Details

analyze1.5s (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
21.8%	67.1%	11.1%	11
21.8%	67.1%	11.1%	12
32.7%	56.1%	11.1%	13
35.1%	53%	11.9%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample5.2s (54.8%)

Results

1.3s	1718×	body	1024	valid
1.3s	2045×	body	1024	invalid
751.0ms	4617×	body	128	valid
511.0ms	1151×	body	512	valid
441.0ms	2632×	body	128	invalid
428.0ms	1047×	body	512	invalid
213.0ms	705×	body	256	valid
139.0ms	490×	body	256	invalid
67.0ms	65×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify68.0ms (0.7%)

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)

localize10.0ms (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))))
✓	6.4b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series46.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

36.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite76.0ms (0.8%)

Algorithm

3×	egg-rewrite
1×	batch-egg-rewrite

Rules

151×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-log-exp_binary64`
138×	`add-cbrt-cube_binary64`

Counts

3 → 0

Calls

3 calls:

76.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
76.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
76.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	295	18
2	33	18
0	6	6
1	130	6
2	71	6
0	8	9
1	169	9
2	73	9
0	14	18
1	295	18
2	33	18

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-def_binary64`
524×	`associate-l_binary64`
430×	`sub-neg_binary64`
401×	`associate-r_binary64`
288×	`associate-+l+_binary64`

Counts

80 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2023
1	367	1649
2	1181	1604
3	4510	1604
4	4809	1604
5	4962	1604
6	4933	1604

prune47.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	3	45

Error

0.0b

Counts

45 → 3

Alt Table

Status	Error	Program
▶	0.3b	(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)
	0.3b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)
✓	16.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 1185 to 712 computations (39.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 1/3 (.f64 (pow.f64 l 3) J))
✓	1.5b	(*.f64 (pow.f64 l 7) J)
✓	3.0b	(*.f64 (pow.f64 l 5) J)
✓	6.2b	(*.f64 (pow.f64 l 3) J)

series53.0ms (0.6%)

Counts

4 → 0

Calls

4 calls:

15.0ms	(*.f64 (pow.f64 l 7) J)
15.0ms	(*.f64 (pow.f64 l 5) J)
13.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) J))
10.0ms	(*.f64 (pow.f64 l 3) J)

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`log-prod_binary64`
241×	`expm1-udef_binary64`
241×	`log1p-udef_binary64`
215×	`log-pow_binary64`
141×	`add-sqr-sqrt_binary64`

Counts

4 → 74

Calls

4 calls:

56.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) J))
56.0ms	(*.f64 (pow.f64 l 7) J)
56.0ms	(*.f64 (pow.f64 l 5) J)
56.0ms	(*.f64 (pow.f64 l 3) J)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	298	31
2	3145	31
3	4999	31

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune99.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Error

0.0b

Counts

77 → 3

Alt Table

Status	Error	Program
✓	0.3b	(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)
▶	0.3b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)
✓	16.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 3024 to 2140 computations (29.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
✓	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

series91.0ms (1%)

Counts

4 → 64

Calls

4 calls:

71.0ms	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
12.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
4.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
3.0ms	(*.f64 1/60 (pow.f64 l 5))

rewrite71.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

325×	`log1p-udef_binary64`
284×	`prod-diff_binary64`
187×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`

Counts

4 → 72

Calls

4 calls:

69.0ms	(*.f64 1/60 (pow.f64 l 5))
69.0ms	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
69.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
69.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	59
1	394	59
2	4134	59
3	4985	59

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

585×	`sub-neg_binary64`
422×	`cancel-sign-sub-inv_binary64`
386×	`*-commutative_binary64`
380×	`associate-+l+_binary64`
352×	`associate--l+_binary64`

Counts

136 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2029
1	346	1827
2	1289	1529
3	3867	1529
4	5147	1529

prune141.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	99	5	104

Error

Counts

104 → 5

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)
▶	0.7b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)
✓	0.3b	(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)
	0.7b	(+.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) 3) U)
✓	0.3b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)

Compiler

Compiled 3127 to 2315 computations (26% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
✓	0.6b	(cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3)

series725.0ms (7.7%)

Counts

2 → 48

Calls

2 calls:

379.0ms	(pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3)
346.0ms	(cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))

rewrite44.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

749×	`log1p-expm1-u_binary64`
749×	`expm1-log1p-u_binary64`
154×	`log1p-udef_binary64`
121×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`

Counts

2 → 60

Calls

2 calls:

43.0ms	(cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))
43.0ms	(pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	187	20
2	1986	20
3	4937	20

simplify116.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-neg_binary64`
351×	`distribute-rgt-neg-in_binary64`
345×	`distribute-lft-neg-in_binary64`
226×	`unswap-sqr_binary64`
211×	`associate-r_binary64`

Counts

108 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	992
1	194	985
2	515	928
3	1793	584
4	4709	576
5	4996	576
6	4921	576

prune177.0ms (1.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	134	5	139

Error

Counts

139 → 5

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)
✓	0.7b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)
✓	0.3b	(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)
	0.7b	(+.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) 3) U)
✓	0.3b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)

Compiler

Compiled 4156 to 3180 computations (23.5% saved)

regimes593.0ms (6.3%)

Accuracy

Total 0.3b remaining (89.6%)

Threshold costs 0.3b (89.6%)

Counts

49 → 1

Compiler

Compiled 12472 to 9628 computations (22.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	52
1	40	52
2	40	52

end141.0ms (1.5%)

Compiler: Compiled 219 to 166 computations (24.2% saved)

Details

analyze1.5s (15.5%)

sample5.2s (54.8%)

simplify68.0ms (0.7%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series46.0ms (0.5%)

rewrite76.0ms (0.8%)

simplify112.0ms (1.2%)

prune47.0ms (0.5%)

localize23.0ms (0.2%)

series53.0ms (0.6%)

rewrite57.0ms (0.6%)

simplify6.0ms (0.1%)

prune99.0ms (1%)

localize14.0ms (0.1%)

series91.0ms (1%)

rewrite71.0ms (0.7%)

simplify70.0ms (0.7%)

prune141.0ms (1.5%)

localize16.0ms (0.2%)

series725.0ms (7.7%)

rewrite44.0ms (0.5%)

simplify116.0ms (1.2%)

prune177.0ms (1.9%)

regimes593.0ms (6.3%)

simplify2.0ms (0%)

end141.0ms (1.5%)

Profiling