Details

analyze1.1s (12%)

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)

sample3.6s (40.2%)

Results

1.3s	1061×	body	2048	valid
961.0ms	1845×	body	1024	valid
537.0ms	4192×	body	128	valid
278.0ms	760×	body	512	valid
237.0ms	64×	body	4096	valid
80.0ms	334×	body	256	valid
29.0ms	196×	body	128	invalid
5.0ms	8×	body	2048	invalid
3.0ms	4×	body	8192	exit

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

16.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.1b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
▶	16.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))

Compiler

Compiled 88 to 48 computations (45.5% saved)

localize49.0ms (0.6%)

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)
✓	4.5b	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
✓	30.8b	(tan.f64 (*.f64 (PI.f64) l))

series104.0ms (1.2%)

Counts

4 → 60

Calls

4 calls:

52.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
36.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
12.0ms	(tan.f64 (*.f64 (PI.f64) l))
3.0ms	(*.f64 (PI.f64) l)

rewrite85.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Counts

4 → 197

Calls

4 calls:

80.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
80.0ms	(*.f64 (PI.f64) l)
80.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
80.0ms	(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

simplify69.0ms (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

257 → 226

Iterations

Useful iterations: 3 (0.0ms)

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

prune388.0ms (4.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	221	21	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	223	21	244

Error

11.4b

Counts

244 → 21

Alt Table

Status	Error	Program
	11.8b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) 2) F) (/.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))
	21.5b	(*.f64 l (-.f64 (PI.f64) (/.f64 (PI.f64) (pow.f64 F 2))))
	26.6b	(-.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))))
	39.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	39.2b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
▶	11.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) (/.f64 1 F)))
	17.0b	(fma.f64 (cbrt.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))) (pow.f64 (cbrt.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))))
	36.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3))) (*.f64 F F)))
	16.9b	(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))))
	16.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	35.3b	(-.f64 (.f64 (PI.f64) l) (.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) (.f64 (sqrt.f64 (tan.f64 (*.f64 (PI.f64) l))) (pow.f64 F -2))))
	16.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3)) (*.f64 F F)))
	49.2b	(sqrt.f64 (pow.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))) 2))
	36.0b	(/.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))))
	36.0b	(.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)))))
	36.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) l))) 1)) (*.f64 F F)))
	21.2b	(-.f64 (.f64 (PI.f64) l) (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	22.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (PI.f64) l)) 2)) (*.f64 F F)))
	39.0b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	38.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2)) (*.f64 F F)))
	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))

Compiler

Compiled 6665 to 1873 computations (71.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) l)
✓	0.2b	(.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) (/.f64 1 F))
✓	0.2b	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)
	30.8b	(tan.f64 (*.f64 (PI.f64) l))

series90.0ms (1%)

Counts

2 → 48

Calls

2 calls:

50.0ms	(.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) (/.f64 1 F))
40.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

rewrite54.0ms (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 → 98

Calls

2 calls:

52.0ms	(.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) (/.f64 1 F))
52.0ms	(/.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

146 → 116

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

prune447.0ms (5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	172	8	180
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	178	23	201

Error

11.4b

Counts

201 → 23

Alt Table

Status	Error	Program
	21.1b	(-.f64 (.f64 (PI.f64) l) (sqrt.f64 (pow.f64 (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F) 2)))
	11.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))
	26.6b	(-.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))))
	39.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	11.7b	(-.f64 (.f64 (PI.f64) l) (.f64 (.f64 (tan.f64 (.f64 (PI.f64) l)) (/.f64 1 F)) (/.f64 1 F)))
	39.2b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	17.0b	(fma.f64 (cbrt.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))) (pow.f64 (cbrt.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))))
	17.7b	(-.f64 (.f64 (PI.f64) l) (.f64 (sqrt.f64 (pow.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) 2)) (/.f64 1 F)))
	36.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3))) (*.f64 F F)))
	16.9b	(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))))
	15.8b	(-.f64 (.f64 (PI.f64) l) (.f64 (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))) (/.f64 1 F)))
	29.5b	(-.f64 (.f64 (PI.f64) l) (.f64 (pow.f64 (/.f64 (pow.f64 (tan.f64 (*.f64 (PI.f64) l)) 3) (pow.f64 F 3)) 1/3) (/.f64 1 F)))
	37.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (tan.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) l)))) F) (/.f64 1 F)))
	49.2b	(sqrt.f64 (pow.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))) 2))
	16.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3)) (*.f64 F F)))
	36.0b	(/.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))))
	36.0b	(.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)))))
	36.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) l))) 1)) (*.f64 F F)))
▶	11.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) F)))
	39.0b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	38.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2)) (*.f64 F F)))
	16.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))

Compiler

Compiled 4539 to 1991 computations (56.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (PI.f64) l)
✓	0.3b	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
✓	0.5b	(/.f64 1 (.f64 (/.f64 F (tan.f64 (.f64 (PI.f64) l))) F))
	30.8b	(tan.f64 (*.f64 (PI.f64) l))

series119.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

66.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
52.0ms	(/.f64 1 (.f64 (/.f64 F (tan.f64 (.f64 (PI.f64) l))) F))

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

530×	`log-prod_binary64`
265×	`pow2_binary64`
188×	`pow1/3_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`

Counts

2 → 68

Calls

2 calls:

55.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
55.0ms	(/.f64 1 (.f64 (/.f64 F (tan.f64 (.f64 (PI.f64) l))) F))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	207	23
2	2530	23
3	5023	23

simplify53.0ms (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

116 → 86

Iterations

Useful iterations: 3 (0.0ms)

