Details

analyze662.0ms (7.6%)

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)

sample204.0ms (2.3%)

Algorithm

1×

intervals

Results

33.0ms	58×	body	1024	valid
29.0ms	60×	body	1024	invalid
12.0ms	136×	body	128	valid
12.0ms	41×	body	512	valid
10.0ms	114×	body	128	invalid
10.0ms	32×	body	512	invalid
3.0ms	18×	body	256	valid
3.0ms	14×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify67.0ms (0.8%)

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

18.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.9b	(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)

localize12.0ms (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))))
✓	4.4b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series49.0ms (0.6%)

Counts

3 → 80

Calls

3 calls:

37.0ms	(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)))

rewrite18.0ms (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)

simplify194.0ms (2.2%)

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

prune169.0ms (1.9%)

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
	0.4b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
▶	0.2b	(fma.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) J)) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (+.f64 (.f64 1/2520 (.f64 (pow.f64 l 7) J)) (.f64 2 (.f64 l J))))) (cos.f64 (/.f64 K 2)) U)
	18.9b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))

Compiler

Compiled 4597 to 1743 computations (62.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 1/3 (.f64 (pow.f64 l 3) J))
✓	2.4b	(*.f64 (pow.f64 l 5) J)
✓	2.6b	(*.f64 (pow.f64 l 7) J)
✓	4.9b	(*.f64 (pow.f64 l 3) J)

series81.0ms (0.9%)

Counts

4 → 0

Calls

4 calls:

27.0ms	(*.f64 (pow.f64 l 5) J)
23.0ms	(*.f64 (pow.f64 l 7) J)
16.0ms	(*.f64 (pow.f64 l 3) J)
14.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) J))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
29×	`associate-l_binary64`
29×	`add-exp-log_binary64`
16×	`prod-exp_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 108

Calls

4 calls:

9.0ms	(*.f64 (pow.f64 l 7) J)
5.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) J))
4.0ms	(*.f64 (pow.f64 l 3) J)
4.0ms	(*.f64 (pow.f64 l 5) J)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
513×	`*-commutative_binary64`
470×	`unswap-sqr_binary64`
344×	`log-prod_binary64`
267×	`associate-+l+_binary64`

Counts

108 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	1227
1	322	1137
2	1110	1112
3	1868	1088
4	4198	1088
5	4949	1088

prune257.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	154	3	157

Error

0.0b

Counts

157 → 3

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
✓	0.2b	(fma.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) J)) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (+.f64 (.f64 1/2520 (.f64 (pow.f64 l 7) J)) (.f64 2 (.f64 l J))))) (cos.f64 (/.f64 K 2)) U)
	18.9b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))

Compiler

Compiled 6424 to 4411 computations (31.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) J)
✓	0.1b	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
✓	0.1b	(.f64 l (.f64 (cos.f64 (*.f64 1/2 K)) J))
✓	4.9b	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))

series118.0ms (1.3%)

Counts

4 → 64

Calls

4 calls:

47.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
40.0ms	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))
22.0ms	(.f64 l (.f64 (cos.f64 (*.f64 1/2 K)) J))
9.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64`
29×	`prod-exp_binary64`
25×	`add-cbrt-cube_binary64`
21×	`associate-l_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

4 → 96

Calls

4 calls:

7.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
7.0ms	(.f64 l (.f64 (cos.f64 (*.f64 1/2 K)) J))
6.0ms	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))
3.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)

simplify106.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-def_binary64`
398×	`associate-r_binary64`
386×	`cancel-sign-sub-inv_binary64`
311×	`associate-l_binary64`
248×	`log-prod_binary64`

Counts

160 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	2863
1	458	2504
2	1864	2432
3	4081	2424
4	4941	2424

prune330.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	211	6	217

Error

Counts

217 → 6

Alt Table

Status	Error	Program
	0.7b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (.f64 (cos.f64 (.f64 1/2 K)) (.f64 (cbrt.f64 J) (cbrt.f64 J))) (cbrt.f64 J)))) U))
✓	0.4b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
✓	0.2b	(fma.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) J)) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (+.f64 (.f64 1/2520 (.f64 (pow.f64 l 7) J)) (.f64 2 (.f64 l J))))) (cos.f64 (/.f64 K 2)) U)
▶	0.4b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 (.f64 l (cos.f64 (.f64 1/2 K))) J)) U))
	0.7b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J)))) (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U))
	18.9b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))

