ms	723×	body	512	valid
261.0ms	70×	body	4096	valid
82.0ms	331×	body	256	valid
21.0ms	158×	body	128	invalid
6.0ms	8×	body	8192	exit
5.0ms	8×	body	2048	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

297×	`fma-def_binary64`
157×	`fma-neg_binary64`
50×	`cancel-sign-sub-inv_binary64`
37×	`associate-/l*_binary64`
33×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20

prune3.0ms (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

16.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	16.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))

Compiler

Compiled 88 to 48 computations (45.5% saved)

localize78.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
✓	0.2b	(*.f64 (PI.f64) l)
✓	3.4b	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
✓	31.2b	(tan.f64 (*.f64 (PI.f64) l))

series133.0ms (1.5%)

Counts

4 → 60

Calls

4 calls:

84.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
35.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
11.0ms	(tan.f64 (*.f64 (PI.f64) l))
2.0ms	(*.f64 (PI.f64) l)

rewrite82.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

532×	`log-prod_binary64`
276×	`fma-def_binary64`
201×	`egg-rr`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`

Counts

4 → 201

Calls

4 calls:

77.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
77.0ms	(*.f64 (PI.f64) l)
77.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
77.0ms	(tan.f64 (*.f64 (PI.f64) l))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	45
1	200	45
2	2689	45
3	5070	45

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-/l/_binary64`
401×	`distribute-rgt-neg-in_binary64`
398×	`distribute-lft-neg-in_binary64`
305×	`distribute-neg-frac_binary64`
268×	`fma-neg_binary64`

Counts

261 → 229

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	1516
1	161	1504
2	570	1502
3	2627	1493
4	5461	1493

prune364.0ms (4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	223	22	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	225	22	247

Error

12.8b

Counts

247 → 22

Alt Table

Status	Error	Program
	24.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
	34.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	16.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) 2) (.f64 (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))) (pow.f64 F -2))))
	16.9b	(fma.f64 (pow.f64 (cbrt.f64 l) 2) (.f64 (cbrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	36.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3))) (*.f64 F F)))
	17.1b	(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) l) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	34.1b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	30.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (-.f64 (exp.f64 (log1p.f64 (tan.f64 (.f64 (PI.f64) l)))) 1) (*.f64 F F)))
	16.3b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3)) (*.f64 F F)))
	23.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 (PI.f64) l))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 (PI.f64) l)))))) (.f64 F F)))
	42.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) l) 3) 1/3)) (*.f64 F F)))
	46.8b	(sqrt.f64 (pow.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))) 2))
	16.8b	(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 l) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	37.0b	(/.f64 1 (/.f64 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)) 2))))
	28.4b	(expm1.f64 (log1p.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	37.0b	(.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (/.f64 1 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))))
	17.1b	(fma.f64 (.f64 l (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
▶	13.2b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) (/.f64 1 F)))
	33.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2)) (*.f64 F F)))
	16.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	22.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (PI.f64) l)) 2)) (*.f64 F F)))
	27.2b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 l F) (+.f64 (/.f64 (PI.f64) F) (/.f64 (.f64 1/3 (.f64 (pow.f64 (PI.f64) 3) (*.f64 l l))) F))))

Compiler

Compiled 6659 to 1899 computations (71.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) (/.f64 1 F))
✓	0.2b	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)
	0.2b	(*.f64 (PI.f64) l)
	31.2b	(tan.f64 (*.f64 (PI.f64) l))

series89.0ms (1%)

Counts

2 → 48

Calls

2 calls:

50.0ms	(.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) (/.f64 1 F))
38.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

524×	`log-prod_binary64`
259×	`pow2_binary64`
186×	`pow1/3_binary64`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`

Counts

2 → 99

Calls

2 calls:

54.0ms	(.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) (/.f64 1 F))
54.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	207	23
2	2502	23
3	4972	23

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
775×	`associate-/r/_binary64`
699×	`associate-/l/_binary64`
535×	`unswap-sqr_binary64`
238×	`times-frac_binary64`

Counts

147 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	1130
1	138	1122
2	423	1118
3	1894	1118
4	4934	1118
5	5586	1118

prune413.0ms (4.6%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	179	25	204

