Details

analyze987.0ms (19.9%)

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
6.2%	93.6%	0.2%	9
28.1%	68.6%	3.3%	10
29.6%	65.5%	4.9%	11
32%	61.7%	6.3%	12
35.5%	56.9%	7.6%	13
48%	38.7%	13.4%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.6s (31.4%)

Symmetry

(sort d2 d4)

Results

997.0ms	8256×	body	128	valid
319.0ms	2317×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify114.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1400×	`fma-neg_binary64`
654×	`fma-def_binary64`
233×	`sub-neg_binary64`
210×	`unsub-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	32	14
2	94	13
3	263	13
4	655	13
5	1556	13
6	1691	13
7	1500	13
8	1500	13
9	2739	13
10	2707	13
11	2707	13
12	2632	13

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize18.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 d3))
✓	0.0b	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))

series144.0ms (2.9%)

Counts

3 → 132

Calls

3 calls:

100.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
27.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
16.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

rewrite109.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

712×	`fma-neg_binary64`
265×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
238×	`egg-rr`
148×	`add-sqr-sqrt_binary64`

Counts

3 → 238

Calls

3 calls:

104.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
104.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))
104.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	284	31
2	4021	31
3	5544	31
0	0	0
1	0	0

simplify305.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

920×	`unsub-neg_binary64`
689×	`distribute-rgt-out--_binary64`
678×	`distribute-rgt-neg-in_binary64`
613×	`fabs-mul_binary64`
568×	`distribute-lft-neg-in_binary64`

Counts

370 → 263

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	33	1589
1	99	1342
2	220	1227
3	587	1227
4	1624	1227
5	2778	1227
6	3226	1227
7	3589	1227
8	4122	1227
9	4229	1227
10	4329	1209
11	3378	1209
12	3625	1209
13	4160	1209
14	4566	1209
15	4996	1209
16	4901	1209

prune180.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	261	4	265

Error

Counts

265 → 4

Alt Table

Status	Error	Program
	0.0b	(fma.f64 d1 (+.f64 (-.f64 d2 d3) d4) (neg.f64 (*.f64 d1 d1)))
▶	0.0b	(-.f64 (fma.f64 d1 d4 (.f64 d1 (-.f64 d2 d3))) (.f64 d1 d1))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
	28.7b	(/.f64 (-.f64 (pow.f64 (.f64 d1 (+.f64 (-.f64 d2 d3) d4)) 2) (pow.f64 d1 4)) (+.f64 (.f64 d1 (+.f64 (-.f64 d2 d3) d4)) (*.f64 d1 d1)))

Compiler

Compiled 5326 to 1207 computations (77.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (-.f64 d2 d3))
✓	0.0b	(fma.f64 d1 d4 (*.f64 d1 (-.f64 d2 d3)))
✓	0.0b	(-.f64 (fma.f64 d1 d4 (.f64 d1 (-.f64 d2 d3))) (.f64 d1 d1))

series88.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

69.0ms	(-.f64 (fma.f64 d1 d4 (.f64 d1 (-.f64 d2 d3))) (.f64 d1 d1))
12.0ms	(fma.f64 d1 d4 (*.f64 d1 (-.f64 d2 d3)))
7.0ms	(*.f64 d1 (-.f64 d2 d3))

rewrite119.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

562×	`log-prod_binary64`
431×	`fma-def_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
194×	`fma-neg_binary64`

Counts

3 → 161

Calls

3 calls:

114.0ms	(*.f64 d1 (-.f64 d2 d3))
114.0ms	(fma.f64 d1 d4 (*.f64 d1 (-.f64 d2 d3)))
114.0ms	(-.f64 (fma.f64 d1 d4 (.f64 d1 (-.f64 d2 d3))) (.f64 d1 d1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	223	33
2	2913	33
3	5631	33
0	0	0
1	0	0

simplify138.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-neg_binary64`
776×	`unsub-neg_binary64`
604×	`cancel-sign-sub-inv_binary64`
502×	`associate-r_binary64`
337×	`neg-sub0_binary64`

Counts

281 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	1469
1	86	1258
2	193	1143
3	527	1143
4	1546	1143
5	3890	1143
6	4111	1143
7	4949	1143
8	4973	1143
9	4921	1143

prune117.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
	0.0b	(fma.f64 d1 (+.f64 (-.f64 d2 d3) d4) (neg.f64 (*.f64 d1 d1)))
✓	0.0b	(-.f64 (fma.f64 d1 d4 (.f64 d1 (-.f64 d2 d3))) (.f64 d1 d1))
▶	0.0b	(fma.f64 d1 (neg.f64 d1) (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 3624 to 862 computations (76.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d1 (neg.f64 d1) (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))

series28.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

18.0ms	(fma.f64 d1 (neg.f64 d1) (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
10.0ms	(*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))

rewrite88.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

484×	`fma-def_binary64`
233×	`fma-neg_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
170×	`log-pow_binary64`