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

prune224.0ms (2.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	13	9	22
Picked	1	0	1
Done	0	0	0
Total	159	14	173

Error

1.3b

Counts

173 → 14

Alt Table

Status	Error	Program
	16.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 F F)) (.f64 (cbrt.f64 F) (/.f64 1 (tan.f64 (.f64 (PI.f64) l))))) F)))
	11.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))
	34.7b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3)) (/.f64 1 (.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) F)))
	1.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 (-.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)))))) F)))
	26.6b	(-.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))))
	39.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	36.0b	(/.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))))
	36.0b	(.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)))))
▶	1.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 (+.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 F (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (pow.f64 l 3) (.f64 (pow.f64 (PI.f64) 3) -1/45))) (.f64 F (.f64 (pow.f64 l 5) (*.f64 (pow.f64 (PI.f64) 5) -2/945))))) F)))
	16.9b	(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))))
	39.0b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	11.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	16.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))

Compiler

Compiled 3745 to 1638 computations (56.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (PI.f64) 3)
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	1.5b	(.f64 (+.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 F (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (pow.f64 l 3) (.f64 (pow.f64 (PI.f64) 3) -1/45))) (.f64 F (.f64 (pow.f64 l 5) (.f64 (pow.f64 (PI.f64) 5) -2/945))))) F)
✓	4.2b	(.f64 F (.f64 (pow.f64 l 5) (*.f64 (pow.f64 (PI.f64) 5) -2/945)))

series162.0ms (1.8%)

Counts

4 → 48

Calls

4 calls:

115.0ms	(.f64 (+.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 F (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (pow.f64 l 3) (.f64 (pow.f64 (PI.f64) 3) -1/45))) (.f64 F (.f64 (pow.f64 l 5) (.f64 (pow.f64 (PI.f64) 5) -2/945))))) F)
46.0ms	(.f64 F (.f64 (pow.f64 l 5) (*.f64 (pow.f64 (PI.f64) 5) -2/945)))
0.0ms	(pow.f64 (PI.f64) 5)
0.0ms	(pow.f64 (PI.f64) 3)

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`add-sqr-sqrt_binary64`
240×	`log1p-expm1-u_binary64`
240×	`expm1-log1p-u_binary64`
234×	`add-cbrt-cube_binary64`
233×	`add-log-exp_binary64`

Counts

4 → 57

Calls

4 calls:

68.0ms	(pow.f64 (PI.f64) 3)
68.0ms	(pow.f64 (PI.f64) 5)
68.0ms	(.f64 (+.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 F (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (pow.f64 l 3) (.f64 (pow.f64 (PI.f64) 3) -1/45))) (.f64 F (.f64 (pow.f64 l 5) (.f64 (pow.f64 (PI.f64) 5) -2/945))))) F)
68.0ms	(.f64 F (.f64 (pow.f64 l 5) (*.f64 (pow.f64 (PI.f64) 5) -2/945)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	82
1	521	73
2	4951	73
3	4838	73

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

859×	`distribute-rgt-neg-in_binary64`
707×	`associate-l_binary64`
589×	`unswap-sqr_binary64`
535×	`associate-r_binary64`
258×	`fma-def_binary64`

Counts

105 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	70	1509
1	179	1509
2	688	1465
3	3321	1465
4	5408	1465

prune156.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	77	13	90

Error

0.8b

Counts

90 → 13

Alt Table

Status	Error	Program
	16.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 F F)) (.f64 (cbrt.f64 F) (/.f64 1 (tan.f64 (.f64 (PI.f64) l))))) F)))
	11.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))
	34.7b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3)) (/.f64 1 (.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) F)))
	26.6b	(-.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))))
	39.0b	(fma.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (PI.f64)) (neg.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	1.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 (+.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 F (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (pow.f64 l 3) (.f64 (pow.f64 (PI.f64) 3) -1/45))) (log1p.f64 (expm1.f64 (.f64 F (.f64 (pow.f64 (*.f64 l (PI.f64)) 5) -2/945)))))) F)))
	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 2) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 2)) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	36.0b	(/.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))))
	36.0b	(.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)))))
	16.9b	(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))))
	39.0b	(-.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) l)) 2) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	11.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	16.8b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) l)) 3) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))

Compiler

Compiled 3385 to 1938 computations (42.7% saved)

regimes1.7s (19%)

Accuracy

Total 0.6b remaining (33.4%)

Threshold costs 0.6b (33.4%)

Counts

208 → 1

Compiler

Compiled 31644 to 19703 computations (37.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	66
1	38	66
2	44	66
3	46	66
4	47	66
5	45	66

end242.0ms (2.7%)

Compiler: Compiled 395 to 239 computations (39.5% 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	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

Details

analyze1.1s (12%)

sample3.6s (40.2%)

simplify22.0ms (0.2%)

prune3.0ms (0%)

localize49.0ms (0.6%)

series104.0ms (1.2%)

rewrite85.0ms (1%)

simplify69.0ms (0.8%)

prune388.0ms (4.3%)

localize9.0ms (0.1%)

series90.0ms (1%)

rewrite54.0ms (0.6%)

simplify64.0ms (0.7%)

prune447.0ms (5%)

localize10.0ms (0.1%)

series119.0ms (1.3%)

rewrite56.0ms (0.6%)

simplify53.0ms (0.6%)

prune224.0ms (2.5%)

localize24.0ms (0.3%)

series162.0ms (1.8%)

rewrite69.0ms (0.8%)

simplify65.0ms (0.7%)

prune156.0ms (1.7%)

regimes1.7s (19%)

simplify3.0ms (0%)

end242.0ms (2.7%)

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