Error

12.8b

Counts

204 → 25

Alt Table

Status	Error	Program
	17.1b	(fma.f64 (.f64 l (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	13.2b	(-.f64 (.f64 (PI.f64) l) (pow.f64 (.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) F) -1))
	21.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 (PI.f64) l)) 2)) F) (/.f64 1 F)))
	13.4b	(-.f64 (.f64 (PI.f64) l) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F)) 3))
	24.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
	34.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	36.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (tan.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) l) 3))) F) (/.f64 1 F)))
	16.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) 2) (.f64 (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))) (pow.f64 F -2))))
	16.9b	(fma.f64 (pow.f64 (cbrt.f64 l) 2) (.f64 (cbrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	34.1b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	30.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (-.f64 (exp.f64 (log1p.f64 (tan.f64 (.f64 (PI.f64) l)))) 1) (*.f64 F F)))
	16.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
▶	13.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	42.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) l) 3) 1/3)) (*.f64 F F)))
	46.8b	(sqrt.f64 (pow.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))) 2))
	27.2b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 l F) (+.f64 (/.f64 (PI.f64) F) (/.f64 (.f64 1/3 (.f64 (pow.f64 (PI.f64) 3) (*.f64 l l))) F))))
	13.3b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (tan.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) l)) 3)) F) (/.f64 1 F)))
	16.5b	(-.f64 (.f64 (PI.f64) l) (.f64 (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))) (/.f64 1 F)))
	16.8b	(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 l) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	37.0b	(/.f64 1 (/.f64 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)) 2))))
	28.4b	(expm1.f64 (log1p.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	37.0b	(.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (/.f64 1 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))))
	17.1b	(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) l) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	33.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2)) (*.f64 F F)))
	20.1b	(-.f64 (.f64 (PI.f64) l) (.f64 (sqrt.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) 2)) (/.f64 1 F)))

Compiler

Compiled 4547 to 2037 computations (55.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))
✓	0.2b	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
	0.2b	(*.f64 (PI.f64) l)
	31.2b	(tan.f64 (*.f64 (PI.f64) l))

series119.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

68.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
51.0ms	(/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`log-prod_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
177×	`pow3_binary64`
172×	`log-pow_binary64`

Counts

2 → 86

Calls

2 calls:

54.0ms	(/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))
54.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	213	23
2	2704	23
3	5021	23

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

515×	`distribute-rgt-neg-in_binary64`
497×	`distribute-lft-neg-in_binary64`
430×	`unswap-sqr_binary64`
383×	`associate-r_binary64`
383×	`associate-l_binary64`

Counts

134 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	1112
1	165	1106
2	584	1102
3	2839	1098
4	5004	1098

prune198.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	17	7	24
Picked	1	0	1
Done	0	0	0
Total	182	12	194

Error

1.1b

Counts

194 → 12

Alt Table

Status	Error	Program
	32.1b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	13.2b	(-.f64 (.f64 (PI.f64) l) (+.f64 0 (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F)))
▶	1.3b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (-.f64 (/.f64 F (.f64 (PI.f64) l)) (+.f64 (.f64 1/3 (.f64 (PI.f64) (.f64 F l))) (+.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (.f64 (pow.f64 l 5) F))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))))
	16.8b	(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 l) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	37.0b	(/.f64 1 (/.f64 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)) 2))))
	13.4b	(-.f64 (.f64 (PI.f64) l) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F)) 3))
	34.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	16.9b	(fma.f64 (pow.f64 (cbrt.f64 l) 2) (.f64 (cbrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	13.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	27.2b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 l F) (+.f64 (/.f64 (PI.f64) F) (/.f64 (.f64 1/3 (.f64 (pow.f64 (PI.f64) 3) (*.f64 l l))) F))))
	37.0b	(.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (/.f64 1 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))))
	16.5b	(-.f64 (.f64 (PI.f64) l) (.f64 (cbrt.f64 (pow.f64 F -2)) (.f64 (/.f64 1 (cbrt.f64 F)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))

Compiler

Compiled 3991 to 1712 computations (57.1% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	2.7b	(/.f64 (/.f64 1 F) (-.f64 (/.f64 F (.f64 (PI.f64) l)) (+.f64 (.f64 1/3 (.f64 (PI.f64) (.f64 F l))) (+.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (.f64 (pow.f64 l 5) F))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (.f64 (pow.f64 l 3) F)))))))
✓	4.3b	(*.f64 (pow.f64 l 3) F)
✓	5.4b	(*.f64 (pow.f64 l 5) F)

series287.0ms (3.2%)

Counts

4 → 48

Calls

4 calls:

263.0ms	(/.f64 (/.f64 1 F) (-.f64 (/.f64 F (.f64 (PI.f64) l)) (+.f64 (.f64 1/3 (.f64 (PI.f64) (.f64 F l))) (+.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (.f64 (pow.f64 l 5) F))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (.f64 (pow.f64 l 3) F)))))))
13.0ms	(*.f64 (pow.f64 l 5) F)
11.0ms	(*.f64 (pow.f64 l 3) F)
0.0ms	(pow.f64 (PI.f64) 5)

rewrite46.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

315×	`log1p-expm1-u_binary64`
315×	`expm1-log1p-u_binary64`
306×	`add-cbrt-cube_binary64`
304×	`add-log-exp_binary64`
303×	`add-exp-log_binary64`