Compiler

Compiled 7111 to 5112 computations (28.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 l (cos.f64 (*.f64 1/2 K))) J)
	0.1b	(.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J)))
✓	0.1b	(.f64 l (cos.f64 (.f64 1/2 K)))
	4.9b	(.f64 (pow.f64 l 3) (.f64 (cos.f64 (*.f64 1/2 K)) J))

series31.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

21.0ms	(.f64 (.f64 l (cos.f64 (*.f64 1/2 K))) J)
9.0ms	(.f64 l (cos.f64 (.f64 1/2 K)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`

Counts

2 → 40

Calls

2 calls:

7.0ms	(.f64 (.f64 l (cos.f64 (*.f64 1/2 K))) J)
3.0ms	(.f64 l (cos.f64 (.f64 1/2 K)))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-def_binary64`
417×	`fma-neg_binary64`
378×	`cancel-sign-sub-inv_binary64`
342×	`distribute-rgt-in_binary64`
341×	`*-commutative_binary64`

Counts

80 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1182
1	232	1054
2	829	1026
3	1583	1017
4	3241	1017
5	4659	1017
6	4958	1017

prune342.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	172	6	178

Error

Counts

178 → 6

Alt Table

Status	Error	Program
	0.7b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (.f64 (cos.f64 (.f64 1/2 K)) (.f64 (cbrt.f64 J) (cbrt.f64 J))) (cbrt.f64 J)))) U))
✓	0.4b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))
✓	0.2b	(fma.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) J)) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) J)) (+.f64 (.f64 1/2520 (.f64 (pow.f64 l 7) J)) (.f64 2 (.f64 l J))))) (cos.f64 (/.f64 K 2)) U)
✓	0.4b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 (.f64 l (cos.f64 (.f64 1/2 K))) J)) U))
	0.7b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J)))) (cbrt.f64 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U))
	18.9b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))

Compiler

Compiled 5670 to 4079 computations (28.1% saved)

regimes1.1s (12.2%)

Accuracy

Total 0.1b remaining (63.1%)

Threshold costs 0.1b (63.1%)

Counts

76 → 1

Compiler

Compiled 24038 to 17943 computations (25.4% 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)

sample4.7s (54.2%)

Algorithm

1×

intervals

Results

1.1s	1693×	body	1024	valid
941.0ms	1938×	body	1024	invalid
423.0ms	4342×	body	128	valid
409.0ms	1228×	body	512	valid
340.0ms	3445×	body	128	invalid
263.0ms	945×	body	512	invalid
158.0ms	672×	body	256	valid
111.0ms	508×	body	256	invalid
57.0ms	65×	body	2048	valid

Compiler

Compiled 242 to 180 computations (25.6% saved)

Details

analyze662.0ms (7.6%)

sample204.0ms (2.3%)

simplify67.0ms (0.8%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series49.0ms (0.6%)

rewrite18.0ms (0.2%)

simplify194.0ms (2.2%)

prune169.0ms (1.9%)

localize22.0ms (0.2%)

series81.0ms (0.9%)

rewrite27.0ms (0.3%)

simplify83.0ms (0.9%)

prune257.0ms (2.9%)

localize14.0ms (0.2%)

series118.0ms (1.3%)

rewrite30.0ms (0.3%)

simplify106.0ms (1.2%)

prune330.0ms (3.8%)

localize16.0ms (0.2%)

series31.0ms (0.4%)

rewrite12.0ms (0.1%)

simplify91.0ms (1%)

prune342.0ms (3.9%)

regimes1.1s (12.2%)

simplify2.0ms (0%)

end1.0ms (0%)

sample4.7s (54.2%)

Profiling