Details

analyze645.0ms (9.1%)

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)

sample187.0ms (2.6%)

Algorithm

1×

intervals

Results

32.0ms	60×	body	1024	valid
25.0ms	56×	body	1024	invalid
12.0ms	145×	body	128	valid
11.0ms	113×	body	128	invalid
9.0ms	32×	body	512	valid
7.0ms	29×	body	512	invalid
3.0ms	18×	body	256	valid
2.0ms	9×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify67.0ms (0.9%)

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

16.8b

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)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	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)
✓	6.8b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series49.0ms (0.7%)

Counts

4 → 92

Calls

4 calls:

35.0ms	(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))

rewrite22.0ms (0.3%)

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)))
2.0ms	(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)

simplify150.0ms (2.1%)

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

prune162.0ms (2.3%)

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
	16.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (expm1.f64 (log1p.f64 (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 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 4868 to 1839 computations (62.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series97.0ms (1.4%)

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

simplify112.0ms (1.6%)

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

prune102.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
	40.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U) (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (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)
	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (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)
	22.5b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

Compiler

Compiled 2373 to 1453 computations (38.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series265.0ms (3.7%)

Counts

3 → 72

Calls

3 calls:

201.0ms	(log1p.f64 (cos.f64 (/.f64 K 2)))
62.0ms	(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))))

simplify99.0ms (1.4%)

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

prune104.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	112	5	117

Error

Counts

117 → 5

Alt Table

Status	Error	Program
	40.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U) (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (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)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (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)
	22.5b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

Compiler

Compiled 2538 to 1635 computations (35.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series67.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

62.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
3.0ms	(exp.f64 (cos.f64 (/.f64 K 2)))
2.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 K 2))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`exp-prod_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

3 → 40

Calls

3 calls:

2.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 K 2))))
2.0ms	(exp.f64 (cos.f64 (/.f64 K 2)))
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)

simplify126.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
465×	`sub-neg_binary64`
452×	`associate-l_binary64`
361×	`associate-r_binary64`
291×	`distribute-rgt-neg-in_binary64`

Counts

112 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2332
1	407	2237
2	1214	1979
3	4124	1979
4	4983	1979
5	4999	1979
6	4953	1979

prune118.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	126	5	131

Error

Counts

131 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (*.f64 (sqrt.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (exp.f64 (cos.f64 (/.f64 K 2)))))) U)
	40.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U) (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (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)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 K 2)))) U)

Compiler

Compiled 2753 to 1787 computations (35.1% saved)

regimes552.0ms (7.8%)

Accuracy

Total 0.0b remaining (61.5%)

Threshold costs 0.0b (61.5%)

Counts

50 → 1

Compiler

Compiled 11173 to 8331 computations (25.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	16	18
2	16	18

end1.0ms (0%)

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

sample4.1s (57.8%)

Algorithm

1×

intervals

Results

885.0ms	2099×	body	1024	invalid
884.0ms	1634×	body	1024	valid
411.0ms	4483×	body	128	valid
344.0ms	1159×	body	512	valid
317.0ms	3577×	body	128	invalid
268.0ms	982×	body	512	invalid
119.0ms	669×	body	256	valid
93.0ms	497×	body	256	invalid
50.0ms	55×	body	2048	valid

Compiler

Compiled 165 to 124 computations (24.8% saved)

Details

analyze645.0ms (9.1%)

sample187.0ms (2.6%)

simplify67.0ms (0.9%)

prune3.0ms (0%)

localize11.0ms (0.2%)

series49.0ms (0.7%)

rewrite22.0ms (0.3%)

simplify150.0ms (2.1%)

prune162.0ms (2.3%)

localize9.0ms (0.1%)

series97.0ms (1.4%)

rewrite7.0ms (0.1%)

simplify112.0ms (1.6%)

prune102.0ms (1.4%)

localize12.0ms (0.2%)

series265.0ms (3.7%)

rewrite2.0ms (0%)

simplify99.0ms (1.4%)

prune104.0ms (1.5%)

localize13.0ms (0.2%)

series67.0ms (0.9%)

rewrite6.0ms (0.1%)

simplify126.0ms (1.8%)

prune118.0ms (1.7%)

regimes552.0ms (7.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.1s (57.8%)

Profiling