Details

analyze1.5s (16.5%)

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 (59.4%)

Results

1.3s	1664×	body	1024	valid
1.3s	1974×	body	1024	invalid
791.0ms	4603×	body	128	valid
556.0ms	1208×	body	512	valid
459.0ms	983×	body	512	invalid
438.0ms	2616×	body	128	invalid
217.0ms	729×	body	256	valid
148.0ms	490×	body	256	invalid
58.0ms	52×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify64.0ms (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

16.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.7b	(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 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 (/.f64 K 2))
✓	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))))
✓	7.1b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series51.0ms (0.6%)

Counts

4 → 92

Calls

4 calls:

37.0ms	(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)))
2.0ms	(cos.f64 (/.f64 K 2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 101

Calls

4 calls:

8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
1.0ms	(cos.f64 (/.f64 K 2))
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify149.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

389×	`cancel-sign-sub-inv_binary64`
374×	`times-frac_binary64`
349×	`fma-neg_binary64`
286×	`associate-l_binary64`
282×	`associate-r_binary64`

Counts

193 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	4156
1	609	3446
2	2164	3222
3	4416	3222
4	4806	3222
5	4942	3222

prune144.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	3	188

Error

0.0b

Counts

188 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	0.3b	(fma.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (.f64 2 (.f64 l J))) (cos.f64 (/.f64 K 2)) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 4874 to 1843 computations (62.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series98.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

63.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
26.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
9.0ms	(sinh.f64 l)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 41

Calls

3 calls:

4.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
1.0ms	(sinh.f64 l)
1.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify106.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
581×	`fma-neg_binary64`
432×	`*-commutative_binary64`
278×	`associate-+l+_binary64`
224×	`associate--l+_binary64`

Counts

125 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2596
1	465	2480
2	1467	2171
3	4147	2171
4	4936	2171
5	4957	2171

prune115.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	104	6	110

Error

Counts

110 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (.f64 2 (.f64 l J))) (cos.f64 (/.f64 K 2)) U)
	8.8b	(fma.f64 (.f64 J (.f64 2 (cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 2369 to 1451 computations (38.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2)))) U)
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(log1p.f64 (cos.f64 (/.f64 K 2)))

series269.0ms (3%)

Counts

3 → 72

Calls

3 calls:

202.0ms	(log1p.f64 (cos.f64 (/.f64 K 2)))
64.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2)))) U)
2.0ms	(expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`expm1-log1p-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms	(log1p.f64 (cos.f64 (/.f64 K 2)))
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2)))) U)
0.0ms	(expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2))))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

937×	`fma-neg_binary64`
612×	`fma-def_binary64`
418×	`associate-l_binary64`
331×	`associate-r_binary64`
248×	`associate-+l+_binary64`

Counts

104 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2201
1	392	2113
2	1161	1861
3	3982	1861
4	4979	1861
5	4983	1861

prune132.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	124	6	130

Error

Counts

130 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (.f64 2 (.f64 l J))) (cos.f64 (/.f64 K 2)) U)
	8.8b	(fma.f64 (.f64 J (.f64 2 (cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2)))) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 2792 to 1787 computations (36% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2)))) U)
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2))))
✓	0.7b	(expm1.f64 (cos.f64 (/.f64 K 2)))

series68.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

63.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2)))) U)
3.0ms	(expm1.f64 (cos.f64 (/.f64 K 2)))
2.0ms	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log1p-expm1-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms	(expm1.f64 (cos.f64 (/.f64 K 2)))
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2)))) U)
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2))))

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-def_binary64`
521×	`sub-neg_binary64`
449×	`associate-l_binary64`
356×	`associate-r_binary64`
278×	`cancel-sign-sub-inv_binary64`

Counts

104 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2233
1	406	2135
2	1233	1879
3	4288	1879
4	4828	1879
5	4977	1879

prune133.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	125	6	131

Error

Counts

131 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (.f64 2 (.f64 l J))) (cos.f64 (/.f64 K 2)) U)
	8.8b	(fma.f64 (.f64 J (.f64 2 (cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2)))) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 2732 to 1734 computations (36.5% saved)

regimes485.0ms (5.4%)

Accuracy

Total 0.0b remaining (56.3%)

Threshold costs 0.0b (56.3%)

Counts

50 → 1

Compiler

Compiled 9701 to 7226 computations (25.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	17	20
2	17	20

end103.0ms (1.1%)

Compiler: Compiled 149 to 111 computations (25.5% saved)

Details

analyze1.5s (16.5%)

sample5.4s (59.4%)

simplify64.0ms (0.7%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series51.0ms (0.6%)

rewrite20.0ms (0.2%)

simplify149.0ms (1.6%)

prune144.0ms (1.6%)

localize10.0ms (0.1%)

series98.0ms (1.1%)

rewrite7.0ms (0.1%)

simplify106.0ms (1.2%)

prune115.0ms (1.3%)

localize12.0ms (0.1%)

series269.0ms (3%)

rewrite2.0ms (0%)

simplify91.0ms (1%)

prune132.0ms (1.5%)

localize14.0ms (0.1%)

series68.0ms (0.8%)

rewrite2.0ms (0%)

simplify93.0ms (1%)

prune133.0ms (1.5%)

regimes485.0ms (5.4%)

simplify2.0ms (0%)

end103.0ms (1.1%)

Profiling