Details

analyze34.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.1s (38.1%)

Results

941.0ms	8256×	body	128	valid
53.0ms	421×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify47.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

13.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 55 to 29 computations (47.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	13.3b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series69.0ms (2.5%)

Counts

3 → 72

Calls

3 calls:

40.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
22.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
7.0ms	(-.f64 (.f64 a a) (.f64 b b))

rewrite132.0ms (4.8%)

Algorithm

2×	batch-egg-rewrite

Rules

177× egg-rr

Counts

3 → 177

Calls

2 calls:

128.0ms	((/.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 a a)) (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 a a)))) (-.f64 (.f64 a a) (.f64 b b)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	212	38
2	2703	38
3	4707	38
4	4641	37
5	5152	37
0	0	0
1	0	0

simplify63.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

735×	`associate-/r*_binary64`
707×	`associate-/l/_binary64`
519×	`associate-/r/_binary64`
498×	`fma-def_binary64`
444×	`fma-neg_binary64`

Counts

249 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	963
1	37	891
2	84	843
3	258	843
4	1055	843
5	4523	843
6	5163	843

prune107.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	3	190

Error

0.0b

Counts

190 → 3

Alt Table

Status	Error	Program
	13.8b	(exp.f64 (.f64 (log1p.f64 (neg.f64 (/.f64 (.f64 b b) (*.f64 a a)))) 1/2))
▶	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
	0.8b	(sqrt.f64 (fabs.f64 1))

Compiler

Compiled 3691 to 1355 computations (63.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
✓	0.0b	(/.f64 (+.f64 a b) a)
✓	0.0b	(/.f64 (-.f64 a b) a)
✓	0.0b	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))

series50.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

25.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
15.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
5.0ms	(/.f64 (-.f64 a b) a)
5.0ms	(/.f64 (+.f64 a b) a)

rewrite80.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

158× egg-rr

Counts

4 → 158

Calls

2 calls:

77.0ms	((.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a)) (/.f64 (-.f64 a b) a) (/.f64 (+.f64 a b) a) (sqrt.f64 (fabs.f64 (.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	50
1	236	45
2	3311	45
3	5056	45
0	0	0
1	0	0

simplify58.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

468×	`cancel-sign-sub-inv_binary64`
378×	`div-sub_binary64`
321×	`fma-neg_binary64`
291×	`fma-def_binary64`
261×	`fabs-div_binary64`

Counts

254 → 170

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	1041
1	74	1041
2	199	1041
3	639	1041
4	2781	1041
5	5183	1041

prune87.0ms (3.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	171	2	173

Error

Counts

173 → 2

Alt Table

Status	Error	Program
	13.8b	(exp.f64 (.f64 (log1p.f64 (neg.f64 (/.f64 (.f64 b b) (*.f64 a a)))) 1/2))
▶	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))

Compiler

Compiled 2819 to 913 computations (67.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
✓	0.0b	(/.f64 a (/.f64 (-.f64 a b) a))
✓	0.0b	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
	0.0b	(/.f64 (-.f64 a b) a)

series51.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
18.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
10.0ms	(/.f64 a (/.f64 (-.f64 a b) a))

rewrite75.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

131× egg-rr

Counts

3 → 131

Calls

2 calls:

72.0ms	((/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a))) (/.f64 a (/.f64 (-.f64 a b) a)) (sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a))))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	240	44
2	3452	44
3	5017	44
0	0	0
1	0	0

simplify95.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
620×	`associate-/l*_binary64`
280×	`fma-neg_binary64`
259×	`cancel-sign-sub-inv_binary64`
199×	`associate-/r/_binary64`

Counts

203 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	1206
1	142	1206
2	426	1152
3	1483	1122
4	4703	1122
5	4947	1122
6	4994	1122
7	4960	1122

prune97.0ms (3.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	196	2	198

Error

Counts

198 → 2

Alt Table

Status	Error	Program
▶	13.8b	(exp.f64 (.f64 (log1p.f64 (neg.f64 (/.f64 (.f64 b b) (*.f64 a a)))) 1/2))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))

Compiler

Compiled 3605 to 1178 computations (67.3% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (neg.f64 (/.f64 (.f64 b b) (.f64 a a))))
✓	32.5b	(/.f64 (.f64 b b) (.f64 a a))

series64.0ms (2.3%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(log1p.f64 (neg.f64 (/.f64 (.f64 b b) (.f64 a a))))
30.0ms	(/.f64 (.f64 b b) (.f64 a a))

rewrite49.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

65× egg-rr

Counts

2 → 65

Calls

2 calls:

48.0ms	((/.f64 (.f64 b b) (.f64 a a)) (log1p.f64 (neg.f64 (/.f64 (.f64 b b) (.f64 a a)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	171	16
2	1934	16
3	5252	16
0	0	0
1	0	0

simplify67.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
373×	`neg-mul-1_binary64`
343×	`sub-neg_binary64`
233×	`fma-def_binary64`
221×	`distribute-rgt-neg-in_binary64`

Counts

113 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	1093
1	240	1065
2	705	1027
3	2760	1027
4	4745	982
5	5173	982

prune76.0ms (2.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	95	2	97

Error

Counts

97 → 2

Alt Table

Status	Error	Program
✓	13.8b	(exp.f64 (.f64 (log1p.f64 (neg.f64 (/.f64 (.f64 b b) (*.f64 a a)))) 1/2))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))

Compiler

Compiled 1725 to 1212 computations (29.7% saved)

regimes336.0ms (12.1%)

Accuracy

Total -0.0b remaining (-610.5%)

Threshold costs -0.0b (-610.5%)

Counts

49 → 1

Compiler

Compiled 5240 to 3932 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`distribute-neg-in_binary64`
1×	`+-commutative_binary64`
1×	`+-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	20	16
2	22	16
3	21	16

end45.0ms (1.6%)

Compiler: Compiled 53 to 39 computations (26.4% saved)

Details

analyze34.0ms (1.2%)

sample1.1s (38.1%)

simplify47.0ms (1.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series69.0ms (2.5%)

rewrite132.0ms (4.8%)

simplify63.0ms (2.3%)

prune107.0ms (3.8%)

localize8.0ms (0.3%)

series50.0ms (1.8%)

rewrite80.0ms (2.9%)

simplify58.0ms (2.1%)

prune87.0ms (3.1%)

localize9.0ms (0.3%)

series51.0ms (1.8%)

rewrite75.0ms (2.7%)

simplify95.0ms (3.4%)

prune97.0ms (3.5%)

localize8.0ms (0.3%)

series64.0ms (2.3%)

rewrite49.0ms (1.8%)

simplify67.0ms (2.4%)

prune76.0ms (2.7%)

regimes336.0ms (12.1%)

simplify2.0ms (0.1%)

end45.0ms (1.6%)

Profiling