Details

analyze137.0ms (4.4%)

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%	10.1%	72.3%	10
18.1%	9.2%	72.7%	11
19.6%	5.5%	74.9%	12
20%	4.8%	75.2%	13
20.7%	2.8%	76.5%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.3s (40.6%)

Results

1.2s	8256×	body	128	valid
77.0ms	598×	body	128	invalid

Compiler

Compiled 46 to 40 computations (13% saved)

preprocess46.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

692×	`fma-def_binary64`
438×	`fma-neg_binary64`
227×	`sub-neg_binary64`
210×	`distribute-rgt-neg-in_binary64`
204×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	52	42
2	141	38
3	395	38
4	1005	38
5	1898	38
6	2873	38
7	4197	38
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify69.0ms (2.2%)

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 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 (0.3%)

Local error

Found 4 expressions with local error:

New	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)))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
✓	0.2b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
✓	0.6b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

series61.0ms (2%)

Counts

4 → 41

Calls

18 calls:

5.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))	a	-inf
5.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))	a	inf
5.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)	a	inf
5.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)	rand	-inf
4.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))	a	0

rewrite108.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`prod-diff_binary64`
142×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`
137×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	308	49
2	3888	49

Stop Event

1×	node limit

Counts

4 → 126

simplify43.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

549×	`fma-def_binary64`
374×	`associate-/l*_binary64`
332×	`times-frac_binary64`
239×	`associate-r_binary64`
236×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1029
1	397	973
2	1459	905

Stop Event

1×	node limit

Counts

167 → 165

prune178.0ms (5.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	159	6	165
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	6	167

Error

Counts

167 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (pow.f64 (cbrt.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 3)))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand (pow.f64 (+.f64 (.f64 a 9) -3) 1/4)) (pow.f64 (+.f64 (*.f64 a 9) -3) 1/4))))
	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 rand (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))
▶	0.1b	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
	7.8b	(+.f64 a (+.f64 -1/3 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))))

Compiler

Compiled 4129 to 3368 computations (18.4% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 -1/3 a))
✓	0.1b	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
✓	0.2b	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))

series33.0ms (1.1%)

Counts

3 → 38

Calls

15 calls:

5.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))	a	inf
4.0ms	(sqrt.f64 (+.f64 -1/3 a))	a	-inf
3.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))	a	-inf
3.0ms	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))	a	inf
3.0ms	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))	a	-inf

rewrite48.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

860×	`log1p-expm1-u_binary64`
860×	`expm1-log1p-u_binary64`
165×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	191	31
2	2281	31

Stop Event

1×	node limit

Counts

3 → 65

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

585×	`associate-/r*_binary64`
369×	`associate-/r/_binary64`
324×	`fma-neg_binary64`
288×	`associate-/l/_binary64`
182×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	661
1	200	621
2	651	607
3	2612	583

Stop Event

1×	node limit

Counts

103 → 97

prune84.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Error

Counts

103 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 1/3 (*.f64 rand (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))) 3)) (+.f64 -1/3 a))
✓	0.1b	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 rand (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))
▶	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))))
	0.1b	(+.f64 -1/3 (fma.f64 rand (*.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) a))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))

Compiler

Compiled 1806 to 1420 computations (21.4% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 -1/3 a))
✓	0.0b	(+.f64 (+.f64 -1/3 a) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))))
✓	0.3b	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))
✓	0.3b	(*.f64 1/3 rand)

series42.0ms (1.4%)

Counts

3 → 34

Calls

15 calls:

13.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))	rand	inf
4.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))	a	inf
4.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))	a	-inf
3.0ms	(+.f64 (+.f64 -1/3 a) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))))	rand	-inf
3.0ms	(+.f64 (+.f64 -1/3 a) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))))	a	inf

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

513×	`log-prod_binary64`
465×	`fma-def_binary64`
200×	`fma-neg_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	224	32
2	2988	32

Stop Event

1×	node limit

Counts

3 → 109

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-/l*_binary64`
671×	`cancel-sign-sub-inv_binary64`
394×	`associate-/r*_binary64`
274×	`fma-neg_binary64`
234×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	615
1	139	585
2	436	573
3	1757	568

Stop Event

1×	node limit

Counts

143 → 132

prune156.0ms (5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	164	6	170

Error

Counts

170 → 6

Alt Table

Status	Error	Program
	0.3b	(fma.f64 1/3 (*.f64 rand (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))) 3)) (+.f64 -1/3 a))
✓	0.1b	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 rand (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))
✓	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))))
▶	0.1b	(+.f64 -1/3 (fma.f64 rand (*.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) a))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))

Compiler

Compiled 3263 to 2540 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 a -1/3))
✓	0.1b	(fma.f64 rand (*.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) a)
✓	0.4b	(*.f64 1/3 (sqrt.f64 (+.f64 a -1/3)))

series27.0ms (0.9%)

Counts

3 → 26

Calls

12 calls:

3.0ms	(fma.f64 rand (*.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) a)	rand	-inf
3.0ms	(*.f64 1/3 (sqrt.f64 (+.f64 a -1/3)))	a	-inf
3.0ms	(*.f64 1/3 (sqrt.f64 (+.f64 a -1/3)))	a	inf
2.0ms	(fma.f64 rand (*.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) a)	a	-inf
2.0ms	(fma.f64 rand (*.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) a)	a	inf

rewrite52.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`log1p-expm1-u_binary64`
849×	`expm1-log1p-u_binary64`
146×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	191	28
2	2260	28

Stop Event

1×	node limit

Counts

3 → 61

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

711×	`associate-*l/_binary64`
566×	`associate-/r*_binary64`
297×	`associate-/r/_binary64`
274×	`associate-/l/_binary64`
263×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	495
1	189	455
2	587	445
3	2259	417

Stop Event

1×	node limit

Counts

87 → 88

prune109.0ms (3.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	88	6	94

Error

Counts

94 → 6

Alt Table

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

Compiler

Compiled 1602 to 1267 computations (20.9% saved)

regimes369.0ms (11.8%)

Accuracy

Total 0.1b remaining (87.1%)

Threshold costs 0.1b (87.1%)

Counts

70 → 1

Compiler

Compiled 4862 to 4026 computations (17.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16

Stop Event

1×

saturated

end97.0ms (3.1%)

Stop Event

1×

fuel

Compiler

Compiled 120 to 96 computations (20% saved)

Details

analyze137.0ms (4.4%)

sample1.3s (40.6%)

preprocess46.0ms (1.5%)

simplify69.0ms (2.2%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series61.0ms (2%)

rewrite108.0ms (3.5%)

simplify43.0ms (1.4%)

prune178.0ms (5.7%)

localize6.0ms (0.2%)

series33.0ms (1.1%)

rewrite48.0ms (1.5%)

simplify34.0ms (1.1%)

prune84.0ms (2.7%)

localize6.0ms (0.2%)

series42.0ms (1.4%)

rewrite61.0ms (1.9%)

simplify34.0ms (1.1%)

prune156.0ms (5%)

localize7.0ms (0.2%)

series27.0ms (0.9%)

rewrite52.0ms (1.7%)

simplify34.0ms (1.1%)

prune109.0ms (3.5%)

regimes369.0ms (11.8%)

simplify2.0ms (0.1%)

end97.0ms (3.1%)

Profiling