Details

analyze1.3s (24.4%)

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)

sample2.0s (36.2%)

Symmetry

(sort d2 d4)

Results

1.2s	8256×	body	128	valid
500.0ms	2361×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify100.0ms (1.8%)

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

prune3.0ms (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 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
▶	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize10.0ms (0.2%)

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 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
✓	0.0b	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

series57.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

25.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
18.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
13.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
6×	`diff-log_binary64`

Counts

3 → 64

Calls

3 calls:

16.0ms	(+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (*.f64 d4 d1))
8.0ms	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))
3.0ms	(-.f64 (.f64 d1 d2) (.f64 d1 d3))

simplify126.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-l_binary64`
685×	`fma-def_binary64`
488×	`fma-neg_binary64`
459×	`distribute-rgt-in_binary64`
440×	`distribute-lft-in_binary64`

Counts

196 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2558
1	361	2139
2	1230	2096
3	4966	2096
4	5229	2096

prune127.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	4	128

Error

Counts

128 → 4

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (fma.f64 d1 (-.f64 d2 d3) (.f64 d4 d1)) (.f64 d1 d1))
	28.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 d1 (-.f64 d2 d3))) (sqrt.f64 (.f64 d1 (-.f64 d2 d3)))) (.f64 d4 d1)) (*.f64 d1 d1))
	0.0b	(-.f64 (+.f64 (fma.f64 d1 d2 (neg.f64 (.f64 d1 d3))) (.f64 d4 d1)) (*.f64 d1 d1))
	0.0b	(-.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1) (.f64 d1 d1))

Compiler

Compiled 2670 to 540 computations (79.8% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series40.0ms (0.7%)

Counts

2 → 96

Calls

2 calls:

23.0ms	(-.f64 (fma.f64 d1 (-.f64 d2 d3) (.f64 d4 d1)) (.f64 d1 d1))
17.0ms	(fma.f64 d1 (-.f64 d2 d3) (*.f64 d4 d1))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-neg_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(-.f64 (fma.f64 d1 (-.f64 d2 d3) (.f64 d4 d1)) (.f64 d1 d1))
0.0ms	(fma.f64 d1 (-.f64 d2 d3) (*.f64 d4 d1))

simplify265.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

977×	`fma-neg_binary64`
250×	`cancel-sign-sub-inv_binary64`
231×	`distribute-rgt-out_binary64`
197×	`distribute-lft-out_binary64`
190×	`fma-def_binary64`

Counts

128 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	1888
1	182	1568
2	449	1485
3	2071	1478
4	4416	1478
5	4952	1478

prune51.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Error

Counts

80 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (fma.f64 d1 (-.f64 d2 d3) (.f64 d4 d1)) (.f64 d1 d1))
	28.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 d1 (-.f64 d2 d3))) (sqrt.f64 (.f64 d1 (-.f64 d2 d3)))) (.f64 d4 d1)) (*.f64 d1 d1))
▶	0.0b	(-.f64 (+.f64 (fma.f64 d1 d2 (neg.f64 (.f64 d1 d3))) (.f64 d4 d1)) (*.f64 d1 d1))
	0.0b	(-.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1) (.f64 d1 d1))

Compiler

Compiled 1414 to 302 computations (78.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series52.0ms (1%)

Counts

3 → 132

Calls

3 calls:

26.0ms	(-.f64 (+.f64 (fma.f64 d1 d2 (neg.f64 (.f64 d1 d3))) (.f64 d4 d1)) (*.f64 d1 d1))
18.0ms	(+.f64 (fma.f64 d1 d2 (neg.f64 (.f64 d1 d3))) (.f64 d4 d1))
8.0ms	(fma.f64 d1 d2 (neg.f64 (*.f64 d1 d3)))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
3×	`fma-neg_binary64`

Counts

3 → 50

Calls

3 calls:

