Details

analyze632.0ms (5.1%)

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)

sample194.0ms (1.6%)

Algorithm

1×

intervals

Results

34.0ms	53×	body	1024	valid
26.0ms	60×	body	1024	invalid
12.0ms	35×	body	512	invalid
12.0ms	140×	body	128	valid
9.0ms	34×	body	512	valid
9.0ms	108×	body	128	invalid
5.0ms	29×	body	256	valid
4.0ms	23×	body	256	invalid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify70.0ms (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

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

18.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.0b	(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 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 l)
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	7.4b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series40.0ms (0.3%)

Counts

3 → 60

Calls

3 calls:

35.0ms	(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)))
1.0ms	(exp.f64 l)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
1.0ms	(exp.f64 l)
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

114 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	2619
1	492	2114
2	1722	2023
3	4468	2023
4	4895	2023

prune91.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	2	116

Error

0.0b

Counts

116 → 2

Alt Table

Status	Error	Program
	0.3b	(+.f64 U (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2787 to 1242 computations (55.4% 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)

series71.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

63.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
8.0ms	(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)

simplify88.0ms (0.7%)

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

prune57.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	62	5	67

Error

0.0b

Counts

67 → 5

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
	34.5b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.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)))
	33.7b	(exp.f64 (log.f64 (fma.f64 (.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 1618 to 981 computations (39.4% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))
✓	0.0b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))

series67.0ms (0.5%)

Counts

3 → 76

Calls

3 calls:

54.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
10.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
3.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

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

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-def_binary64`
366×	`cancel-sign-sub-inv_binary64`
353×	`*-commutative_binary64`
352×	`sub-neg_binary64`
334×	`distribute-rgt-neg-in_binary64`

Counts

116 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	2609
1	351	2094
2	1262	2057
3	3893	2057
4	4829	2057
5	5024	2057

prune95.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	97	6	103

Error

Counts

103 → 6

Alt Table

Status	Error	Program
	43.6b	(.f64 (+.f64 (.f64 2 (.f64 l (cos.f64 (.f64 1/2 K)))) (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))) J)
✓	0.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
	34.5b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.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)))
	33.7b	(exp.f64 (log.f64 (fma.f64 (.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 2554 to 1799 computations (29.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series4.4s (35.6%)

Counts

3 → 144

Calls

3 calls:

3.0s

(*.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)))

1.3s

(cbrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))

65.0ms

(*.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)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

10.0ms

(*.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)))

4.0ms

(*.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)))

1.0ms

(cbrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))

simplify369.0ms (3%)

Algorithm

1×	egg-herbie

Rules

865×	`*-commutative_binary64`
626×	`associate-r_binary64`
334×	`fma-def_binary64`
282×	`associate-+r+_binary64`
166×	`sub-neg_binary64`

Counts

237 → 251

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1728	27004
1	4603	26557
2	5014	26557

prune1.2s (10%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	533	0	533
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	533	6	539

Error

Counts

539 → 6

Alt Table

Status	Error	Program
	43.6b	(.f64 (+.f64 (.f64 2 (.f64 l (cos.f64 (.f64 1/2 K)))) (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))) J)
✓	0.3b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
	34.5b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.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)))
	33.7b	(exp.f64 (log.f64 (fma.f64 (.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 63198 to 40670 computations (35.6% saved)

regimes594.0ms (4.8%)

Accuracy

Total 0.1b remaining (70.3%)

Threshold costs 0.1b (70.3%)

Counts

56 → 1

Compiler

Compiled 13039 to 9509 computations (27.1% 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)

sample4.1s (32.9%)

Algorithm

1×

intervals

Results

915.0ms	1665×	body	1024	valid
825.0ms	1958×	body	1024	invalid
401.0ms	4407×	body	128	valid
349.0ms	1174×	body	512	valid
304.0ms	3527×	body	128	invalid
259.0ms	1018×	body	512	invalid
127.0ms	685×	body	256	valid
87.0ms	520×	body	256	invalid
60.0ms	69×	body	2048	valid

Compiler

Compiled 185 to 137 computations (25.9% saved)

Details

analyze632.0ms (5.1%)

sample194.0ms (1.6%)

simplify70.0ms (0.6%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series40.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify89.0ms (0.7%)

prune91.0ms (0.7%)

localize9.0ms (0.1%)

series71.0ms (0.6%)

rewrite2.0ms (0%)

simplify88.0ms (0.7%)

prune57.0ms (0.5%)

localize11.0ms (0.1%)

series67.0ms (0.5%)

rewrite5.0ms (0%)

simplify102.0ms (0.8%)

prune95.0ms (0.8%)

localize16.0ms (0.1%)

series4.4s (35.6%)

rewrite23.0ms (0.2%)

simplify369.0ms (3%)

prune1.2s (10%)

regimes594.0ms (4.8%)

simplify2.0ms (0%)

end1.0ms (0%)

sample4.1s (32.9%)

Profiling