Details

analyze613.0ms (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.2%	10.3%	12
55%	30%	15%	13
59.5%	25.3%	15.3%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.2s (11.8%)

Results

917.0ms	7598×	body	128	valid
102.0ms	272×	body	1024	valid
61.0ms	563×	body	128	invalid
58.0ms	217×	body	512	valid
31.0ms	169×	body	256	valid

Compiler

Compiled 34 to 26 computations (23.5% saved)

preprocess31.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

594×	`distribute-rgt-in_binary64`
467×	`distribute-lft-in_binary64`
338×	`associate-+r+_binary64`
314×	`associate-l_binary64`
299×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	64
1	57	56
2	164	56
3	669	48
4	2158	48
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 12 computations (25% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

436×	`unsub-neg_binary64`
376×	`fma-def_binary64`
247×	`distribute-rgt-in_binary64`
216×	`associate-+l+_binary64`
214×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	23	14
2	60	14
3	204	12
4	640	12
5	1991	12
6	3879	12

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (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
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series12.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

1.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)	y	-inf
1.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)	x	-inf
1.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)	x	inf
1.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)	y	inf
1.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)	y	0

rewrite44.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`prod-diff_binary64`
403×	`log-prod_binary64`
204×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	194	17
2	2401	17

Stop Event

1×	node limit

Counts

2 → 55

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1259×	`fma-neg_binary64`
445×	`fma-def_binary64`
153×	`sub-neg_binary64`
122×	`cancel-sign-sub-inv_binary64`
116×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	819
1	121	721
2	316	643
3	760	562
4	1947	562
5	2587	562
6	2877	562
7	2946	562
8	2971	562
9	2973	562
10	4006	562
11	4006	562

Stop Event

1×

saturated

Counts

103 → 75

prune78.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Error

0.0b

Counts

77 → 3

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 1115 to 677 computations (39.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -6 4)
✓	0.0b	(fma.f64 6 z -3)
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(*.f64 y (fma.f64 z -6 4))

series27.0ms (0.3%)

Counts

3 → 72

Calls

18 calls:

6.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))	x	inf
2.0ms	(*.f64 y (fma.f64 z -6 4))	y	-inf
2.0ms	(*.f64 y (fma.f64 z -6 4))	y	inf
2.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))	y	-inf
2.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))	x	-inf

rewrite52.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

467×	`log-prod_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
187×	`pow3_binary64`
176×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	244	29
2	2665	29

Stop Event

1×	node limit

Counts

3 → 77

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1255×	`fma-neg_binary64`
441×	`fma-def_binary64`
151×	`sub-neg_binary64`
122×	`cancel-sign-sub-inv_binary64`
118×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1014
1	122	931
2	316	829
3	757	748
4	1937	748
5	2576	748
6	2857	748
7	2926	748
8	2951	748
9	2953	748
10	3986	748
11	3986	748

Stop Event

1×

saturated

Counts

149 → 100

prune123.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	131	3	134

Error

0.0b

Counts

134 → 3

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
▶	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 2207 to 1595 computations (27.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
✓	0.0b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.2b	(.f64 6 (.f64 y z))
✓	0.2b	(.f64 6 (.f64 z x))

series35.0ms (0.3%)

Counts

4 → 18

Calls

30 calls:

5.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))	z	0
2.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))	x	-inf
2.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))	y	-inf
2.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))	y	inf
2.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))	x	inf

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
172×	`add-cbrt-cube_binary64`
167×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	362	49

Stop Event

1×	node limit

Counts

4 → 123

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
566×	`fma-neg_binary64`
191×	`cancel-sign-sub-inv_binary64`
135×	`associate-l_binary64`
98×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	150
1	107	133
2	265	127
3	595	127
4	1289	127
5	2108	127
6	2744	127
7	3043	127
8	3088	127
9	3098	127
10	3098	127

Stop Event

1×

saturated

Counts

141 → 140

prune124.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	139	4	143

Error

Counts

143 → 4

Alt Table

Status	Error	Program
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
	29.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 (sqrt.f64 (.f64 x 3)) (sqrt.f64 (.f64 x 3)) (.f64 y (*.f64 z 6))))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 4107 to 2596 computations (36.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -6 4)
	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))
✓	0.8b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)

series6.1s (60.9%)

Counts

2 → 24

Calls

18 calls:

3.2s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)	z
2.7s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)	y
81.0ms	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)	x
16.0ms	(cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))	x
14.0ms	(cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))	y

rewrite54.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

469×	`log-prod_binary64`
423×	`prod-diff_binary64`
214×	`fma-def_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	253	26
2	2843	26

Stop Event

1×	node limit

Counts

2 → 73

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

518×	`associate-r_binary64`
467×	`fma-def_binary64`
393×	`fma-neg_binary64`
392×	`associate-l_binary64`
279×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	4677
1	1060	3909
2	4410	3825

Stop Event

1×	node limit

Counts

97 → 113

prune206.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	188	4	192

Error

Counts

192 → 4

Alt Table

Status	Error	Program
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) 3)
	29.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 (sqrt.f64 (.f64 x 3)) (sqrt.f64 (.f64 x 3)) (.f64 y (*.f64 z 6))))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 7223 to 5092 computations (29.5% saved)

regimes783.0ms (7.8%)

Accuracy

Total 0.1b remaining (79.5%)

Threshold costs 0.1b (79.5%)

Counts

152 → 1

Compiler

Compiled 12212 to 9026 computations (26.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	22	18

Stop Event

1×

saturated

end83.0ms (0.8%)

Stop Event

1×

fuel

Compiler

Compiled 111 to 82 computations (26.1% saved)

Details

analyze613.0ms (6.1%)

sample1.2s (11.8%)

preprocess31.0ms (0.3%)

simplify24.0ms (0.2%)

prune7.0ms (0.1%)

localize6.0ms (0.1%)

series12.0ms (0.1%)

rewrite44.0ms (0.4%)

simplify88.0ms (0.9%)

prune78.0ms (0.8%)

localize8.0ms (0.1%)

series27.0ms (0.3%)

rewrite52.0ms (0.5%)

simplify102.0ms (1%)

prune123.0ms (1.2%)

localize16.0ms (0.2%)

series35.0ms (0.3%)

rewrite56.0ms (0.6%)

simplify57.0ms (0.6%)

prune124.0ms (1.2%)

localize11.0ms (0.1%)

series6.1s (60.9%)

rewrite54.0ms (0.5%)

simplify89.0ms (0.9%)

prune206.0ms (2.1%)

regimes783.0ms (7.8%)

simplify2.0ms (0%)

end83.0ms (0.8%)

Profiling