Details

analyze130.0ms (3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
0%	50%	50%	5
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	9.8%	72.7%	10
18.1%	8.8%	73.1%	11
19.6%	5.2%	75.2%	12
20%	4.5%	75.5%	13
20.7%	2.7%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.6s (37.4%)

Results

1.3s	8256×	body	128	valid
73.0ms	556×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
173×	`cancel-sign-sub-inv_binary64`
156×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	75	19
3	168	19
4	358	19
5	678	19
6	901	19
7	1446	19
8	1914	19
9	1873	19
10	1916	19
11	1915	19
12	1912	19
13	2465	19
14	2465	19
15	2321	19

Stop Event

saturated

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 9 -3)
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series200.0ms (4.6%)

Counts

4 → 50

Calls

4 calls:

167.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
25.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
6.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite79.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`prod-diff_binary64`
237×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Counts

4 → 127

Calls

4 calls:

76.0ms	(fma.f64 a 9 -3)
76.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
76.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
76.0ms	(sqrt.f64 (fma.f64 a 9 -3))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	286	40
2	3481	40
3	4837	40

Stop Event

node limit

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

689×	`fma-neg_binary64`
397×	`associate-+l+_binary64`
381×	`fma-def_binary64`
282×	`associate-/l*_binary64`
276×	`times-frac_binary64`

Counts

177 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1065
1	320	1019
2	1084	867
3	4794	849
4	5374	849

Stop Event

node limit

prune350.0ms (8.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	157	7	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Error

0.0b

Counts

166 → 7

Alt Table

Status	Error	Program
	1.8b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2)))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	33.4b	(/.f64 (*.f64 (fma.f64 a a -1/9) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (+.f64 a 1/3))
	32.8b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 2)))
	0.1b	(+.f64 a (+.f64 -1/3 (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (-.f64 a 1/3))))
	1.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 a 9 -3)))))))
	10.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))

Compiler

Compiled 3679 to 2860 computations (22.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.2b	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.5b	(/.f64 1 (fma.f64 a 9 -3))

series50.0ms (1.2%)

Counts

4 → 36

Calls

4 calls:

28.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
10.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
9.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite69.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
209×	`prod-diff_binary64`
194×	`log-pow_binary64`

Counts

4 → 146

Calls

4 calls:

66.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
66.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
66.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
66.0ms	(/.f64 1 (fma.f64 a 9 -3))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	278	46
2	3109	46
3	5540	46

Stop Event

node limit

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
635×	`fma-def_binary64`
457×	`times-frac_binary64`
317×	`associate-/l*_binary64`
204×	`associate-l_binary64`

Counts

182 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	1003
1	414	851
2	1335	772
3	4839	766
4	5464	766

Stop Event

node limit

prune242.0ms (5.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	189	6	195

Error

0.0b

Counts

195 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f64 a (fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))
	33.4b	(/.f64 (*.f64 (fma.f64 a a -1/9) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (+.f64 a 1/3))
	32.8b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 2)))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3))
	0.1b	(+.f64 a (+.f64 -1/3 (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (-.f64 a 1/3))))
	10.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))

Compiler

Compiled 4662 to 3611 computations (22.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a 9 -3)
✓	0.2b	(fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3)
✓	0.3b	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
✓	0.4b	(pow.f64 (fma.f64 a 9 -3) -1/2)

series44.0ms (1%)

Counts

3 → 32

Calls

3 calls:

28.0ms	(fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3)
11.0ms	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
4.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite64.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
209×	`prod-diff_binary64`
184×	`log-pow_binary64`

Counts

3 → 99

Calls

3 calls:

62.0ms	(fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3)
62.0ms	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
62.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	266	40
2	2975	40
3	5246	40

Stop Event

node limit

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-def_binary64`
581×	`fma-neg_binary64`
449×	`times-frac_binary64`
307×	`associate-/l*_binary64`
298×	`associate-+l+_binary64`

Counts

131 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1167
1	389	996
2	1181	879
3	4609	873
4	5077	873

Stop Event

node limit

prune215.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	175	6	181

Error

0.0b

Counts

181 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 a (fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))
	33.4b	(/.f64 (*.f64 (fma.f64 a a -1/9) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (+.f64 a 1/3))
	32.8b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 2)))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3))
	0.1b	(+.f64 a (+.f64 -1/3 (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (-.f64 a 1/3))))
	10.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))

Compiler

Compiled 4635 to 3628 computations (21.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a 9 -3)
✓	0.2b	(fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)
✓	0.3b	(/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3)))
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series36.0ms (0.8%)

Counts

2 → 20

Calls

2 calls:

27.0ms	(fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)
9.0ms	(/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3)))

rewrite59.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

491×	`log-prod_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
174×	`log-pow_binary64`
114×	`add-sqr-sqrt_binary64`

Counts

2 → 62

Calls

2 calls:

58.0ms	(fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)
58.0ms	(/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	238	30
2	2811	30
3	4908	30

Stop Event

node limit

simplify59.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-neg_binary64`
394×	`fma-def_binary64`
391×	`times-frac_binary64`
307×	`cancel-sign-sub-inv_binary64`
261×	`associate-/l*_binary64`

Counts

82 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	680
1	263	537
2	837	488
3	3556	467
4	4896	467
5	5008	467

Stop Event

node limit

prune154.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	145	7	152

Error

Counts

152 → 7

Alt Table

Status	Error	Program
	28.9b	(+.f64 a (fma.f64 rand (*.f64 (cbrt.f64 (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3)))) (cbrt.f64 (/.f64 (pow.f64 (+.f64 a -1/3) 2) (fma.f64 a 9 -3)))) -1/3))
	10.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))
	33.4b	(/.f64 (*.f64 (fma.f64 a a -1/9) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (+.f64 a 1/3))
	32.8b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 2)))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3))
	0.1b	(+.f64 a (+.f64 -1/3 (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (-.f64 a 1/3))))

Compiler

Compiled 3238 to 2508 computations (22.5% saved)

regimes510.0ms (11.8%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

115 → 1

Compiler

Compiled 9018 to 7206 computations (20.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	16	21
2	16	21

Stop Event

saturated

end124.0ms (2.9%)

Compiler: Compiled 182 to 142 computations (22% saved)

Details

analyze130.0ms (3%)

sample1.6s (37.4%)

simplify96.0ms (2.2%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series200.0ms (4.6%)

rewrite79.0ms (1.8%)

simplify61.0ms (1.4%)

prune350.0ms (8.1%)

localize11.0ms (0.2%)

series50.0ms (1.2%)

rewrite69.0ms (1.6%)

simplify67.0ms (1.6%)

prune242.0ms (5.6%)

localize11.0ms (0.3%)

series44.0ms (1%)

rewrite64.0ms (1.5%)

simplify61.0ms (1.4%)

prune215.0ms (5%)

localize10.0ms (0.2%)

series36.0ms (0.8%)

rewrite59.0ms (1.4%)

simplify59.0ms (1.4%)

prune154.0ms (3.5%)

regimes510.0ms (11.8%)

simplify2.0ms (0%)

end124.0ms (2.9%)

Profiling