Counts

4 → 60

Calls

4 calls:

45.0ms	(pow.f64 (PI.f64) 5)
45.0ms	(/.f64 (/.f64 1 F) (-.f64 (/.f64 F (.f64 (PI.f64) l)) (+.f64 (.f64 1/3 (.f64 (PI.f64) (.f64 F l))) (+.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (.f64 (pow.f64 l 5) F))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (.f64 (pow.f64 l 3) F)))))))
45.0ms	(*.f64 (pow.f64 l 3) F)
45.0ms	(*.f64 (pow.f64 l 5) F)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	80
1	678	74
2	4954	74

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

868×	`unswap-sqr_binary64`
551×	`associate-/r*_binary64`
434×	`associate-l_binary64`
399×	`associate-r_binary64`
380×	`fma-neg_binary64`

Counts

108 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1422
1	249	1416
2	910	1408
3	4221	1408
4	6047	1408

prune136.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Error

0.1b

Counts

93 → 13

Alt Table

Status	Error	Program
	13.4b	(-.f64 (.f64 (PI.f64) l) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F)) 3))
	0.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (-.f64 (/.f64 F (.f64 (PI.f64) l)) (+.f64 (.f64 1/3 (.f64 (PI.f64) (.f64 F l))) (+.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (log.f64 (pow.f64 (exp.f64 (pow.f64 l 5)) F)))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (.f64 (pow.f64 l 3) F))))))))
	25.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 -945/2 (.f64 (pow.f64 (PI.f64) 5) (.f64 F (.f64 F (pow.f64 l 5))))))
	34.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	32.1b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	13.2b	(-.f64 (.f64 (PI.f64) l) (+.f64 0 (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F)))
	16.8b	(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 l) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	37.0b	(/.f64 1 (/.f64 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)) 2))))
	16.9b	(fma.f64 (pow.f64 (cbrt.f64 l) 2) (.f64 (cbrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	13.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	27.2b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 l F) (+.f64 (/.f64 (PI.f64) F) (/.f64 (.f64 1/3 (.f64 (pow.f64 (PI.f64) 3) (*.f64 l l))) F))))
	37.0b	(.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (/.f64 1 (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))))
	16.5b	(-.f64 (.f64 (PI.f64) l) (.f64 (cbrt.f64 (pow.f64 F -2)) (.f64 (/.f64 1 (cbrt.f64 F)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))

Compiler

Compiled 3916 to 2235 computations (42.9% saved)

regimes1.7s (19%)

Accuracy

Total 0.5b remaining (64%)

Threshold costs 0.5b (64%)

Counts

210 → 1

Compiler

Compiled 29869 to 19157 computations (35.9% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
23×	`+-commutative_binary64`
21×	`sub-neg_binary64`
19×	`neg-sub0_binary64`
19×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	76
1	50	76
2	63	76
3	88	76
4	124	76
5	159	76
6	187	76
7	205	76
8	213	76
9	214	76
10	209	76

end225.0ms (2.5%)

Compiler: Compiled 406 to 263 computations (35.2% saved)

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20

Iter	Nodes	Cost
0	33	76
1	50	76
2	63	76
3	88	76
4	124	76
5	159	76
6	187	76
7	205	76
8	213	76
9	214	76
10	209	76

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20

Iter	Nodes	Cost
0	33	76
1	50	76
2	63	76
3	88	76
4	124	76
5	159	76
6	187	76
7	205	76
8	213	76
9	214	76
10	209	76

Details

analyze1.0s (11.5%)

sample3.7s (40.6%)

simplify22.0ms (0.2%)

prune3.0ms (0%)

localize78.0ms (0.9%)

series133.0ms (1.5%)

rewrite82.0ms (0.9%)

simplify70.0ms (0.8%)

prune364.0ms (4%)

localize8.0ms (0.1%)

series89.0ms (1%)

rewrite56.0ms (0.6%)

simplify64.0ms (0.7%)

prune413.0ms (4.6%)

localize8.0ms (0.1%)

series119.0ms (1.3%)

rewrite56.0ms (0.6%)

simplify52.0ms (0.6%)

prune198.0ms (2.2%)

localize26.0ms (0.3%)

series287.0ms (3.2%)

rewrite46.0ms (0.5%)

simplify62.0ms (0.7%)

prune136.0ms (1.5%)

regimes1.7s (19%)

simplify8.0ms (0.1%)

end225.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20

Iter	Nodes	Cost
0	33	76
1	50	76
2	63	76
3	88	76
4	124	76
5	159	76
6	187	76
7	205	76
8	213	76
9	214	76
10	209	76