Details

analyze1.3s (7.1%)

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)

sample221.0ms (1.2%)

Algorithm

1×

intervals

Results

54.0ms	55×	body	1024	valid
45.0ms	59×	body	1024	invalid
25.0ms	147×	body	128	valid
19.0ms	37×	body	512	valid
17.0ms	104×	body	128	invalid
13.0ms	30×	body	512	invalid
6.0ms	20×	body	256	invalid
6.0ms	15×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify93.0ms (0.5%)

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

17.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.0b	(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)

localize23.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	5.5b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite36.0ms (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:

15.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
8.0ms	(-.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)

series222.0ms (1.2%)

Counts

3 → 80

Calls

3 calls:

174.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
42.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
5.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify359.0ms (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 → 306

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

prune216.0ms (1.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	304	2	306
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	2	307

Error

0.0b

Counts

307 → 2

Alt Table

Status	Error	Program
	0.2b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4408 to 1610 computations (63.5% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite14.0ms (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:

9.0ms	(.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)

series360.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

256.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
85.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
18.0ms	(sinh.f64 l)

simplify188.0ms (1%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-def_binary64`
673×	`fma-neg_binary64`
293×	`associate-+l+_binary64`
245×	`cancel-sign-sub-inv_binary64`
238×	`associate--l+_binary64`

Counts

125 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2684
1	485	2227
2	1573	2164
3	4658	2164
4	5226	2164

prune135.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	211	5	216

Error

0.0b

Counts

216 → 5

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	30.5b	(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)
	33.1b	(.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)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2075 to 1240 computations (40.2% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 50

Calls

3 calls:

7.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
6.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
1.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

series362.0ms (1.9%)

Counts

3 → 76

Calls

3 calls:

156.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
147.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
58.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

simplify160.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
409×	`fma-def_binary64`
381×	`*-commutative_binary64`
328×	`cancel-sign-sub-inv_binary64`
307×	`distribute-lft-out--_binary64`

Counts

126 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1977
1	294	1809
2	1038	1772
3	2450	1761
4	4893	1761
5	4986	1761

prune181.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	224	5	229

Error

Counts

229 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	0.5b	(fma.f64 2 (.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 l) (.f64 J (cos.f64 (*.f64 1/2 K))))) U)
▶	0.4b	(fma.f64 2 (.f64 (.f64 (cbrt.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) (cbrt.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))))) (cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))) U)
	30.5b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.f64 (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 1955 to 1278 computations (34.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) (cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))))
	14.8b	(cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))
	14.8b	(cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))
✓	14.8b	(cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`pow1/3_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

9.0ms	(.f64 (cbrt.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) (cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))))
9.0ms	(cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))

series5.8s (31.1%)

Counts

2 → 72

Calls

2 calls:

3.4s	(.f64 (cbrt.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) (cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))))
2.5s	(cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))

simplify203.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

724×	`unswap-sqr_binary64`
550×	`fma-neg_binary64`
371×	`fma-def_binary64`
333×	`*-commutative_binary64`
269×	`exp-sum_binary64`

Counts

116 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	3121
1	412	2865
2	1154	2520
3	2912	2075
4	5563	2075

prune442.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	473	0	473
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	473	5	478

Error

Counts

478 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	0.5b	(fma.f64 2 (.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 l) (.f64 J (cos.f64 (*.f64 1/2 K))))) U)
✓	0.4b	(fma.f64 2 (.f64 (.f64 (cbrt.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) (cbrt.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))))) (cbrt.f64 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))) U)
	30.5b	(fma.f64 (.f64 J (.f64 2 (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.f64 (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 5871 to 4087 computations (30.4% saved)

regimes840.0ms (4.5%)

Accuracy

Total 0.5b remaining (89.2%)

Threshold costs 0.5b (89.2%)

Compiler

Compiled 7894 to 5689 computations (27.9% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	17	23
2	17	23

end1.0ms (0%)

Compiler: Compiled 20 to 15 computations (25% saved)

sample7.5s (39.7%)

Algorithm

1×

intervals

Results

1.6s	1614×	body	1024	valid
1.6s	1947×	body	1024	invalid
747.0ms	4460×	body	128	valid
650.0ms	1191×	body	512	valid
597.0ms	3483×	body	128	invalid
485.0ms	1004×	body	512	invalid
266.0ms	682×	body	256	valid
195.0ms	510×	body	256	invalid
87.0ms	53×	body	2048	valid

Compiler

Compiled 154 to 111 computations (27.9% saved)

Details

analyze1.3s (7.1%)

sample221.0ms (1.2%)

simplify93.0ms (0.5%)

prune6.0ms (0%)

localize23.0ms (0.1%)

rewrite36.0ms (0.2%)

series222.0ms (1.2%)

simplify359.0ms (1.9%)

prune216.0ms (1.1%)

localize18.0ms (0.1%)

rewrite14.0ms (0.1%)

series360.0ms (1.9%)

simplify188.0ms (1%)

prune135.0ms (0.7%)

localize16.0ms (0.1%)

rewrite19.0ms (0.1%)

series362.0ms (1.9%)

simplify160.0ms (0.9%)

prune181.0ms (1%)

localize24.0ms (0.1%)

rewrite23.0ms (0.1%)

series5.8s (31.1%)

simplify203.0ms (1.1%)

prune442.0ms (2.4%)

regimes840.0ms (4.5%)

simplify6.0ms (0%)

end1.0ms (0%)

sample7.5s (39.7%)

Profiling