Details

analyze676.0ms (8.8%)

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)

sample139.0ms (1.8%)

Algorithm

1×

intervals

Results

35.0ms	65×	body	1024	valid
32.0ms	76×	body	1024	invalid
12.0ms	126×	body	128	invalid
11.0ms	41×	body	512	valid
11.0ms	128×	body	128	valid
8.0ms	35×	body	512	invalid
4.0ms	21×	body	256	valid
3.0ms	18×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify69.0ms (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

19.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.1b	(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)

localize11.0ms (0.1%)

Local error

Found 2 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)
✓	6.2b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series43.0ms (0.6%)

Counts

2 → 56

Calls

2 calls:

40.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

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)

simplify134.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

447×	`sub-neg_binary64`
374×	`cancel-sign-sub-inv_binary64`
282×	`associate-+l+_binary64`
269×	`times-frac_binary64`
242×	`associate--l+_binary64`

Counts

97 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2515
1	456	2012
2	1638	1922
3	4312	1922
4	4861	1922
5	4993	1922
6	4843	1922

prune74.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Error

0.0b

Counts

94 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	19.1b	(fma.f64 (*.f64 J (fma.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 l)) (neg.f64 (exp.f64 (neg.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 2425 to 1065 computations (56.1% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series76.0ms (1%)

Counts

2 → 60

Calls

2 calls:

67.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
9.0ms	(sinh.f64 l)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

1.0ms	(sinh.f64 l)
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-neg_binary64`
564×	`fma-def_binary64`
390×	`associate-l_binary64`
389×	`sub-neg_binary64`
319×	`associate-r_binary64`

Counts

80 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	1972
1	348	1907
2	1075	1647
3	3681	1619
4	4845	1619
5	4950	1619

prune68.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	62	6	68

Error

0.0b

Counts

68 → 6

Alt Table

Status	Error	Program
	32.0b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	0.4b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	1.4b	(.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)))
	38.0b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 2 (sinh.f64 l)) (.f64 J (cos.f64 (/.f64 K 2))) U) 3))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
▶	0.1b	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (*.f64 J (cos.f64 (/.f64 K 2))))) U)

Compiler

Compiled 1664 to 1009 computations (39.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series184.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

67.0ms	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (*.f64 J (cos.f64 (/.f64 K 2))))) U)
58.0ms	(.f64 2 (.f64 (sinh.f64 l) (*.f64 J (cos.f64 (/.f64 K 2)))))
50.0ms	(.f64 (sinh.f64 l) (.f64 J (cos.f64 (/.f64 K 2))))
9.0ms	(*.f64 J (cos.f64 (/.f64 K 2)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
20×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`

Counts

4 → 79

Calls

4 calls:

6.0ms	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (*.f64 J (cos.f64 (/.f64 K 2))))) U)
6.0ms	(.f64 2 (.f64 (sinh.f64 l) (*.f64 J (cos.f64 (/.f64 K 2)))))
4.0ms	(.f64 (sinh.f64 l) (.f64 J (cos.f64 (/.f64 K 2))))
3.0ms	(*.f64 J (cos.f64 (/.f64 K 2)))

simplify151.0ms (2%)

Algorithm

1×	egg-herbie

Rules

576×	`cancel-sign-sub-inv_binary64`
480×	`fma-neg_binary64`
379×	`associate-r_binary64`
280×	`associate-l_binary64`
267×	`fma-def_binary64`

Counts

223 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	301	5411
1	795	5137
2	2883	4848
3	4335	4842
4	4965	4842

prune183.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	38.0b	(cbrt.f64 (pow.f64 (fma.f64 2 (.f64 (.f64 J (cos.f64 (/.f64 K 2))) (sinh.f64 l)) U) 3))
	23.7b	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (cbrt.f64 (pow.f64 (*.f64 J (cos.f64 (/.f64 K 2))) 3)))) U)
▶	0.4b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	1.4b	(.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)))
✓	0.1b	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (*.f64 J (cos.f64 (/.f64 K 2))))) U)
	0.4b	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (*.f64 (cbrt.f64 J) (cos.f64 (/.f64 K 2)))))) U)

Compiler

Compiled 4700 to 2872 computations (38.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series851.0ms (11%)

Counts

4 → 84

Calls

4 calls:

456.0ms	(*.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l)))
322.0ms	(cbrt.f64 (sinh.f64 l))
64.0ms	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
9.0ms	(.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
17×	`cbrt-div_binary64`
17×	`sinh-def_binary64`

Counts

4 → 114

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))
5.0ms	(*.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l)))
1.0ms	(cbrt.f64 (sinh.f64 l))
0.0ms	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
550×	`fma-neg_binary64`
406×	`*-commutative_binary64`
294×	`associate-+l+_binary64`
235×	`associate--l+_binary64`

Counts

198 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	3668
1	592	3496
2	1706	3148
3	4554	3148
4	4992	3148

prune249.0ms (3.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	254	7	261

Error

Counts

261 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	38.0b	(cbrt.f64 (pow.f64 (fma.f64 2 (.f64 (.f64 J (cos.f64 (/.f64 K 2))) (sinh.f64 l)) U) 3))
	23.7b	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (cbrt.f64 (pow.f64 (*.f64 J (cos.f64 (/.f64 K 2))) 3)))) U)
✓	0.4b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	1.4b	(.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)))
✓	0.1b	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (*.f64 J (cos.f64 (/.f64 K 2))))) U)
	0.4b	(+.f64 (.f64 2 (.f64 (sinh.f64 l) (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (*.f64 (cbrt.f64 J) (cos.f64 (/.f64 K 2)))))) U)

Compiler

Compiled 6854 to 3238 computations (52.8% saved)

regimes490.0ms (6.3%)

Accuracy

Total 0.0b remaining (51.4%)

Threshold costs 0.0b (51.4%)

Counts

50 → 1

Compiler

Compiled 11137 to 8049 computations (27.7% 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

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample4.0s (52%)

Algorithm

1×

intervals

Results

915.0ms	1711×	body	1024	valid
822.0ms	2026×	body	1024	invalid
380.0ms	4396×	body	128	valid
330.0ms	1162×	body	512	valid
311.0ms	3478×	body	128	invalid
234.0ms	985×	body	512	invalid
127.0ms	674×	body	256	valid
109.0ms	516×	body	256	invalid
51.0ms	57×	body	2048	valid

Compiler

Compiled 207 to 150 computations (27.5% saved)

Details

analyze676.0ms (8.8%)

sample139.0ms (1.8%)

simplify69.0ms (0.9%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series43.0ms (0.6%)

rewrite7.0ms (0.1%)

simplify134.0ms (1.7%)

prune74.0ms (1%)

localize9.0ms (0.1%)

series76.0ms (1%)

rewrite2.0ms (0%)

simplify95.0ms (1.2%)

prune68.0ms (0.9%)

localize10.0ms (0.1%)

series184.0ms (2.4%)

rewrite25.0ms (0.3%)

simplify151.0ms (2%)

prune183.0ms (2.4%)

localize12.0ms (0.2%)

series851.0ms (11%)

rewrite22.0ms (0.3%)

simplify118.0ms (1.5%)

prune249.0ms (3.2%)

regimes490.0ms (6.3%)

simplify2.0ms (0%)

end1.0ms (0%)

sample4.0s (52%)

Profiling