Details

analyze1.6s (16.8%)

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)

sample5.3s (54.7%)

Results

1.3s	1717×	body	1024	valid
1.3s	2047×	body	1024	invalid
807.0ms	4487×	body	128	valid
558.0ms	1278×	body	512	valid
442.0ms	2671×	body	128	invalid
406.0ms	964×	body	512	invalid
213.0ms	708×	body	256	valid
146.0ms	505×	body	256	invalid
67.0ms	66×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify66.0ms (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)

localize10.0ms (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)))

series48.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

35.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
10.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite76.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Counts

3 → 0

Calls

2 calls:

76.0ms	((-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (fma.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	295	18
2	33	18
0	6	6
1	130	6
2	71	6
0	8	9
1	169	9
2	73	9
0	14	18
1	295	18
2	33	18
0	0	0
1	0	0

simplify111.0ms (1.1%)

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

prune49.0ms (0.5%)

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
	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)))
	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)

Compiler

Compiled 1251 to 747 computations (40.3% saved)

localize13.0ms (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))

series102.0ms (1.1%)

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))
18.0ms	(.f64 l (.f64 (cos.f64 (*.f64 1/2 K)) J))
9.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)

rewrite71.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

70× egg-rr

Counts

4 → 70

Calls

2 calls:

69.0ms

((*.f64 (pow.f64 l 3) (*.f64 (cos.f64 (*.f64 1/2 K)) J)) (*.f64 1/3 (*.f64 (pow.f64 l 3) (*.f64 (cos.f64 (*.f64 1/2 K)) J))) (*.f64 (cos.f64 (*.f64 1/2 K)) J) (*.f64 l (*.f64 (cos.f64 (*.f64 1/2 K)) J)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
1	289	54
2	3227	54
3	5480	54
0	0	0
1	0	0

simplify58.0ms (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

134 → 107

Iterations

Useful iterations: 2 (0.0ms)

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

prune164.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Error

0.0b

Counts

138 → 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)))
▶	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))
	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 (pow.f64 (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) 3)) 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))
	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)

Compiler

Compiled 4490 to 3279 computations (27% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series65.0ms (0.7%)

Counts

3 → 64

Calls

3 calls:

54.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
8.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
3.0ms	(*.f64 1/3 (pow.f64 l 3))

rewrite113.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

51× egg-rr

Counts

3 → 51

Calls

2 calls:

112.0ms	((.f64 1/3 (pow.f64 l 3)) (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) U))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	324	39
2	3431	39
3	4911	39
4	4970	39
5	4874	39
0	0	0
1	0	0

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
584×	`associate-l_binary64`
517×	`associate-r_binary64`
418×	`sub-neg_binary64`
352×	`cancel-sign-sub-inv_binary64`

Counts

115 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	1726
1	263	1469
2	948	1292
3	4423	1292
4	4898	1292
5	5000	1292

prune114.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	81	7	88

Error

Counts

88 → 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)))
✓	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))
	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 (pow.f64 (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) 3)) U))
	36.0b	(/.f64 (+.f64 (pow.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) 3) (pow.f64 U 3)) (fma.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) (-.f64 (.f64 U U) (.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) U))))
	0.6b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) 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)

Compiler

Compiled 2348 to 1672 computations (28.8% 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)))

series169.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

123.0ms	(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)
38.0ms	(.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
4.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
3.0ms	(*.f64 1/60 (pow.f64 l 5))

rewrite75.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

76× egg-rr

Counts

4 → 76

Calls

2 calls:

73.0ms

((fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))) (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) (*.f64 1/60 (pow.f64 l 5)) (*.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	72
1	399	72
2	4277	72
3	5264	72
0	0	0
1	0	0

simplify82.0ms (0.8%)

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

160 → 117

Iterations

Useful iterations: 2 (0.0ms)

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

prune192.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	117	7	124

Error

Counts

124 → 7

Alt Table

Status	Error	Program
	0.6b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
	10.0b	(fma.f64 (cbrt.f64 (pow.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)
	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)))
✓	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))
	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))
	36.0b	(/.f64 (+.f64 (pow.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) 3) (pow.f64 U 3)) (fma.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) (-.f64 (.f64 U U) (.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (.f64 1/3 (pow.f64 l 3)))) 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)

Compiler

Compiled 3620 to 2645 computations (26.9% saved)

regimes859.0ms (8.9%)

Accuracy

Total 0.2b remaining (53.1%)

Threshold costs 0.2b (53.1%)

Counts

66 → 1

Compiler

Compiled 17648 to 13396 computations (24.1% 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

end207.0ms (2.1%)

Compiler: Compiled 305 to 224 computations (26.6% saved)

Iter	Nodes	Cost
0	14	18
1	295	18
2	33	18
0	6	6
1	130	6
2	71	6
0	8	9
1	169	9
2	73	9
0	14	18
1	295	18
2	33	18
0	0	0
1	0	0

Iter	Nodes	Cost
0	14	18
1	295	18
2	33	18
0	6	6
1	130	6
2	71	6
0	8	9
1	169	9
2	73	9
0	14	18
1	295	18
2	33	18
0	0	0
1	0	0

Details

analyze1.6s (16.8%)

sample5.3s (54.7%)

simplify66.0ms (0.7%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series48.0ms (0.5%)

rewrite76.0ms (0.8%)

simplify111.0ms (1.1%)

prune49.0ms (0.5%)

localize13.0ms (0.1%)

series102.0ms (1.1%)

rewrite71.0ms (0.7%)

simplify58.0ms (0.6%)

prune164.0ms (1.7%)

localize12.0ms (0.1%)

series65.0ms (0.7%)

rewrite113.0ms (1.2%)

simplify85.0ms (0.9%)

prune114.0ms (1.2%)

localize14.0ms (0.1%)

series169.0ms (1.7%)

rewrite75.0ms (0.8%)

simplify82.0ms (0.8%)

prune192.0ms (2%)

regimes859.0ms (8.9%)

simplify2.0ms (0%)

end207.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	14	18
1	295	18
2	33	18
0	6	6
1	130	6
2	71	6
0	8	9
1	169	9
2	73	9
0	14	18
1	295	18
2	33	18
0	0	0
1	0	0