Details

analyze1.4s (12.2%)

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)

sample5.4s (47.3%)

Results

1.3s	1710×	body	1024	valid
1.2s	1930×	body	1024	invalid
754.0ms	4571×	body	128	valid
686.0ms	1225×	body	512	valid
466.0ms	2627×	body	128	invalid
415.0ms	1048×	body	512	invalid
210.0ms	689×	body	256	valid
183.0ms	477×	body	256	invalid
70.0ms	61×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

448×	`fma-neg_binary64`
331×	`fma-def_binary64`
267×	`rules-11_binary64`
252×	`rules-40_binary64`
252×	`rules-42_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	85	22
2	263	22
3	996	22
4	98	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

18.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.5b	(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))))
✓	5.6b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series86.0ms (0.8%)

Counts

3 → 80

Calls

3 calls:

75.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
9.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite113.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`prod-diff_binary64`
260×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`
135×	`expm1-log1p-u_binary64`

Counts

3 → 260

Calls

3 calls:

106.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
106.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
106.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	323	33
2	4123	33
3	5451	33
0	0	0
1	0	0

simplify176.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

603×	`rules-21_binary64`
393×	`fma-def_binary64`
324×	`fma-neg_binary64`
284×	`rules-13_binary64`
263×	`rules-20_binary64`

Counts

340 → 305

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2030
1	902	1646
2	4586	1642
3	4635	1642
4	4998	1642
5	4880	1642

prune334.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	300	5	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	5	306

Error

0.0b

Counts

306 → 5

Alt Table

Status	Error	Program
	39.1b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2)) U) 3))
▶	0.1b	(fma.f64 (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) (cos.f64 (/.f64 K 2)) U)
	37.4b	(.f64 (sqrt.f64 U) (+.f64 (sqrt.f64 U) (/.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2))) (sqrt.f64 U))))
	0.3b	(+.f64 (fma.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))) U) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))
	30.4b	(fma.f64 (+.f64 (fma.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l))) (neg.f64 (.f64 0 J))) (fma.f64 0 J (.f64 0 J))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 9398 to 3959 computations (57.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 l)
✓	0.1b	(fma.f64 (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J))

series95.0ms (0.8%)

Counts

3 → 84

Calls

3 calls:

60.0ms	(fma.f64 (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) (cos.f64 (/.f64 K 2)) U)
24.0ms	(/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J))
9.0ms	(sinh.f64 l)

rewrite76.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

408×	`prod-diff_binary64`
244×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
131×	`egg-rr`
127×	`log1p-expm1-u_binary64`

Counts

3 → 131

Calls

3 calls:

74.0ms	(sinh.f64 l)
73.0ms	(fma.f64 (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) (cos.f64 (/.f64 K 2)) U)
73.0ms	(/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	317	30
2	3810	30
3	5041	30
0	0	0
1	0	0

simplify151.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

594×	`rules-21_binary64`
341×	`fma-def_binary64`
276×	`fma-neg_binary64`
259×	`rules-13_binary64`
258×	`rules-7-rev_binary64`

Counts

215 → 176

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	141	1996
1	879	1812
2	4334	1812
3	4895	1812
4	4952	1812
5	4998	1812
6	4858	1812

prune194.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	176	5	181

Error

0.0b

Counts

181 → 5

Alt Table

Status	Error	Program
	39.1b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.1b	(fma.f64 (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) (cos.f64 (/.f64 K 2)) U)
	37.4b	(.f64 (sqrt.f64 U) (+.f64 (sqrt.f64 U) (/.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2))) (sqrt.f64 U))))
▶	0.3b	(+.f64 (fma.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))) U) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))
	30.4b	(fma.f64 (+.f64 (fma.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l))) (neg.f64 (.f64 0 J))) (fma.f64 0 J (.f64 0 J))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 3864 to 2483 computations (35.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
✓	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
✓	3.9b	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))

series111.0ms (1%)

Counts

4 → 76

Calls

4 calls:

79.0ms	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))
19.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
9.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
4.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

rewrite120.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

534×	`prod-diff_binary64`
243×	`egg-rr`
176×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`

Counts

4 → 243

Calls

4 calls:

