Details

analyze122.0ms (2.6%)

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 (32.5%)

Results

1.2s	8256×	body	128	valid
83.0ms	565×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify103.0ms (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

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)

localize9.0ms (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)))))
✓	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.3b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series71.0ms (1.5%)

Counts

4 → 50

Calls

4 calls:

34.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
26.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
9.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite75.0ms (1.6%)

Algorithm

2×	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:

73.0ms	(fma.f64 a 9 -3)
73.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
73.0ms	(sqrt.f64 (fma.f64 a 9 -3))
73.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

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

simplify58.0ms (1.2%)

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

prune195.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	6	163
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	158	7	165

Error

0.0b

Counts

165 → 7

Alt Table

Status	Error	Program
	33.1b	(/.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 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	8.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (cbrt.f64 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.8b	(-.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 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3664 to 2850 computations (22.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series174.0ms (3.7%)

Counts

3 → 60

Calls

3 calls:

86.0ms	(*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
82.0ms	(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
5.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite59.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

555×	`unpow-prod-down_binary64`
428×	`log-prod_binary64`
280×	`pow2_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`

Counts

3 → 93

Calls

3 calls:

57.0ms	(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
57.0ms	(*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
57.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	243	35
2	2421	35
3	5452	35
0	0	0
1	0	0

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

912×	`fma-neg_binary64`
380×	`associate-l_binary64`
345×	`associate-r_binary64`
256×	`times-frac_binary64`
221×	`associate-/l*_binary64`

Counts

153 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	2100
1	562	2002
2	1757	1736
3	5000	1730
4	5855	1730

prune543.0ms (11.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	360	7	367

Error

0.0b

Counts

367 → 7

Alt Table

Status	Error	Program
	33.1b	(/.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 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	8.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (cbrt.f64 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.8b	(-.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 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 12557 to 10150 computations (19.2% 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)
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
✓	0.3b	(/.f64 1 (fma.f64 9 a -3))

series60.0ms (1.3%)

Counts

4 → 36

Calls

4 calls:

34.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
13.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
11.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
3.0ms	(/.f64 1 (fma.f64 9 a -3))

rewrite85.0ms (1.8%)

Algorithm

2×	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:

82.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
82.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
82.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
82.0ms	(/.f64 1 (fma.f64 9 a -3))

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

simplify65.0ms (1.4%)

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

prune303.0ms (6.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	188	7	195

Error

0.0b

Counts

195 → 7

Alt Table

Status	Error	Program
	33.1b	(/.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 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	8.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (cbrt.f64 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.8b	(-.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 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4654 to 3609 computations (22.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.3b	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
✓	1.4b	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)

series84.0ms (1.8%)

Counts

3 → 48

Calls

3 calls:

34.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
32.0ms	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)
17.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

rewrite71.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

519×	`prod-diff_binary64`
264×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Counts

3 → 120

Calls

3 calls:

69.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
69.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
69.0ms	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	328	39
2	3811	39
3	5180	39
0	0	0
1	0	0

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

567×	`sub-neg_binary64`
375×	`times-frac_binary64`
315×	`associate-/l*_binary64`
286×	`fma-def_binary64`
285×	`associate--r+_binary64`

Counts

168 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1192
1	295	1112
2	1029	974
3	4710	974
4	5237	974

prune237.0ms (5.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	182	7	189

Error

0.0b

Counts

189 → 7

Alt Table

Status	Error	Program
	33.1b	(/.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 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	7.8b	(-.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 (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 1 rand))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
✓	0.1b	(+.f64 (.f64 a (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4174 to 3295 computations (21.1% saved)

regimes545.0ms (11.7%)

Accuracy

Total 0.1b remaining (84.2%)

Threshold costs 0.1b (84.2%)

Counts

125 → 1

Compiler

Compiled 10034 to 7970 computations (20.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	25	21
2	27	21
3	24	21

end115.0ms (2.5%)

Compiler: Compiled 177 to 142 computations (19.8% saved)

Details

analyze122.0ms (2.6%)

sample1.5s (32.5%)

simplify103.0ms (2.2%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series71.0ms (1.5%)

rewrite75.0ms (1.6%)

simplify58.0ms (1.2%)

prune195.0ms (4.2%)

localize11.0ms (0.2%)

series174.0ms (3.7%)

rewrite59.0ms (1.3%)

simplify81.0ms (1.7%)

prune543.0ms (11.6%)

localize10.0ms (0.2%)

series60.0ms (1.3%)

rewrite85.0ms (1.8%)

simplify65.0ms (1.4%)

prune303.0ms (6.5%)

localize9.0ms (0.2%)

series84.0ms (1.8%)

rewrite71.0ms (1.5%)

simplify61.0ms (1.3%)

prune237.0ms (5.1%)

regimes545.0ms (11.7%)

simplify2.0ms (0%)

end115.0ms (2.5%)

Profiling