Details

analyze62.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample902.0ms (27.6%)

Results

882.0ms	8256×	body	128	valid
8.0ms	58×	body	128	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

preprocess37.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

820×	`fma-neg_binary64`
648×	`times-frac_binary64`
255×	`associate-/l*_binary64`
195×	`fma-def_binary64`
182×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	32	32
2	68	28
3	159	28
4	592	28
5	1906	28
6	4511	28
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

913×	`fma-neg_binary64`
812×	`fma-def_binary64`
281×	`div-sub_binary64`
243×	`cancel-sign-sub-inv_binary64`
198×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	85	14
4	280	14
5	726	14
6	1858	14
7	3236	14
8	4027	14
9	4373	14
10	4984	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series23.0ms (0.7%)

Counts

3 → 56

Calls

15 calls:

2.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)	v	0
2.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)	v	-inf
2.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)	v	inf
2.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)	v	-inf
2.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)	m	-inf

rewrite53.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

501×	`prod-diff_binary64`
179×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`
174×	`fma-neg_binary64`
172×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	201	33
2	2901	31

Stop Event

1×	node limit

Counts

3 → 103

simplify32.0ms (1%)

Algorithm

1×	egg-herbie

Rules

459×	`fma-def_binary64`
425×	`associate-/l*_binary64`
379×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
223×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	638
1	67	584
2	143	584
3	368	584
4	1388	584

Stop Event

1×	node limit

Counts

159 → 125

prune126.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	120	7	127

Error

0.0b

Counts

127 → 7

Alt Table

Status	Error	Program
	11.9b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	16.2b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 3) -1) m) (+.f64 (pow.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))
	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
▶	0.2b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)
	0.6b	(.f64 (-.f64 (.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) (pow.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) 2)) 1) m)
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 2140 to 1323 computations (38.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (-.f64 1 (.f64 m m)) m)
✓	0.0b	(/.f64 (/.f64 (.f64 (-.f64 1 (.f64 m m)) m) (+.f64 m 1)) v)
✓	0.1b	(/.f64 (.f64 (-.f64 1 (.f64 m m)) m) (+.f64 m 1))
✓	0.1b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)

series52.0ms (1.6%)

Counts

4 → 72

Calls

18 calls:

7.0ms	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)	v	-inf
6.0ms	(/.f64 (/.f64 (.f64 (-.f64 1 (.f64 m m)) m) (+.f64 m 1)) v)	v	-inf
5.0ms	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)	v	inf
5.0ms	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)	v	0
5.0ms	(/.f64 (/.f64 (.f64 (-.f64 1 (.f64 m m)) m) (+.f64 m 1)) v)	v	inf

rewrite73.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

664×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
145×	`*-un-lft-identity_binary64`
145×	`pow1_binary64`
138×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	70
1	281	43
2	4336	43

Stop Event

1×	node limit

Counts

4 → 132

simplify50.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

942×	`fma-neg_binary64`
542×	`associate-/l*_binary64`
289×	`associate-l_binary64`
270×	`associate-r_binary64`
250×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1006
1	111	1006
2	276	839
3	973	797
4	4705	797

Stop Event

1×	node limit

Counts

204 → 162

prune177.0ms (5.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	162	7	169

Error

0.0b

Counts

169 → 7

Alt Table

Status	Error	Program
	11.9b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	16.2b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 3) -1) m) (+.f64 (pow.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))
	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)
	0.6b	(.f64 (-.f64 (.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) (pow.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) 2)) 1) m)
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 3116 to 2011 computations (35.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.1b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

series24.0ms (0.7%)

Counts

3 → 64

Calls

18 calls:

2.0ms	(/.f64 (-.f64 1 m) v)	m	0
2.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))	v	-inf
2.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))	v	inf
2.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))	m	-inf
2.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))	v	0

rewrite55.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

452×	`log-prod_binary64`
201×	`prod-diff_binary64`
173×	`pow1/3_binary64`
165×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	186	32
2	2441	32

Stop Event

1×	node limit

Counts

3 → 125

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-l_binary64`
406×	`fma-def_binary64`
291×	`associate-/l*_binary64`
282×	`fma-neg_binary64`
252×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	814
1	84	715
2	168	689
3	391	676
4	1237	676

Stop Event

1×	node limit

Counts

189 → 151

prune158.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	151	7	158

Error

0.0b

Counts

158 → 7

Alt Table

Status	Error	Program
	11.9b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	16.2b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 3) -1) m) (+.f64 (pow.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))
▶	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)
	0.6b	(.f64 (-.f64 (.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) (pow.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) 2)) 1) m)
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 3468 to 2014 computations (41.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.3b	(/.f64 m (sqrt.f64 v))
✓	0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

series86.0ms (2.6%)

Counts

4 → 64

Calls

24 calls:

21.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)	v	-inf
10.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))	v	-inf
8.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))	v	-inf
7.0ms	(/.f64 m (sqrt.f64 v))	v	-inf
3.0ms	(/.f64 m (sqrt.f64 v))	m	0

rewrite79.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`prod-diff_binary64`
127×	`add-sqr-sqrt_binary64`
123×	`*-un-lft-identity_binary64`
123×	`pow1_binary64`
117×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	250	41
2	3680	41

Stop Event

1×	node limit

Counts

4 → 194

simplify38.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-def_binary64`
343×	`associate-/l*_binary64`
331×	`fma-neg_binary64`
281×	`cancel-sign-sub-inv_binary64`
218×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	791
1	80	746
2	154	701
3	378	677
4	1401	677

Stop Event

1×	node limit

Counts

258 → 218

prune258.0ms (7.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	217	8	225

Error

0.0b

Counts

225 → 8

Alt Table

Status	Error	Program
	11.9b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	16.2b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 3) -1) m) (+.f64 (pow.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))
	37.1b	(/.f64 (-.f64 1 m) (/.f64 v (*.f64 m m)))
✓	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.2b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 1 (*.f64 m m)) m) (+.f64 m 1)) v) 1) m)
	0.6b	(.f64 (-.f64 (.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) (pow.f64 (cbrt.f64 (.f64 (/.f64 m v) (-.f64 1 m))) 2)) 1) m)
	5.9b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 5399 to 2849 computations (47.2% saved)

regimes752.0ms (23.1%)

Accuracy

Total 0.2b remaining (90.3%)

Threshold costs 0.2b (90.3%)

Counts

235 → 1

Compiler

Compiled 11582 to 8171 computations (29.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	16	20
2	21	20
3	24	20
4	25	20

Stop Event

1×

saturated

end115.0ms (3.5%)

Stop Event

1×

fuel

Compiler

Compiled 189 to 122 computations (35.4% saved)

Details

analyze62.0ms (1.9%)

sample902.0ms (27.6%)

preprocess37.0ms (1.1%)

simplify41.0ms (1.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series23.0ms (0.7%)

rewrite53.0ms (1.6%)

simplify32.0ms (1%)

prune126.0ms (3.9%)

localize9.0ms (0.3%)

series52.0ms (1.6%)

rewrite73.0ms (2.2%)

simplify50.0ms (1.5%)

prune177.0ms (5.4%)

localize6.0ms (0.2%)

series24.0ms (0.7%)

rewrite55.0ms (1.7%)

simplify34.0ms (1.1%)

prune158.0ms (4.8%)

localize8.0ms (0.3%)

series86.0ms (2.6%)

rewrite79.0ms (2.4%)

simplify38.0ms (1.2%)

prune258.0ms (7.9%)

regimes752.0ms (23.1%)

simplify2.0ms (0.1%)

end115.0ms (3.5%)

Profiling