Details

analyze39.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.8%	87.2%	0
0%	12.8%	87.2%	1
0%	12.8%	87.2%	2
6.4%	6.4%	87.2%	3
6.4%	4.8%	88.8%	4
7.2%	3.2%	89.6%	5
7.2%	2.4%	90.4%	6
7.6%	1.6%	90.8%	7
7.6%	1.2%	91.2%	8
7.8%	0.8%	91.4%	9
7.8%	0.6%	91.5%	10
7.9%	0.4%	91.7%	11
8%	0.3%	91.7%	12
8.1%	0.2%	91.7%	13
8.1%	0.2%	91.8%	14

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.4s (45.9%)

Results

539.0ms	5149×	body	128	valid
384.0ms	1165×	body	1024	valid
301.0ms	1175×	body	512	valid
129.0ms	725×	body	256	valid
18.0ms	42×	body	2048	valid
9.0ms	78×	body	128	invalid

Compiler

Compiled 50 to 34 computations (32% saved)

preprocess25.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

144×	`fma-neg_binary64`
96×	`fma-def_binary64`
54×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
26×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 6 computations (40% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

107×	`fma-def_binary64`
72×	`fma-neg_binary64`
29×	`cancel-sign-sub-inv_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

26.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	3.7b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series32.0ms (1%)

Counts

3 → 56

Calls

18 calls:

4.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))	eps	-inf
4.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))	eps	inf
3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))	eps	0
3.0ms	(sqrt.f64 (-.f64 (*.f64 x x) eps))	eps	-inf
3.0ms	(sqrt.f64 (-.f64 (*.f64 x x) eps))	eps	inf

rewrite54.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`log1p-expm1-u_binary64`
871×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
85×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
1	162	28
2	2412	28

Stop Event

1×	node limit

Counts

3 → 104

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

615×	`cancel-sign-sub-inv_binary64`
324×	`fma-neg_binary64`
230×	`associate-/r/_binary64`
224×	`associate-/l/_binary64`
193×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	858
1	214	844
2	615	834
3	2433	816

Stop Event

1×	node limit

Counts

160 → 155

prune91.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	5	156

Error

Counts

156 → 5

Alt Table

Status	Error	Program
	29.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	26.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	27.2b	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	0.6b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))

Compiler

Compiled 2534 to 1010 computations (60.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

series71.0ms (2.3%)

Counts

2 → 32

Calls

12 calls:

17.0ms	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))	eps	-inf
16.0ms	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))	eps	inf
15.0ms	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))	x	inf
5.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))	eps	inf
3.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))	eps	-inf

rewrite71.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
308×	`fma-neg_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	261	24
2	4003	24

Stop Event

1×	node limit

Counts

2 → 177

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

759×	`cancel-sign-sub-inv_binary64`
355×	`fma-neg_binary64`
304×	`times-frac_binary64`
279×	`distribute-neg-frac_binary64`
214×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	786
1	202	759
2	613	751
3	2862	717

Stop Event

1×	node limit

Counts

209 → 206

prune155.0ms (5.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	301	5	306

Error

Counts

306 → 5

Alt Table

Status	Error	Program
	29.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	26.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	27.2b	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	0.6b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

Compiler

Compiled 7647 to 1921 computations (74.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	0.0b	(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
✓	0.1b	(/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps)
✓	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

series94.0ms (3.1%)

Counts

4 → 64

Calls

24 calls:

17.0ms	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)	eps	-inf
17.0ms	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)	eps	inf
7.0ms	(/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps)	eps	-inf
6.0ms	(sqrt.f64 (fma.f64 x x (neg.f64 eps)))	x	inf
6.0ms	(/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps)	eps	inf

rewrite63.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

846×	`prod-diff_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
111×	`add-sqr-sqrt_binary64`
106×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	54
1	218	39
2	3022	39

Stop Event

1×	node limit

Counts

4 → 137

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
519×	`times-frac_binary64`
345×	`associate-/l*_binary64`
319×	`associate-/r*_binary64`
284×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1484
1	339	1437
2	1072	1415
3	4884	1411

Stop Event

1×	node limit

Counts

201 → 209

prune94.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	209	5	214

Error

Counts

214 → 5

Alt Table

Status	Error	Program
	29.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	26.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	27.2b	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.6b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

Compiler

Compiled 3701 to 1620 computations (56.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.7b	(cbrt.f64 x)
✓	26.9b	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))

series67.0ms (2.2%)

Counts

3 → 11

Calls

12 calls:

19.0ms	(pow.f64 (cbrt.f64 x) 2)	x	-inf
10.0ms	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))	x	-inf
10.0ms	(cbrt.f64 x)	x	-inf
5.0ms	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))	eps	0
5.0ms	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))	eps	-inf

rewrite52.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

915×	`log1p-expm1-u_binary64`
915×	`expm1-log1p-u_binary64`
116×	`add-sqr-sqrt_binary64`
110×	`pow1_binary64`
109×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	236	21
2	2881	21

Stop Event

1×	node limit

Counts

3 → 65

simplify23.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/r*_binary64`
414×	`fma-def_binary64`
401×	`associate-l_binary64`
379×	`associate-*l/_binary64`
279×	`associate-*r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	200
1	137	196
2	371	194
3	1344	188

Stop Event

1×	node limit

Counts

76 → 85

prune120.0ms (4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	156	5	161

Error

Counts

161 → 5

Alt Table

Status	Error	Program
	29.7b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	26.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	27.2b	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	0.6b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) eps) -1)

Compiler

Compiled 2729 to 1030 computations (62.3% saved)

regimes335.0ms (11%)

Accuracy

Total 0.3b remaining (96.2%)

Threshold costs 0.3b (96.2%)

Counts

96 → 1

Compiler

Compiled 4350 to 2692 computations (38.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	23	19
2	35	19
3	43	19
4	45	19

Stop Event

1×

saturated

end68.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 95 to 55 computations (42.1% saved)

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Details

analyze39.0ms (1.3%)

sample1.4s (45.9%)

preprocess25.0ms (0.8%)

simplify12.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series32.0ms (1%)

rewrite54.0ms (1.8%)

simplify44.0ms (1.5%)

prune91.0ms (3%)

localize8.0ms (0.3%)

series71.0ms (2.3%)

rewrite71.0ms (2.3%)

simplify39.0ms (1.3%)

prune155.0ms (5.1%)

localize9.0ms (0.3%)

series94.0ms (3.1%)

rewrite63.0ms (2.1%)

simplify62.0ms (2%)

prune94.0ms (3.1%)

localize9.0ms (0.3%)

series67.0ms (2.2%)

rewrite52.0ms (1.7%)

simplify23.0ms (0.8%)

prune120.0ms (4%)

regimes335.0ms (11%)

simplify4.0ms (0.1%)

end68.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	349	24
7	501	24
8	603	24
9	655	24
10	665	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12