Details

analyze1.7s (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
21.8%	67.1%	11.1%	11
21.8%	67.1%	11.1%	12
32.7%	56.1%	11.1%	13
35.1%	53%	11.9%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample6.1s (50.4%)

Results

1.6s	1717×	body	1024	valid
1.5s	2047×	body	1024	invalid
972.0ms	4487×	body	128	valid
584.0ms	1278×	body	512	valid
518.0ms	2671×	body	128	invalid
398.0ms	964×	body	512	invalid
220.0ms	708×	body	256	valid
154.0ms	505×	body	256	invalid
82.0ms	66×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
657×	`div-sub_binary64`
464×	`fma-neg_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	53	22
3	105	22
4	233	22
5	540	22
6	1242	22
7	2242	22
8	3501	22
9	4490	22
10	4976	22

prune3.0ms (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

19.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.3b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	5.7b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series50.0ms (0.4%)

Counts

3 → 80

Calls

3 calls:

37.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
11.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite58.0ms (0.5%)

Algorithm

3×	egg-rewrite

Counts

3 → 0

Calls

3 calls:

24.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
18.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
16.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	1
1	130	1
2	71	1
0	8	1
1	169	1
2	73	1
0	14	1
1	295	1
2	33	1

simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-def_binary64`
524×	`associate-l_binary64`
430×	`sub-neg_binary64`
401×	`associate-r_binary64`
288×	`associate-+l+_binary64`

Counts

80 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2023
1	367	1649
2	1181	1604
3	4510	1604
4	4809	1604
5	4962	1604
6	4933	1604

prune51.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	4	45

Error

0.0b

Counts

45 → 4

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
▶	0.3b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
	44.0b	(-.f64 (+.f64 (fma.f64 1/8 (.f64 (/.f64 J (exp.f64 l)) (.f64 K K)) U) (.f64 (exp.f64 l) (-.f64 J (.f64 1/8 (.f64 J (.f64 K K)))))) (/.f64 J (exp.f64 l)))

Compiler

Compiled 1251 to 747 computations (40.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 l (.f64 (cos.f64 (*.f64 1/2 K)) J))
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) J)
✓	0.1b	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
✓	5.8b	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))

series103.0ms (0.8%)

Counts

4 → 64

Calls

4 calls:

41.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
34.0ms	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))
19.0ms	(.f64 l (.f64 (cos.f64 (*.f64 1/2 K)) J))
8.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)

rewrite290.0ms (2.4%)

Algorithm

4×	egg-rewrite

Rules

44×	`egg`
37×	`egg`
36×	`egg`
32×	`egg`

Counts

4 → 149

Calls

4 calls:

114.0ms	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))
73.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)
53.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
47.0ms	(.f64 l (.f64 (cos.f64 (*.f64 1/2 K)) J))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	224	15
2	2452	15
3	4957	15
4	4972	15
5	4939	15
0	13	18
1	267	18
2	2923	18
3	4944	18
0	7	9
1	138	9
2	1528	9
3	4893	9
4	5134	9
0	9	12
1	179	12
2	2044	12
3	4943	12

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

752×	`distribute-rgt-neg-in_binary64`
730×	`associate-l_binary64`
715×	`distribute-lft-neg-in_binary64`
674×	`associate-r_binary64`
408×	`fma-def_binary64`

Counts

213 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	70	1066
1	223	1007
2	800	936
3	3647	936
4	5353	936

prune301.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	221	4	225
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	222	7	229

Error

Counts

229 → 7

Alt Table

Status	Error	Program
	44.0b	(-.f64 (+.f64 (fma.f64 1/8 (.f64 (/.f64 J (exp.f64 l)) (.f64 K K)) U) (.f64 (exp.f64 l) (-.f64 J (.f64 1/8 (.f64 J (.f64 K K)))))) (/.f64 J (exp.f64 l)))
	16.3b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (sqrt.f64 (cos.f64 (.f64 1/2 K))) (.f64 (sqrt.f64 (cos.f64 (.f64 1/2 K))) J)))) U))
✓	0.3b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
▶	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
	8.5b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (expm1.f64 (log1p.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U))
	0.7b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J)) 3))) U))
	17.1b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cbrt.f64 (.f64 J J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))))) U))

Compiler

Compiled 7278 to 5287 computations (27.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
✓	0.0b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

series161.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

114.0ms	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
39.0ms	(.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
5.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
3.0ms	(*.f64 1/60 (pow.f64 l 5))

rewrite255.0ms (2.1%)

