Details

analyze130.0ms (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 (29.4%)

Results

1.2s	8256×	body	128	valid
85.0ms	553×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify99.0ms (1.9%)

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)))
▶	0.2b	(*.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))

series59.0ms (1.2%)

Counts

4 → 50

Calls

4 calls:

28.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
23.0ms	(*.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)

rewrite77.0ms (1.5%)

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 → 131

Calls

4 calls:

71.0ms	(fma.f64 a 9 -3)
71.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
71.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
71.0ms	(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

simplify58.0ms (1.1%)

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

181 → 167

Iterations

Useful iterations: 3 (0.0ms)

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

prune252.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	160	7	167
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	161	8	169

Error

0.0b

Counts

169 → 8

Alt Table

Status	Error	Program
	8.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (cbrt.f64 (/.f64 (*.f64 rand rand) (fma.f64 a 9 -3))))))
	42.6b	(/.f64 (.f64 (+.f64 (pow.f64 a 3) -1/27) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (fma.f64 a a (+.f64 1/9 (.f64 a 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))))
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
▶	0.1b	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	11.8b	(-.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))

Compiler

Compiled 3759 to 2922 computations (22.3% saved)

localize10.0ms (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 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
✓	0.4b	(pow.f64 (fma.f64 a 9 -3) -1/2)

series144.0ms (2.8%)

Counts

3 → 60

Calls

3 calls:

74.0ms	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
66.0ms	(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
5.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite56.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log-prod_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
184×	`log-pow_binary64`
129×	`add-sqr-sqrt_binary64`

Counts

3 → 79

Calls

3 calls:

54.0ms	(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
54.0ms	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
54.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	275	38
2	2933	38
3	4781	38

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-l_binary64`
352×	`times-frac_binary64`
342×	`associate-r_binary64`
251×	`sub-neg_binary64`
237×	`fma-neg_binary64`

Counts

139 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2271
1	546	2155
2	1688	1801
3	4746	1519
4	4975	1519

prune267.0ms (5.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	192	2	194
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	196	6	202

Error

0.0b

Counts

202 → 6

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
▶	0.1b	(fma.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1) (*.f64 -1/3 (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1)))
	0.8b	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (/.f64 -9 (/.f64 -1 a)) -1/2) 1))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	11.8b	(-.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))

Compiler

Compiled 4643 to 3717 computations (19.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series274.0ms (5.4%)

Counts

3 → 72

Calls

3 calls:

132.0ms

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

71.0ms

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

70.0ms

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

rewrite94.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

482×	`log-prod_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
190×	`pow3_binary64`
179×	`log-pow_binary64`

Counts

3 → 78

Calls

3 calls:

92.0ms

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

92.0ms

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

92.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	57
1	264	45
2	2695	45
3	4915	45
4	4784	45

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-neg_binary64`
390×	`times-frac_binary64`
241×	`distribute-neg-in_binary64`
234×	`distribute-rgt-in_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

150 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2645
1	682	2513
2	2247	2130
3	4788	2100
4	4989	2100

prune778.0ms (15.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	310	7	317

Error

0.0b

Counts

317 → 7

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(fma.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1) (*.f64 -1/3 (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1)))
	37.3b	(/.f64 (-.f64 (.f64 (.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1)) (.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1))) (.f64 1/9 (pow.f64 (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1) 2))) (-.f64 (.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1)) (.f64 -1/3 (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1))))
	0.8b	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (/.f64 -9 (/.f64 -1 a)) -1/2) 1))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	11.8b	(-.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))

Compiler

Compiled 10443 to 8304 computations (20.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.1b	(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))

series53.0ms (1%)

Counts

4 → 36

Calls

4 calls:

30.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
11.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
10.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite82.0ms (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 → 148

Calls

4 calls:

79.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
79.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
79.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
79.0ms	(/.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

simplify63.0ms (1.2%)

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

184 → 190

Iterations

Useful iterations: 3 (0.0ms)

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

prune261.0ms (5.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	189	8	197

Error

Counts

197 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(fma.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1) (*.f64 -1/3 (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1)))
	37.3b	(/.f64 (-.f64 (.f64 (.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1)) (.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1))) (.f64 1/9 (pow.f64 (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1) 2))) (-.f64 (.f64 a (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1)) (.f64 -1/3 (fma.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand 1))))
	0.8b	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (/.f64 -9 (/.f64 -1 a)) -1/2) 1))
	11.8b	(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.8b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3))

Compiler

Compiled 4640 to 3594 computations (22.5% saved)

regimes458.0ms (9%)

Accuracy

Total 0.1b remaining (83.8%)

Threshold costs 0.1b (83.8%)

Counts

105 → 1

Compiler

Compiled 7418 to 5946 computations (19.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	16	30
2	15	30

end166.0ms (3.3%)

Compiler: Compiled 234 to 185 computations (20.9% saved)

Details

analyze130.0ms (2.6%)

sample1.5s (29.4%)

simplify99.0ms (1.9%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series59.0ms (1.2%)

rewrite77.0ms (1.5%)

simplify58.0ms (1.1%)

prune252.0ms (5%)

localize10.0ms (0.2%)

series144.0ms (2.8%)

rewrite56.0ms (1.1%)

simplify76.0ms (1.5%)

prune267.0ms (5.2%)

localize14.0ms (0.3%)

series274.0ms (5.4%)

rewrite94.0ms (1.8%)

simplify89.0ms (1.7%)

prune778.0ms (15.3%)

localize11.0ms (0.2%)

series53.0ms (1%)

rewrite82.0ms (1.6%)

simplify63.0ms (1.2%)

prune261.0ms (5.1%)

regimes458.0ms (9%)

simplify2.0ms (0%)

end166.0ms (3.3%)

Profiling