Details

analyze151.0ms (3.9%)

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 (37.6%)

Results

1.1s	8256×	body	128	valid
75.0ms	560×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify87.0ms (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`

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

1×

saturated

Counts

1 → 2

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

series85.0ms (2.2%)

Counts

4 → 50

Calls

4 calls:

56.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
20.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
7.0ms	(sqrt.f64 (fma.f64 a 9 -3))
1.0ms	(fma.f64 a 9 -3)

rewrite67.0ms (1.7%)

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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 127

Calls

4 calls:

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

simplify58.0ms (1.5%)

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`

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

1×	node limit

Counts

177 → 164

prune199.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	159	5	164
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	160	6	166

Error

0.0b

Counts

166 → 6

Alt Table

Status	Error	Program
	9.1b	(-.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 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.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))))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
	8.4b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (-.f64 a 1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3636 to 2826 computations (22.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(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))))
✓	0.2b	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
✓	0.4b	(pow.f64 (fma.f64 a 9 -3) -1/2)

series55.0ms (1.4%)

Counts

3 → 46

Calls

3 calls:

27.0ms	(*.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))))
4.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite66.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`prod-diff_binary64`
251×	`log1p-udef_binary64`
145×	`add-sqr-sqrt_binary64`
142×	`log1p-expm1-u_binary64`
142×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 74

Calls

3 calls:

65.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
65.0ms	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
65.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

simplify47.0ms (1.2%)

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`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

120 → 120

prune180.0ms (4.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

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

Error

0.0b

Counts

159 → 6

Alt Table

Status	Error	Program
	9.1b	(-.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 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.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))))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
	8.4b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (-.f64 a 1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3838 to 3047 computations (20.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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))

series48.0ms (1.2%)

Counts

4 → 36

Calls

4 calls:

27.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
9.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
7.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
4.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite73.0ms (1.9%)

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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 146

Calls

4 calls:

70.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
70.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
70.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
70.0ms	(/.f64 1 (fma.f64 a 9 -3))

simplify57.0ms (1.5%)

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`

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

1×	node limit

Counts

182 → 188

prune252.0ms (6.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	188	6	194

Error

Counts

194 → 6

Alt Table

Status	Error	Program
	9.1b	(-.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 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
▶	0.1b	(+.f64 a (fma.f64 rand (fma.f64 a (pow.f64 (fma.f64 a 9 -3) -1/2) (/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3)))) -1/3))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -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))))
	8.4b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (-.f64 a 1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4649 to 3604 computations (22.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 a (pow.f64 (fma.f64 a 9 -3) -1/2) (/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3))))
	0.4b	(pow.f64 (fma.f64 a 9 -3) -1/2)
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.4b	(/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3)))

series20.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

10.0ms	(fma.f64 a (pow.f64 (fma.f64 a 9 -3) -1/2) (/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3))))
9.0ms	(/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3)))

rewrite62.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

418×	`log-prod_binary64`
271×	`pow2_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
186×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	237	31
2	2468	31
3	4947	31
4	4846	31

Stop Event

1×	node limit

Counts

2 → 57

Calls

2 calls:

61.0ms	(fma.f64 a (pow.f64 (fma.f64 a 9 -3) -1/2) (/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3))))
60.0ms	(/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3)))

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

845×	`associate-/l*_binary64`
544×	`associate-+l+_binary64`
444×	`fma-def_binary64`
434×	`associate-+r+_binary64`
186×	`+-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	440
1	252	417
2	769	355
3	3481	302
4	5645	302

Stop Event

1×	node limit

Counts

69 → 78

prune202.0ms (5.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	147	6	153

Error

Counts

153 → 6

Alt Table

Status	Error	Program
	9.1b	(-.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 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(+.f64 a (fma.f64 rand (fma.f64 a (pow.f64 (fma.f64 a 9 -3) -1/2) (/.f64 -1/3 (sqrt.f64 (fma.f64 a 9 -3)))) -1/3))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -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))))
	8.4b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (-.f64 a 1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4353 to 3461 computations (20.5% saved)

regimes526.0ms (13.5%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Counts

121 → 1

Compiler

Compiled 9434 to 7454 computations (21% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`distribute-rgt-neg-in_binary64`
21×	`cancel-sign-sub-inv_binary64`
15×	`distribute-neg-in_binary64`
13×	`distribute-lft-neg-in_binary64`
13×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	24	22
2	42	22
3	71	22
4	98	22
5	118	22
6	133	22
7	137	22
8	139	22
9	140	22
10	134	22

Stop Event

1×

saturated

end108.0ms (2.8%)

Compiler: Compiled 162 to 128 computations (21% saved)

Iter	Nodes	Cost
0	13	22
1	24	22
2	42	22
3	71	22
4	98	22
5	118	22
6	133	22
7	137	22
8	139	22
9	140	22
10	134	22

Iter	Nodes	Cost
0	13	22
1	24	22
2	42	22
3	71	22
4	98	22
5	118	22
6	133	22
7	137	22
8	139	22
9	140	22
10	134	22

Details

analyze151.0ms (3.9%)

sample1.5s (37.6%)

simplify87.0ms (2.2%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series85.0ms (2.2%)

rewrite67.0ms (1.7%)

simplify58.0ms (1.5%)

prune199.0ms (5.1%)

localize10.0ms (0.3%)

series55.0ms (1.4%)

rewrite66.0ms (1.7%)

simplify47.0ms (1.2%)

prune180.0ms (4.6%)

localize10.0ms (0.2%)

series48.0ms (1.2%)

rewrite73.0ms (1.9%)

simplify57.0ms (1.5%)

prune252.0ms (6.5%)

localize13.0ms (0.3%)

series20.0ms (0.5%)

rewrite62.0ms (1.6%)

simplify44.0ms (1.1%)

prune202.0ms (5.2%)

regimes526.0ms (13.5%)

simplify4.0ms (0.1%)

end108.0ms (2.8%)

Profiling

Iter	Nodes	Cost
0	13	22
1	24	22
2	42	22
3	71	22
4	98	22
5	118	22
6	133	22
7	137	22
8	139	22
9	140	22
10	134	22