Algorithm

4×	egg-rewrite

Rules

43×	`egg`
36×	`egg`
23×	`egg`
23×	`egg`

Counts

4 → 125

Calls

4 calls:

80.0ms	(*.f64 1/60 (pow.f64 l 5))
67.0ms	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
57.0ms	(.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
48.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	213	14
2	2130	14
3	4998	14
0	19	30
1	399	30
2	4277	30
3	5264	30
0	6	7
1	127	7
2	1310	7
3	4944	7
4	6454	7
0	14	21
1	293	21
2	2986	21
3	5038	21

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

771×	`associate-r_binary64`
607×	`sub-neg_binary64`
506×	`associate-+l+_binary64`
406×	`associate--l+_binary64`
360×	`cancel-sign-sub-inv_binary64`

Counts

209 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	2896
1	345	2553
2	1261	2149
3	4463	2149
4	5052	2149

prune283.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	166	7	173

Error

Counts

173 → 7

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) 3) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
✓	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
	8.5b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (expm1.f64 (log1p.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U))
▶	0.7b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J)) 3))) U))
	44.0b	(-.f64 (+.f64 (fma.f64 1/8 (.f64 (/.f64 J (exp.f64 l)) (.f64 K K)) U) (.f64 (exp.f64 l) (-.f64 J (.f64 1/8 (.f64 J (.f64 K K)))))) (/.f64 J (exp.f64 l)))
	17.1b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cbrt.f64 (.f64 J J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))))) U))

Compiler

Compiled 5209 to 3829 computations (26.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
✓	0.6b	(cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J))
✓	0.8b	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J)) 3)
	5.8b	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))

series989.0ms (8.1%)

Counts

2 → 48

Calls

2 calls:

512.0ms	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J)) 3)
477.0ms	(cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J))

rewrite93.0ms (0.8%)

Algorithm

2×	egg-rewrite

Rules

40×	`egg`
26×	`egg`

Counts

2 → 66

Calls

2 calls:

47.0ms	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J)) 3)
45.0ms	(cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	9
1	187	9
2	1986	9
3	4937	9
0	8	11
1	156	11
2	1723	11
3	5259	11

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-neg_binary64`
351×	`distribute-rgt-neg-in_binary64`
345×	`distribute-lft-neg-in_binary64`
226×	`unswap-sqr_binary64`
211×	`associate-r_binary64`

Counts

114 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	800
1	194	793
2	515	704
3	1793	584
4	4709	576
5	4996	576
6	4921	576

prune289.0ms (2.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	191	7	198

Error

Counts

198 → 7

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) 3) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
✓	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
	8.5b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (expm1.f64 (log1p.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U))
✓	0.7b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (pow.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 K)) J)) 3))) U))
	44.0b	(-.f64 (+.f64 (fma.f64 1/8 (.f64 (/.f64 J (exp.f64 l)) (.f64 K K)) U) (.f64 (exp.f64 l) (-.f64 J (.f64 1/8 (.f64 J (.f64 K K)))))) (/.f64 J (exp.f64 l)))
	17.1b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cbrt.f64 (.f64 J J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))))) U))

Compiler

Compiled 6561 to 4930 computations (24.9% saved)

regimes704.0ms (5.8%)

Accuracy

Total 0.2b remaining (53.1%)

Threshold costs 0.2b (53.1%)

Counts

57 → 1

Compiler

Compiled 16314 to 12368 computations (24.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	27	38
2	27	38

end164.0ms (1.3%)

Compiler: Compiled 271 to 199 computations (26.6% saved)

Details

analyze1.7s (13.9%)

sample6.1s (50.4%)

simplify79.0ms (0.7%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series50.0ms (0.4%)

rewrite58.0ms (0.5%)

simplify127.0ms (1%)

prune51.0ms (0.4%)

localize14.0ms (0.1%)

series103.0ms (0.8%)

rewrite290.0ms (2.4%)

simplify69.0ms (0.6%)

prune301.0ms (2.5%)

localize14.0ms (0.1%)

series161.0ms (1.3%)

rewrite255.0ms (2.1%)

simplify105.0ms (0.9%)

prune283.0ms (2.3%)

localize17.0ms (0.1%)

series989.0ms (8.1%)

rewrite93.0ms (0.8%)

simplify97.0ms (0.8%)

prune289.0ms (2.4%)

regimes704.0ms (5.8%)

simplify2.0ms (0%)

end164.0ms (1.3%)

Profiling