Details

analyze1.4s (11.3%)

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)

sample6.5s (52.7%)

Results

1.7s	1718×	body	1024	valid
1.5s	2045×	body	1024	invalid
962.0ms	4617×	body	128	valid
591.0ms	1151×	body	512	valid
548.0ms	1047×	body	512	invalid
518.0ms	2632×	body	128	invalid
377.0ms	705×	body	256	valid
161.0ms	490×	body	256	invalid
86.0ms	65×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify71.0ms (0.6%)

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

prune6.0ms (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

16.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.8b	(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)

localize26.0ms (0.2%)

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))))
✓	6.4b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series107.0ms (0.9%)

Counts

3 → 80

Calls

3 calls:

87.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
16.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
3.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite32.0ms (0.3%)

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:

14.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
7.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
1.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify287.0ms (2.3%)

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

prune259.0ms (2.1%)

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
	0.3b	(+.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)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4507 to 1677 computations (62.8% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

series171.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

108.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
45.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
17.0ms	(sinh.f64 l)

rewrite11.0ms (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:

7.0ms	(.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)

simplify171.0ms (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

prune157.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Error

Counts

91 → 4

Alt Table

Status	Error	Program
▶	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)
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2033 to 1221 computations (39.9% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(.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)))))
✓	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)))

series178.0ms (1.4%)

Counts

4 → 64

Calls

4 calls:

144.0ms	(.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)))))
21.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
7.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
6.0ms	(*.f64 1/60 (pow.f64 l 5))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`

Counts

4 → 79

Calls

4 calls:

8.0ms	(.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)))))
7.0ms	(*.f64 1/60 (pow.f64 l 5))
6.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
1.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

simplify196.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
572×	`distribute-lft-in_binary64`
436×	`cancel-sign-sub-inv_binary64`
328×	`associate-r_binary64`
314×	`associate-l_binary64`

Counts

143 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3721
1	566	2949
2	2106	2900
3	5374	2900

prune339.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
✓	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)
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
▶	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4436 to 3261 computations (26.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
✓	0.5b	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
✓	0.6b	(cbrt.f64 J)

series505.0ms (4.1%)

Counts

4 → 72

Calls

4 calls:

296.0ms	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
72.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
71.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
65.0ms	(cbrt.f64 J)

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 110

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
10.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
8.0ms	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
1.0ms	(cbrt.f64 J)

simplify219.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

479×	`fma-def_binary64`
377×	`unswap-sqr_binary64`
304×	`associate-r_binary64`
286×	`associate-l_binary64`
250×	`exp-prod_binary64`

Counts

182 → 166

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	2350
1	367	2086
2	1519	2014
3	3400	1787
4	4552	1775
5	4959	1775
6	5000	1775
7	4898	1775

prune337.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	204	4	208

Error

Counts

208 → 4

Alt Table

Status	Error	Program
✓	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)
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
✓	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4990 to 2406 computations (51.8% saved)

regimes1.1s (8.6%)

Accuracy

Total 0.1b remaining (64.8%)

Threshold costs 0.1b (64.8%)

Counts

54 → 1

Compiler

Compiled 11899 to 8699 computations (26.9% saved)

simplify3.0ms (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

end168.0ms (1.4%)

Compiler: Compiled 142 to 102 computations (28.2% saved)

Details

analyze1.4s (11.3%)

sample6.5s (52.7%)

simplify71.0ms (0.6%)

prune6.0ms (0%)

localize26.0ms (0.2%)

series107.0ms (0.9%)

rewrite32.0ms (0.3%)

simplify287.0ms (2.3%)

prune259.0ms (2.1%)

localize18.0ms (0.1%)

series171.0ms (1.4%)

rewrite11.0ms (0.1%)

simplify171.0ms (1.4%)

prune157.0ms (1.3%)

localize33.0ms (0.3%)

series178.0ms (1.4%)

rewrite33.0ms (0.3%)

simplify196.0ms (1.6%)

prune339.0ms (2.7%)

localize23.0ms (0.2%)

series505.0ms (4.1%)

rewrite54.0ms (0.4%)

simplify219.0ms (1.8%)

prune337.0ms (2.7%)

regimes1.1s (8.6%)

simplify3.0ms (0%)

end168.0ms (1.4%)

Profiling