Counts

2 → 84

Calls

2 calls:

86.0ms	(fma.f64 d1 (neg.f64 d1) (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
86.0ms	(*.f64 d1 (+.f64 d4 (-.f64 d2 d3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	230	23
2	2927	23
3	4961	23
4	4945	23
0	0	0
1	0	0

simplify148.0ms (3%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
454×	`cancel-sign-sub-inv_binary64`
448×	`distribute-rgt-neg-in_binary64`
413×	`associate-l_binary64`
396×	`distribute-rgt-out--_binary64`

Counts

180 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	1255
1	75	1102
2	154	987
3	389	987
4	1190	987
5	2926	987
6	4315	987
7	4914	987
8	4958	987
9	4998	987
10	4943	987

prune65.0ms (1.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	104	4	108

Error

Counts

108 → 4

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 d1 (+.f64 (-.f64 d2 d3) d4) (neg.f64 (*.f64 d1 d1)))
✓	0.0b	(-.f64 (fma.f64 d1 d4 (.f64 d1 (-.f64 d2 d3))) (.f64 d1 d1))
✓	0.0b	(fma.f64 d1 (neg.f64 d1) (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 1674 to 428 computations (74.4% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d1 (+.f64 (-.f64 d2 d3) d4) (neg.f64 (*.f64 d1 d1)))

series19.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

19.0ms

(fma.f64 d1 (+.f64 (-.f64 d2 d3) d4) (neg.f64 (*.f64 d1 d1)))

rewrite62.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
485×	`fma-def_binary64`
247×	`fma-neg_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`

Counts

1 → 34

Calls

1 calls:

61.0ms

(fma.f64 d1 (+.f64 (-.f64 d2 d3) d4) (neg.f64 (*.f64 d1 d1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	227	14
2	2814	14
3	5551	14
0	0	0
1	0	0

simplify96.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

636×	`sub-neg_binary64`
532×	`fma-neg_binary64`
445×	`unswap-sqr_binary64`
443×	`distribute-rgt-neg-in_binary64`
408×	`cancel-sign-sub-inv_binary64`

Counts

82 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	816
1	59	663
2	142	548
3	354	548
4	1116	548
5	2796	548
6	4186	548
7	4498	548
8	5304	548

prune26.0ms (0.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	50	4	54

Error

Counts

54 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 d1 (+.f64 (-.f64 d2 d3) d4) (neg.f64 (*.f64 d1 d1)))
✓	0.0b	(-.f64 (fma.f64 d1 d4 (.f64 d1 (-.f64 d2 d3))) (.f64 d1 d1))
✓	0.0b	(fma.f64 d1 (neg.f64 d1) (*.f64 d1 (+.f64 d4 (-.f64 d2 d3))))
✓	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 741 to 195 computations (73.7% saved)

regimes451.0ms (9.1%)

Accuracy

Total 0.0b remaining (79.3%)

Threshold costs 0.0b (79.3%)

Counts

72 → 1

Compiler

Compiled 5428 to 3314 computations (38.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	23	16
3	26	16
4	27	16
5	27	16

end69.0ms (1.4%)

Remove: (sort d2 d4)
Compiler: Compiled 125 to 74 computations (40.8% saved)

Details

analyze987.0ms (19.9%)

sample1.6s (31.4%)

simplify114.0ms (2.3%)

prune6.0ms (0.1%)

localize18.0ms (0.4%)

series144.0ms (2.9%)

rewrite109.0ms (2.2%)

simplify305.0ms (6.1%)

prune180.0ms (3.6%)

localize8.0ms (0.2%)

series88.0ms (1.8%)

rewrite119.0ms (2.4%)

simplify138.0ms (2.8%)

prune117.0ms (2.3%)

localize9.0ms (0.2%)

series28.0ms (0.6%)

rewrite88.0ms (1.8%)

simplify148.0ms (3%)

prune65.0ms (1.3%)

localize7.0ms (0.1%)

series19.0ms (0.4%)

rewrite62.0ms (1.3%)

simplify96.0ms (1.9%)

prune26.0ms (0.5%)

regimes451.0ms (9.1%)

simplify3.0ms (0.1%)

end69.0ms (1.4%)

Profiling