114.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
114.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
114.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
114.0ms	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (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	18	60
1	421	60
2	4900	60
3	5746	60
0	0	0
1	0	0

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

929×	`rules-42_binary64`
929×	`rules-43_binary64`
307×	`fma-neg_binary64`
243×	`rules-20_binary64`
222×	`fma-def_binary64`

Counts

319 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	102	1802
1	739	1536
2	3675	1536
3	4891	1536

prune528.0ms (4.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	348	1	349
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	348	6	354

Error

Counts

354 → 6

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (fma.f64 2 (/.f64 l (/.f64 1 (.f64 J (cos.f64 (.f64 1/2 K))))) U) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
	30.4b	(fma.f64 (+.f64 (fma.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l))) (neg.f64 (.f64 0 J))) (fma.f64 0 J (.f64 0 J))) (cos.f64 (/.f64 K 2)) U)
	39.1b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.1b	(fma.f64 (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) (cos.f64 (/.f64 K 2)) U)
	37.4b	(.f64 (sqrt.f64 U) (+.f64 (sqrt.f64 U) (/.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2))) (sqrt.f64 U))))
✓	0.3b	(+.f64 (fma.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))) U) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))

Compiler

Compiled 15517 to 11578 computations (25.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
✓	0.2b	(/.f64 l (/.f64 1 (.f64 J (cos.f64 (.f64 1/2 K)))))
	3.9b	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))

series19.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

19.0ms

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

rewrite94.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

879×	`fma-neg_binary64`
369×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`

Counts

1 → 81

Calls

1 calls:

92.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	12
1	246	12
2	2936	12
3	4961	12
4	4939	12
0	0	0
1	0	0

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-neg_binary64`
527×	`rules-21_binary64`
488×	`rules-11_binary64`
289×	`fma-def_binary64`
221×	`rules-40_binary64`

Counts

117 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	484
1	216	478
2	936	463
3	4746	462
4	4626	462
5	4991	462

prune587.0ms (5.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	357	0	357
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	357	6	363

Error

Counts

363 → 6

Alt Table

Status	Error	Program
✓	0.4b	(+.f64 (fma.f64 2 (/.f64 l (/.f64 1 (.f64 J (cos.f64 (.f64 1/2 K))))) U) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
	30.4b	(fma.f64 (+.f64 (fma.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l))) (neg.f64 (.f64 0 J))) (fma.f64 0 J (.f64 0 J))) (cos.f64 (/.f64 K 2)) U)
	39.1b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.1b	(fma.f64 (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) (cos.f64 (/.f64 K 2)) U)
	37.4b	(.f64 (sqrt.f64 U) (+.f64 (sqrt.f64 U) (/.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (cos.f64 (/.f64 K 2))) (sqrt.f64 U))))
✓	0.3b	(+.f64 (fma.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))) U) (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))

Compiler

Compiled 16028 to 12070 computations (24.7% saved)

regimes1.6s (13.7%)

Accuracy

Total 0.1b remaining (60.7%)

Threshold costs 0.1b (60.7%)

Counts

149 → 1

Compiler

Compiled 35177 to 26511 computations (24.6% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	14	21

end121.0ms (1.1%)

Compiler: Compiled 196 to 147 computations (25% saved)

Details

analyze1.4s (12.2%)

sample5.4s (47.3%)

simplify33.0ms (0.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series86.0ms (0.8%)

rewrite113.0ms (1%)

simplify176.0ms (1.5%)

prune334.0ms (2.9%)

localize10.0ms (0.1%)

series95.0ms (0.8%)

rewrite76.0ms (0.7%)

simplify151.0ms (1.3%)

prune194.0ms (1.7%)

localize17.0ms (0.1%)

series111.0ms (1%)

rewrite120.0ms (1.1%)

simplify75.0ms (0.7%)

prune528.0ms (4.6%)

localize18.0ms (0.2%)

series19.0ms (0.2%)

rewrite94.0ms (0.8%)

simplify83.0ms (0.7%)

prune587.0ms (5.1%)

regimes1.6s (13.7%)

simplify1.0ms (0%)

end121.0ms (1.1%)

Profiling