Details

analyze61.0ms (1.8%)

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)

sample879.0ms (26.5%)

Results

859.0ms	8256×	body	128	valid
4.0ms	43×	body	128	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

preprocess33.0ms (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)

simplify40.0ms (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 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

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

series29.0ms (0.9%)

Counts

3 → 68

Calls

18 calls:

3.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)	m	-inf
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 m (-.f64 1 m)) v)	v	-inf
2.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)	v	inf

rewrite55.0ms (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	39
1	202	39
2	2893	35

Stop Event

1×	node limit

Counts

3 → 132

simplify35.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

472×	`fma-def_binary64`
424×	`fma-neg_binary64`
423×	`associate-/l*_binary64`
311×	`cancel-sign-sub-inv_binary64`
227×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	860
1	77	761
2	163	761
3	410	761
4	1467	761

Stop Event

1×	node limit

Counts

200 → 153

prune137.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
	38.5b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 2)
	0.8b	(.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 m (-.f64 1 m))) 2) (sqrt.f64 v)) (/.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) (sqrt.f64 v)) -1) m)
	6.2b	(-.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))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 3)
	19.1b	(/.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)))
	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) m)

Compiler

Compiled 2703 to 1688 computations (37.6% 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))

series22.0ms (0.7%)

Counts

3 → 64

Calls

18 calls:

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

rewrite54.0ms (1.6%)

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	187	32
2	2444	32

Stop Event

1×	node limit

Counts

3 → 125

simplify32.0ms (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

prune137.0ms (4.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	152	6	158

Error

0.0b

Counts

158 → 6

Alt Table

Status	Error	Program
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.8b	(.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 m (-.f64 1 m))) 2) (sqrt.f64 v)) (/.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) (sqrt.f64 v)) -1) m)
	1.4b	(pow.f64 (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 3)
	38.5b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) 2)
	19.1b	(/.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)))
▶	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) m)

Compiler

Compiled 3447 to 2007 computations (41.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (-.f64 1 m))
✓	0.1b	(/.f64 (/.f64 v (-.f64 1 m)) m)
✓	0.1b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) m)
✓	0.3b	(pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1)

series104.0ms (3.1%)

Counts

4 → 84

Calls

24 calls:

15.0ms	(pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1)	v	-inf
15.0ms	(pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1)	v	inf
9.0ms	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) m)	v	-inf
8.0ms	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) m)	v	inf
8.0ms	(/.f64 (/.f64 v (-.f64 1 m)) m)	v	-inf

rewrite60.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

394×	`prod-diff_binary64`
211×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
149×	`egg-rr`
124×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	248	43
2	3509	43

Stop Event

1×	node limit

Counts

4 → 149

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
328×	`fma-neg_binary64`
209×	`times-frac_binary64`
208×	`associate-r_binary64`
207×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1132
1	189	1079
2	506	1057
3	1441	1010

Stop Event

1×	node limit

Counts

233 → 199

prune187.0ms (5.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	198	7	205

Error

0.0b

Counts

205 → 7

Alt Table

Status	Error	Program
	19.1b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (/.f64 v m) (-.f64 1 m)) -3) -1) m) (+.f64 (pow.f64 (/.f64 (/.f64 v m) (-.f64 1 m)) -2) (+.f64 1 (.f64 m (/.f64 (-.f64 1 m) v)))))
▶	0.8b	(.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 m (-.f64 1 m))) 2) (sqrt.f64 v)) (/.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) (sqrt.f64 v)) -1) m)
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 3)
	38.5b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) 2)
	19.1b	(/.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)))
✓	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) m)

Compiler

Compiled 3666 to 2460 computations (32.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) (sqrt.f64 v))
✓	0.4b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) 2) (sqrt.f64 v))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) 2)
✓	0.6b	(cbrt.f64 (*.f64 m (-.f64 1 m)))

series154.0ms (4.6%)

Counts

4 → 48

Calls

18 calls:

41.0ms	(/.f64 (pow.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) 2) (sqrt.f64 v))	v	-inf
22.0ms	(/.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) (sqrt.f64 v))	v	-inf
17.0ms	(/.f64 (pow.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) 2) (sqrt.f64 v))	m	-inf
15.0ms	(pow.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) 2)	m	-inf
12.0ms	(/.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) (sqrt.f64 v))	m	-inf

rewrite58.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`log-prod_binary64`
205×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
204×	`prod-diff_binary64`
186×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	255	52
2	3191	52

Stop Event

1×	node limit

Counts

4 → 128

simplify50.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

686×	`cancel-sign-sub-inv_binary64`
391×	`fma-neg_binary64`
288×	`distribute-rgt-neg-in_binary64`
261×	`distribute-lft-neg-in_binary64`
205×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	2213
1	660	2137
2	2149	1729

Stop Event

1×	node limit

Counts

176 → 224

prune309.0ms (9.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	276	7	283

Error

0.0b

Counts

283 → 7

Alt Table

Status	Error	Program
	19.1b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (/.f64 v m) (-.f64 1 m)) -3) -1) m) (+.f64 (pow.f64 (/.f64 (/.f64 v m) (-.f64 1 m)) -2) (+.f64 1 (.f64 m (/.f64 (-.f64 1 m) v)))))
✓	0.8b	(.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 m (-.f64 1 m))) 2) (sqrt.f64 v)) (/.f64 (cbrt.f64 (*.f64 m (-.f64 1 m))) (sqrt.f64 v)) -1) m)
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 3)
	38.5b	(pow.f64 (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) 2)
	19.1b	(/.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)))
✓	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) m)

Compiler

Compiled 9952 to 7050 computations (29.2% saved)

regimes698.0ms (21.1%)

Accuracy

Total 0.1b remaining (77.2%)

Threshold costs 0.1b (77.2%)

Counts

221 → 1

Compiler

Compiled 11696 to 8303 computations (29% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	16	16
2	21	16
3	23	16
4	24	16

Stop Event

1×

saturated

end109.0ms (3.3%)

Stop Event

1×

fuel

Compiler

Compiled 181 to 123 computations (32% saved)

Details

analyze61.0ms (1.8%)

sample879.0ms (26.5%)

preprocess33.0ms (1%)

simplify40.0ms (1.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series29.0ms (0.9%)

rewrite55.0ms (1.6%)

simplify35.0ms (1.1%)

prune137.0ms (4.1%)

localize6.0ms (0.2%)

series22.0ms (0.7%)

rewrite54.0ms (1.6%)

simplify32.0ms (1%)

prune137.0ms (4.1%)

localize7.0ms (0.2%)

series104.0ms (3.1%)

rewrite60.0ms (1.8%)

simplify38.0ms (1.1%)

prune187.0ms (5.7%)

localize11.0ms (0.3%)

series154.0ms (4.6%)

rewrite58.0ms (1.8%)

simplify50.0ms (1.5%)

prune309.0ms (9.3%)

regimes698.0ms (21.1%)

simplify2.0ms (0.1%)

end109.0ms (3.3%)

Profiling