Details

analyze118.0ms (3.4%)

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)

sample1.2s (35.8%)

Results

1.1s	8256×	body	128	valid
69.0ms	560×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify68.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
177×	`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	82	19
3	199	19
4	510	19
5	969	19
6	1470	19
7	2421	19
8	3626	19
9	4073	19
10	4231	19
11	4272	19
12	4275	19
13	4828	19
14	4828	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 (/.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)

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))

series72.0ms (2.1%)

Counts

4 → 50

Calls

4 calls:

38.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
26.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
6.0ms	(sqrt.f64 (fma.f64 a 9 -3))
1.0ms	(fma.f64 a 9 -3)

rewrite66.0ms (1.9%)

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	288	40
2	3706	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))

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

374×	`fma-def_binary64`
347×	`associate-+l+_binary64`
282×	`associate-/l*_binary64`
276×	`times-frac_binary64`
231×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1065
1	321	1019
2	1143	867

Stop Event

1×	node limit

Counts

177 → 164

prune206.0ms (5.9%)

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
	0.1b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))
	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)))))
	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))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (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))))

Compiler

Compiled 3639 to 2839 computations (22% 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)

series90.0ms (2.6%)

Counts

3 → 46

Calls

3 calls:

56.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
29.0ms	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
4.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite54.0ms (1.6%)

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	309	37
2	3746	37

Stop Event

1×	node limit

Counts

3 → 74

Calls

3 calls:

53.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
53.0ms	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
53.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

simplify33.0ms (1%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-def_binary64`
398×	`associate-+l+_binary64`
283×	`times-frac_binary64`
275×	`associate-/l*_binary64`
234×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1410
1	400	1342
2	1341	1122

Stop Event

1×	node limit

Counts

120 → 121

prune215.0ms (6.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	154	6	160

Error

0.0b

Counts

160 → 6

Alt Table

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

Compiler

Compiled 3858 to 3074 computations (20.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.3b	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))
✓	0.5b	(/.f64 1 (fma.f64 a 9 -3))

series51.0ms (1.5%)

Counts

4 → 36

Calls

4 calls:

29.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -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))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite67.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
209×	`prod-diff_binary64`
194×	`log-pow_binary64`
156×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	280	45
2	3416	45

Stop Event

1×	node limit

Counts

4 → 140

Calls

4 calls:

65.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
65.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
65.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))
64.0ms	(/.f64 1 (fma.f64 a 9 -3))

simplify32.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-def_binary64`
457×	`times-frac_binary64`
360×	`associate-+l+_binary64`
317×	`associate-/l*_binary64`
179×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	861
1	380	818
2	1290	769

Stop Event

1×	node limit

Counts

176 → 179

prune236.0ms (6.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	179	6	185

Error

Counts

185 → 6

Alt Table

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

Compiler

Compiled 4446 to 3466 computations (22% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a 9 -3)
✓	0.3b	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
✓	0.3b	(.f64 rand (.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)

series40.0ms (1.1%)

Counts

2 → 20

Calls

2 calls:

29.0ms	(.f64 rand (.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)))
11.0ms	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))

rewrite55.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	267	31
2	3261	31

Stop Event

1×	node limit

Counts

2 → 85

Calls

2 calls:

53.0ms	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
53.0ms	(.f64 rand (.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)))

simplify44.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

465×	`associate-/l/_binary64`
391×	`times-frac_binary64`
322×	`fma-def_binary64`
272×	`fma-neg_binary64`
261×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	540
1	226	506
2	769	487
3	3431	469

Stop Event

1×	node limit

Counts

105 → 103

prune211.0ms (6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	176	6	182

Error

Counts

182 → 6

Alt Table

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

Compiler

Compiled 4646 to 3673 computations (20.9% saved)

regimes389.0ms (11.1%)

Accuracy

Total 0.1b remaining (84.2%)

Threshold costs 0.1b (84.2%)

Counts

89 → 1

Compiler

Compiled 6830 to 5434 computations (20.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	20	19
2	21	19

Stop Event

1×

saturated

end109.0ms (3.1%)

Compiler: Compiled 143 to 114 computations (20.3% saved)

Details

analyze118.0ms (3.4%)

sample1.2s (35.8%)

simplify68.0ms (2%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series72.0ms (2.1%)

rewrite66.0ms (1.9%)

simplify31.0ms (0.9%)

prune206.0ms (5.9%)

localize10.0ms (0.3%)

series90.0ms (2.6%)

rewrite54.0ms (1.6%)

simplify33.0ms (1%)

prune215.0ms (6.2%)

localize15.0ms (0.4%)

series51.0ms (1.5%)

rewrite67.0ms (1.9%)

simplify32.0ms (0.9%)

prune236.0ms (6.8%)

localize13.0ms (0.4%)

series40.0ms (1.1%)

rewrite55.0ms (1.6%)

simplify44.0ms (1.3%)

prune211.0ms (6%)

regimes389.0ms (11.1%)

simplify2.0ms (0.1%)

end109.0ms (3.1%)

Profiling