Details

analyze1.5s (16.6%)

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)

sample5.2s (58.7%)

Results

1.3s	1697×	body	1024	valid
1.2s	1911×	body	1024	invalid
783.0ms	4651×	body	128	valid
536.0ms	1179×	body	512	valid
463.0ms	2716×	body	128	invalid
426.0ms	1021×	body	512	invalid
210.0ms	670×	body	256	valid
144.0ms	471×	body	256	invalid
78.0ms	59×	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

17.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.1b	(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)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	6.1b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series50.0ms (0.6%)

Counts

3 → 80

Calls

3 calls:

36.0ms	(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)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
27×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

7.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify184.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

374×	`times-frac_binary64`
336×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
281×	`associate-r_binary64`
279×	`associate-l_binary64`

Counts

172 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	3960
1	572	3266
2	2075	3044
3	4373	3044
4	4843	3044
5	4992	3044
6	4994	3044
7	4848	3044

prune173.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	2	170

Error

0.0b

Counts

170 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	0.3b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)

Compiler

Compiled 4507 to 1677 computations (62.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series95.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

61.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
27.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
8.0ms	(sinh.f64 l)

rewrite6.0ms (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)
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify125.0ms (1.4%)

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

prune73.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Error

0.0b

Counts

91 → 5

Alt Table

Status	Error	Program
	35.3b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
▶	0.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	9.5b	(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)
	22.6b	(fma.f64 (.f64 (sqrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (sqrt.f64 (.f64 J (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2023 to 1213 computations (40% 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 l 2 (*.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))

series74.0ms (0.8%)

Counts

3 → 64

Calls

3 calls:

59.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
11.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
3.0ms	(*.f64 1/3 (pow.f64 l 3))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
10×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 63

Calls

3 calls:

6.0ms	(*.f64 1/3 (pow.f64 l 3))
3.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
0.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)

simplify86.0ms (1%)

Algorithm

1×	egg-herbie

Rules

977×	`fma-neg_binary64`
746×	`fma-def_binary64`
366×	`cancel-sign-sub-inv_binary64`
307×	`associate-+l+_binary64`
295×	`associate--l+_binary64`

Counts

127 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	2683
1	428	2151
2	1489	2101
3	4454	2096
4	5277	2096

prune133.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	118	5	123

Error

Counts

123 → 5

Alt Table

Status	Error	Program
	35.3b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	22.6b	(fma.f64 (.f64 (sqrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (sqrt.f64 (.f64 J (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
▶	0.6b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)

Compiler

Compiled 2928 to 2043 computations (30.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K))))
✓	0.5b	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
✓	0.6b	(cbrt.f64 J)

series274.0ms (3.1%)

Counts

4 → 72

Calls

4 calls:

183.0ms	(.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))
36.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
34.0ms	(cbrt.f64 J)
22.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K))))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K))))
4.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
4.0ms	(.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))
1.0ms	(cbrt.f64 J)

simplify144.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
457×	`*-commutative_binary64`
421×	`cancel-sign-sub-inv_binary64`
385×	`unswap-sqr_binary64`
323×	`sub-neg_binary64`

Counts

175 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1945
1	299	1727
2	1130	1668
3	2242	1652
4	4280	1554
5	4570	1554
6	4885	1554
7	4873	1554

prune176.0ms (2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	187	5	192

Error

Counts

192 → 5

Alt Table

Status	Error	Program
	35.3b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	22.6b	(fma.f64 (.f64 (sqrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (sqrt.f64 (.f64 J (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.6b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)

Compiler

Compiled 5279 to 2957 computations (44% saved)

regimes340.0ms (3.8%)

Accuracy

Total 0.0b remaining (46.4%)

Threshold costs 0.0b (46.4%)

Counts

33 → 1

Compiler

Compiled 6499 to 4729 computations (27.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	14	18
2	14	18

end98.0ms (1.1%)

Compiler: Compiled 141 to 101 computations (28.4% saved)

Details

analyze1.5s (16.6%)

sample5.2s (58.7%)

simplify66.0ms (0.7%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series50.0ms (0.6%)

rewrite17.0ms (0.2%)

simplify184.0ms (2.1%)

prune173.0ms (1.9%)

localize9.0ms (0.1%)

series95.0ms (1.1%)

rewrite6.0ms (0.1%)

simplify125.0ms (1.4%)

prune73.0ms (0.8%)

localize12.0ms (0.1%)

series74.0ms (0.8%)

rewrite12.0ms (0.1%)

simplify86.0ms (1%)

prune133.0ms (1.5%)

localize15.0ms (0.2%)

series274.0ms (3.1%)

rewrite23.0ms (0.3%)

simplify144.0ms (1.6%)

prune176.0ms (2%)

regimes340.0ms (3.8%)

simplify2.0ms (0%)

end98.0ms (1.1%)

Profiling