Details

analyze1.4s (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)

sample5.0s (53.5%)

Results

1.2s	1716×	body	1024	valid
1.2s	1984×	body	1024	invalid
718.0ms	4568×	body	128	valid
502.0ms	1196×	body	512	valid
418.0ms	2656×	body	128	invalid
382.0ms	982×	body	512	invalid
214.0ms	725×	body	256	valid
154.0ms	503×	body	256	invalid
56.0ms	51×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify75.0ms (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

16.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.0b	(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	(*.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)
✓	5.1b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series49.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

33.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
13.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite81.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite
3×	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:

81.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
81.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
81.0ms	(-.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	14	18
1	295	18
2	33	18
0	8	9
1	169	9
2	73	9
0	0	0
1	0	0

simplify119.0ms (1.3%)

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

prune40.0ms (0.4%)

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
	0.4b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
▶	0.4b	(fma.f64 (.f64 J (.f64 2 l)) (cos.f64 (/.f64 K 2)) U)
✓	16.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 1125 to 666 computations (40.8% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series21.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

21.0ms

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

rewrite80.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

554×	`log-prod_binary64`
239×	`prod-diff_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
189×	`pow3_binary64`

Counts

1 → 29

Calls

1 calls:

79.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	227	16
2	2648	16
3	4975	16
4	5037	16
0	0	0
1	0	0

simplify124.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

626×	`sub-neg_binary64`
493×	`distribute-rgt-neg-in_binary64`
444×	`distribute-lft-neg-in_binary64`
442×	`fma-neg_binary64`
299×	`*-commutative_binary64`

Counts

77 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	755
1	103	743
2	325	733
3	1167	725
4	2537	725
5	4189	725
6	4631	725
7	4838	725
8	4942	725

prune48.0ms (0.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	38	5	43
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	38	8	46

Error

0.0b

Counts

46 → 8

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
	40.2b	(log1p.f64 (expm1.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)))
	40.3b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U) 3))
	29.3b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) 2)
	1.7b	(pow.f64 (cbrt.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) 3)
✓	0.4b	(fma.f64 (.f64 J (.f64 2 l)) (cos.f64 (/.f64 K 2)) U)
	1.7b	(.f64 (cbrt.f64 (fma.f64 (.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) (pow.f64 (cbrt.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) 2))
✓	16.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 1035 to 588 computations (43.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 l (*.f64 1/3 (pow.f64 l 3)))
✓	0.0b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
✓	0.2b	(*.f64 1/3 (pow.f64 l 3))

series72.0ms (0.8%)

Counts

4 → 76

Calls

4 calls:

58.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
8.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
3.0ms	(fma.f64 2 l (*.f64 1/3 (pow.f64 l 3)))
3.0ms	(*.f64 1/3 (pow.f64 l 3))

rewrite123.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

312×	`prod-diff_binary64`
274×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`
198×	`fma-udef_binary64`
193×	`fma-neg_binary64`

Counts

4 → 74

Calls

4 calls:

122.0ms	(fma.f64 2 l (*.f64 1/3 (pow.f64 l 3)))
122.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
122.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
122.0ms	(*.f64 1/3 (pow.f64 l 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	50
1	324	50
2	3431	50
3	4911	50
4	4970	50
5	4874	50
0	0	0
1	0	0

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
609×	`associate-l_binary64`
517×	`associate-r_binary64`
360×	`sub-neg_binary64`
352×	`cancel-sign-sub-inv_binary64`

Counts

150 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1843
1	268	1508
2	962	1409
3	4499	1409
4	4974	1409
5	4987	1409

prune135.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	2	5
Picked	1	0	1
Done	0	2	2
Total	109	7	116

Error

0.0b

Counts

116 → 7

Alt Table

Status	Error	Program
✓	16.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	0.7b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (pow.f64 (cbrt.f64 (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3)))) 3) U)
	29.3b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) 2)
	1.7b	(pow.f64 (cbrt.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) 3)
✓	0.4b	(fma.f64 (.f64 J (.f64 2 l)) (cos.f64 (/.f64 K 2)) U)
	30.1b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (pow.f64 (sqrt.f64 (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3)))) 2) U)
▶	0.7b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)

Compiler

Compiled 2670 to 1917 computations (28.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
	0.2b	(*.f64 1/3 (pow.f64 l 3))
✓	0.6b	(cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))
✓	0.8b	(pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3)

series952.0ms (10.3%)

Counts

2 → 48

Calls

2 calls:

489.0ms	(pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3)
463.0ms	(cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))

rewrite44.0ms (0.5%)

Algorithm

2×	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 → 59

Calls

2 calls:

42.0ms	(cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))
42.0ms	(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
0	0	0
1	0	0

simplify98.0ms (1.1%)

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

107 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	992
1	194	985
2	515	832
3	1793	584
4	4709	576
5	4996	576
6	4921	576

prune144.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	118	8	126

Error

Counts

126 → 8

Alt Table

Status	Error	Program
✓	16.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	0.7b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (pow.f64 (cbrt.f64 (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3)))) 3) U)
	29.3b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) 2)
	1.7b	(pow.f64 (cbrt.f64 (fma.f64 (*.f64 J (+.f64 l l)) (cos.f64 (/.f64 K 2)) U)) 3)
✓	0.4b	(fma.f64 (.f64 J (.f64 2 l)) (cos.f64 (/.f64 K 2)) U)
	30.1b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (pow.f64 (sqrt.f64 (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3)))) 2) U)
	0.6b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 K))) 2) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 K))) J)) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)
✓	0.7b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) 3) (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))) U)

Compiler

Compiled 2973 to 2211 computations (25.6% saved)

regimes401.0ms (4.3%)

Accuracy

Total 0.4b remaining (87.5%)

Threshold costs 0.4b (87.5%)

Counts

40 → 1

Compiler

Compiled 8222 to 6068 computations (26.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	13	16
2	13	16

end129.0ms (1.4%)

Compiler: Compiled 197 to 149 computations (24.4% saved)

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

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

Details

analyze1.4s (15.5%)

sample5.0s (53.5%)

simplify75.0ms (0.8%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series49.0ms (0.5%)

rewrite81.0ms (0.9%)

simplify119.0ms (1.3%)

prune40.0ms (0.4%)

localize8.0ms (0.1%)

series21.0ms (0.2%)

rewrite80.0ms (0.9%)

simplify124.0ms (1.3%)

prune48.0ms (0.5%)

localize11.0ms (0.1%)

series72.0ms (0.8%)

rewrite123.0ms (1.3%)

simplify92.0ms (1%)

prune135.0ms (1.5%)

localize13.0ms (0.1%)

series952.0ms (10.3%)

rewrite44.0ms (0.5%)

simplify98.0ms (1.1%)

prune144.0ms (1.6%)

regimes401.0ms (4.3%)

simplify2.0ms (0%)

end129.0ms (1.4%)

Profiling

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