Details

analyze126.0ms (2.8%)

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)

sample1.5s (33.6%)

Results

1.1s	8256×	body	128	valid
113.0ms	548×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify94.0ms (2.1%)

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

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 (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize9.0ms (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)))))
✓	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series69.0ms (1.6%)

Counts

4 → 50

Calls

4 calls:

30.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
29.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
8.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite115.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

127× egg-rr

Counts

4 → 127

Calls

2 calls:

113.0ms	((/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (fma.f64 a 9 -3)) (*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (fma.f64 a 9 -3))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify72.0ms (1.6%)

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 → 163

Iterations

Useful iterations: 3 (0.0ms)

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

prune419.0ms (9.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	157	6	163
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	6	165

Error

0.0b

Counts

165 → 6

Alt Table

Status	Error	Program
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
	7.7b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (cbrt.f64 (.f64 rand rand)) (.f64 (cbrt.f64 rand) (pow.f64 (fma.f64 a 9 -3) -1/2)))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
	34.1b	(/.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))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.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 3641 to 2830 computations (22.3% saved)

localize11.0ms (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 (pow.f64 (fma.f64 a 9 -3) -1/2))))
✓	0.1b	(pow.f64 (fma.f64 a 9 -3) -1/2)
✓	0.3b	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))

series62.0ms (1.4%)

Counts

3 → 46

Calls

3 calls:

31.0ms	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
24.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
6.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite66.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

74× egg-rr

Counts

3 → 74

Calls

2 calls:

64.0ms	((.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2)) (pow.f64 (fma.f64 a 9 -3) -1/2) (.f64 (-.f64 a 1/3) (+.f64 1 (*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	308	37
2	3503	37
3	4827	37
0	0	0
1	0	0

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-def_binary64`
442×	`associate-+l+_binary64`
283×	`times-frac_binary64`
274×	`associate-/l*_binary64`
234×	`associate-r_binary64`

Counts

120 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1410
1	399	1342
2	1278	1122
3	4975	1122

prune275.0ms (6.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	153	6	159

Error

0.0b

Counts

159 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
	34.1b	(/.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))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.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))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3) -1/2))))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))

Compiler

Compiled 3846 to 3059 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
✓	0.2b	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
✓	0.3b	(/.f64 1 (fma.f64 9 a -3))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))

series58.0ms (1.3%)

Counts

4 → 36

Calls

4 calls:

31.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
12.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
10.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
3.0ms	(/.f64 1 (fma.f64 9 a -3))

rewrite150.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

146× egg-rr

Counts

4 → 146

Calls

2 calls:

147.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	278	46
2	3110	46
3	5540	46
0	0	0
1	0	0

simplify58.0ms (1.3%)

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

prune277.0ms (6.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
	0.9b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
	45.1b	(+.f64 a (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 9 a -3))) rand -1/3)) 2))
	34.1b	(/.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))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.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))
▶	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))

Compiler

Compiled 4664 to 3614 computations (22.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (fma.f64 a 9 -3) 1/4)
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
✓	0.2b	(/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2)

series95.0ms (2.1%)

Counts

4 → 58

Calls

4 calls:

48.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
30.0ms	(/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))
12.0ms	(pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2)
5.0ms	(pow.f64 (fma.f64 a 9 -3) 1/4)

rewrite80.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

118× egg-rr

Counts

4 → 118

Calls

2 calls:

78.0ms

((pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2) (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2)) (*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2)))) (pow.f64 (fma.f64 a 9 -3) 1/4))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	359	43
2	3993	43
3	4857	43
0	0	0
1	0	0

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
430×	`fma-neg_binary64`
390×	`cancel-sign-sub-inv_binary64`
387×	`times-frac_binary64`
183×	`sub-neg_binary64`

Counts

176 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1979
1	567	1885
2	1907	1501
3	4634	1275
4	4962	1275

prune198.0ms (4.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	189	7	196

Error

0.0b

Counts

196 → 7

Alt Table

Status	Error	Program
	0.9b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
	45.1b	(+.f64 a (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 9 a -3))) rand -1/3)) 2))
	34.1b	(/.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))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.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))
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))

Compiler

Compiled 4710 to 3754 computations (20.3% saved)

regimes437.0ms (9.9%)

Accuracy

Total 0.1b remaining (83.8%)

Threshold costs 0.1b (83.8%)

Counts

102 → 1

Compiler

Compiled 7982 to 6362 computations (20.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	14	20
2	14	20

end117.0ms (2.7%)

Compiler: Compiled 169 to 132 computations (21.9% saved)

Details

analyze126.0ms (2.8%)

sample1.5s (33.6%)

simplify94.0ms (2.1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series69.0ms (1.6%)

rewrite115.0ms (2.6%)

simplify72.0ms (1.6%)

prune419.0ms (9.5%)

localize11.0ms (0.2%)

series62.0ms (1.4%)

rewrite66.0ms (1.5%)

simplify42.0ms (1%)

prune275.0ms (6.2%)

localize10.0ms (0.2%)

series58.0ms (1.3%)

rewrite150.0ms (3.4%)

simplify58.0ms (1.3%)

prune277.0ms (6.3%)

localize15.0ms (0.3%)

series95.0ms (2.1%)

rewrite80.0ms (1.8%)

simplify72.0ms (1.6%)

prune198.0ms (4.5%)

regimes437.0ms (9.9%)

simplify2.0ms (0%)

end117.0ms (2.7%)

Profiling