Details

analyze656.0ms (6.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
49.9%	49.9%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
53%	46.8%	0.2%	8
57.7%	42.1%	0.2%	9
61.6%	38.2%	0.2%	10
63.5%	30%	6.4%	11
63.5%	30%	6.4%	12
67.6%	25.9%	6.4%	13
68.9%	24.7%	6.4%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample214.0ms (2.1%)

Algorithm

1×

intervals

Results

33.0ms	45×	body	1024	valid
29.0ms	61×	body	1024	invalid
20.0ms	51×	body	512	valid
12.0ms	129×	body	128	valid
11.0ms	120×	body	128	invalid
11.0ms	40×	body	512	invalid
5.0ms	29×	body	256	valid
2.0ms	12×	body	256	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify68.0ms (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

prune4.0ms (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)

localize13.0ms (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))))
✓	4.6b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series53.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

40.0ms	(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))))
3.0ms	(-.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)

simplify197.0ms (1.9%)

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

prune139.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	3	170

Error

0.0b

Counts

170 → 3

Alt Table

Status	Error	Program
	16.9b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (*.f64 (cbrt.f64 J) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	1.0b	(+.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 4557 to 1709 computations (62.5% saved)

localize10.0ms (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)))
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

series106.0ms (1%)

Counts

3 → 84

Calls

3 calls:

65.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
29.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
12.0ms	(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)
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify114.0ms (1.1%)

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

prune82.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	87	5	92

Error

0.0b

Counts

92 → 5

Alt Table

Status	Error	Program
	1.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
✓	0.1b	(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)
	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	32.1b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

Compiler

Compiled 2059 to 1239 computations (39.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)

series315.0ms (3.1%)

Counts

4 → 72

Calls

4 calls:

197.0ms	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
44.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
40.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
34.0ms	(cbrt.f64 J)

rewrite30.0ms (0.3%)

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:

14.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
5.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
5.0ms	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
1.0ms	(cbrt.f64 J)

simplify147.0ms (1.4%)

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	2038
2	1519	1958
3	3400	1731
4	4552	1719
5	4959	1719
6	5000	1719
7	4898	1719

prune212.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	203	6	209

Error

0.0b

Counts

209 → 6

Alt Table

Status	Error	Program
	1.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	0.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J))) (cbrt.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)
✓	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)
▶	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	32.1b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

Compiler

Compiled 5132 to 2511 computations (51.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (*.f64 2 (sinh.f64 l)))))
✓	11.1b	(cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))

series2.3s (22.5%)

Counts

4 → 120

Calls

4 calls:

1.3s	(.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (*.f64 2 (sinh.f64 l)))))
822.0ms	(cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))
114.0ms	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
60.0ms	(.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`associate-*r/_binary64`
30×	`pow1_binary64`
17×	`cbrt-div_binary64`
17×	`sinh-def_binary64`
16×	`pow1/3_binary64`

Counts

4 → 100

Calls

4 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))))
5.0ms	(.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (*.f64 2 (sinh.f64 l)))))
3.0ms	(cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))
0.0ms	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)

simplify161.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

556×	`fma-neg_binary64`
274×	`associate-r_binary64`
269×	`associate-l_binary64`
248×	`associate--l+_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

220 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	5712
1	772	5254
2	2323	4642
3	4851	4642
4	5268	4642

prune303.0ms (3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	254	6	260

Error

0.0b

Counts

260 → 6

Alt Table

Status	Error	Program
	1.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	0.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J))) (cbrt.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)
✓	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)
✓	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	32.1b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

Compiler

Compiled 9094 to 5866 computations (35.5% saved)

regimes782.0ms (7.7%)

Accuracy

Total 0.0b remaining (62.4%)

Threshold costs 0.0b (62.4%)

Counts

75 → 1

Compiler

Compiled 19263 to 12739 computations (33.9% 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

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample4.2s (41.4%)

Algorithm

1×

intervals

Results

938.0ms	1606×	body	1024	valid
877.0ms	1895×	body	1024	invalid
413.0ms	4416×	body	128	valid
399.0ms	1220×	body	512	valid
332.0ms	3377×	body	128	invalid
267.0ms	958×	body	512	invalid
128.0ms	692×	body	256	valid
97.0ms	515×	body	256	invalid
54.0ms	66×	body	2048	valid

Compiler

Compiled 194 to 136 computations (29.9% saved)

Details

analyze656.0ms (6.4%)

sample214.0ms (2.1%)

simplify68.0ms (0.7%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series53.0ms (0.5%)

rewrite17.0ms (0.2%)

simplify197.0ms (1.9%)

prune139.0ms (1.4%)

localize10.0ms (0.1%)

series106.0ms (1%)

rewrite7.0ms (0.1%)

simplify114.0ms (1.1%)

prune82.0ms (0.8%)

localize15.0ms (0.2%)

series315.0ms (3.1%)

rewrite30.0ms (0.3%)

simplify147.0ms (1.4%)

prune212.0ms (2.1%)

localize13.0ms (0.1%)

series2.3s (22.5%)

rewrite27.0ms (0.3%)

simplify161.0ms (1.6%)

prune303.0ms (3%)

regimes782.0ms (7.7%)

simplify2.0ms (0%)

end1.0ms (0%)

sample4.2s (41.4%)

Profiling