4.0ms	(-.f64 (+.f64 (fma.f64 d1 d2 (neg.f64 (.f64 d1 d3))) (.f64 d4 d1)) (*.f64 d1 d1))
2.0ms	(+.f64 (fma.f64 d1 d2 (neg.f64 (.f64 d1 d3))) (.f64 d4 d1))
0.0ms	(fma.f64 d1 d2 (neg.f64 (*.f64 d1 d3)))

simplify108.0ms (2%)

Algorithm

1×	egg-herbie

Rules

889×	`fma-neg_binary64`
422×	`fma-def_binary64`
418×	`associate-l_binary64`
404×	`distribute-rgt-in_binary64`
384×	`distribute-lft-in_binary64`

Counts

182 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2615
1	277	2025
2	826	1929
3	4533	1929
4	5256	1929

prune72.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Error

Counts

110 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (fma.f64 d1 (-.f64 d2 d3) (.f64 d4 d1)) (.f64 d1 d1))
	28.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 d1 (-.f64 d2 d3))) (sqrt.f64 (.f64 d1 (-.f64 d2 d3)))) (.f64 d4 d1)) (*.f64 d1 d1))
✓	0.0b	(-.f64 (+.f64 (fma.f64 d1 d2 (neg.f64 (.f64 d1 d3))) (.f64 d4 d1)) (*.f64 d1 d1))
▶	0.0b	(-.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1) (.f64 d1 d1))

Compiler

Compiled 2225 to 422 computations (81% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series48.0ms (0.9%)

Counts

3 → 93

Calls

3 calls:

25.0ms	(-.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1) (.f64 d1 d1))
15.0ms	(*.f64 (-.f64 (+.f64 d2 d4) d3) d1)
8.0ms	(-.f64 (+.f64 d2 d4) d3)

rewrite63.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
13×	`prod-diff_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 79

Calls

3 calls:

46.0ms	(-.f64 (.f64 (-.f64 (+.f64 d2 d4) d3) d1) (.f64 d1 d1))
7.0ms	(*.f64 (-.f64 (+.f64 d2 d4) d3) d1)
5.0ms	(-.f64 (+.f64 d2 d4) d3)

simplify119.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

553×	`fma-def_binary64`
539×	`distribute-rgt-in_binary64`
528×	`distribute-lft-in_binary64`
515×	`fma-neg_binary64`
145×	`cancel-sign-sub-inv_binary64`

Counts

172 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	2417
1	314	1934
2	1068	1839
3	4609	1839
4	4992	1839
5	4937	1839

prune125.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	140	3	143

Error

Counts

143 → 3

Alt Table

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

Compiler

Compiled 2467 to 569 computations (76.9% saved)

regimes425.0ms (7.8%)

Accuracy

Total 0.0b remaining (67.1%)

Threshold costs 0.0b (67.1%)

Counts

68 → 1

Compiler

Compiled 5493 to 3269 computations (40.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	18	17
2	28	17
3	34	17
4	37	17
5	37	17

end271.0ms (5%)

Compiler: Compiled 114 to 65 computations (43% saved)

Details

analyze1.3s (24.4%)

sample2.0s (36.2%)

simplify100.0ms (1.8%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series57.0ms (1.1%)

rewrite33.0ms (0.6%)

simplify126.0ms (2.3%)

prune127.0ms (2.3%)

localize10.0ms (0.2%)

series40.0ms (0.7%)

rewrite4.0ms (0.1%)

simplify265.0ms (4.9%)

prune51.0ms (0.9%)

localize10.0ms (0.2%)

series52.0ms (1%)

rewrite10.0ms (0.2%)

simplify108.0ms (2%)

prune72.0ms (1.3%)

localize7.0ms (0.1%)

series48.0ms (0.9%)

rewrite63.0ms (1.2%)

simplify119.0ms (2.2%)

prune125.0ms (2.3%)

regimes425.0ms (7.8%)

simplify3.0ms (0.1%)

end271.0ms (5%)

Profiling