Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.1s (44.9%)

Results

422.0ms	2128×	body	512	valid
383.0ms	4659×	body	128	valid
147.0ms	1068×	body	256	valid
101.0ms	401×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

15.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	2.6b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite63.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

896×	`expm1-log1p-u_binary64`
733×	`prod-diff_binary64`
135×	`egg-rr`
85×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`

Counts

2 → 135

Calls

2 calls:

60.0ms	(/.f64 1 (+.f64 x 1))
60.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	168	20
2	2226	20
3	5239	20
0	0	0
1	0	0

simplify78.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
429×	`cancel-sign-sub-inv_binary64`
405×	`associate-/r*_binary64`
338×	`div-sub_binary64`
334×	`sub-neg_binary64`

Counts

159 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	372
1	98	366
2	234	366
3	577	364
4	1646	363
5	4272	363
6	4983	363
7	4917	363

prune117.0ms (4.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	3	164

Error

0.2b

Counts

164 → 3

Alt Table

Status	Error	Program
▶	15.4b	(/.f64 (-.f64 x (+.f64 1 x)) (*.f64 x (+.f64 1 x)))
	31.1b	(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
	27.5b	(-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) 3) (/.f64 1 x))

Compiler

Compiled 3433 to 2562 computations (25.4% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 1 x))
✓	0.0b	(/.f64 (-.f64 x (+.f64 1 x)) (*.f64 x (+.f64 1 x)))
✓	2.2b	(-.f64 x (+.f64 1 x))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(/.f64 (-.f64 x (+.f64 1 x)) (*.f64 x (+.f64 1 x)))
2.0ms	(*.f64 x (+.f64 1 x))
1.0ms	(-.f64 x (+.f64 1 x))

rewrite77.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

467×	`log-prod_binary64`
407×	`fma-def_binary64`
233×	`egg-rr`
216×	`fma-neg_binary64`
188×	`log-div_binary64`

Counts

3 → 233

Calls

3 calls:

72.0ms	(*.f64 x (+.f64 1 x))
72.0ms	(/.f64 (-.f64 x (+.f64 1 x)) (*.f64 x (+.f64 1 x)))
72.0ms	(-.f64 x (+.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
1	167	30
2	2558	26
3	5152	26
0	0	0
1	0	0

simplify90.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

517×	`distribute-neg-frac_binary64`
428×	`associate-l_binary64`
405×	`associate-/r*_binary64`
302×	`associate-r_binary64`
292×	`fma-def_binary64`

Counts

269 → 253

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	285
1	73	265
2	159	265
3	380	265
4	979	265
5	3552	265
6	4942	265
7	4991	265
8	4880	265

prune148.0ms (6.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	253	3	256

Error

0.2b

Counts

256 → 3

Alt Table

Status	Error	Program
▶	15.4b	(.f64 (/.f64 (/.f64 (-.f64 x (+.f64 x 1)) x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
✓	15.4b	(/.f64 (-.f64 x (+.f64 1 x)) (*.f64 x (+.f64 1 x)))
	31.1b	(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))

Compiler

Compiled 4774 to 2842 computations (40.5% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (-.f64 x (+.f64 x 1)) x) (-.f64 1 (*.f64 x x)))
✓	0.0b	(.f64 (/.f64 (/.f64 (-.f64 x (+.f64 x 1)) x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
✓	2.2b	(-.f64 x (+.f64 x 1))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 (/.f64 (-.f64 x (+.f64 x 1)) x) (-.f64 1 (*.f64 x x)))
3.0ms	(.f64 (/.f64 (/.f64 (-.f64 x (+.f64 x 1)) x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
1.0ms	(-.f64 x (+.f64 x 1))

rewrite85.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite
3×	egg-rewrite

Rules

138×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`
130×	`add-log-exp_binary64`
129×	`add-cbrt-cube_binary64`

Counts

3 → 0

Calls

3 calls:

85.0ms	(/.f64 (/.f64 (-.f64 x (+.f64 x 1)) x) (-.f64 1 (*.f64 x x)))
85.0ms	(.f64 (/.f64 (/.f64 (-.f64 x (+.f64 x 1)) x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
85.0ms	(-.f64 x (+.f64 x 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	270	21
2	131	21
0	5	7
1	115	7
2	73	7
0	11	25
1	270	25
2	131	25
0	9	19
1	223	19
2	131	19
0	0	0
1	0	0

simplify78.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

598×	`cancel-sign-sub-inv_binary64`
472×	`associate-/r*_binary64`
349×	`sub-neg_binary64`
338×	`div-sub_binary64`
322×	`fma-def_binary64`

Counts

36 → 29

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	426
1	123	418
2	316	417
3	808	417
4	2084	417
5	4178	417
6	4920	417
7	4931	417

prune19.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	28	4	32

Error

0.1b

Counts

32 → 4

Alt Table

Status	Error	Program
	37.1b	(*.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 1 x))
▶	5.5b	(.f64 (/.f64 (/.f64 -1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
✓	15.4b	(/.f64 (-.f64 x (+.f64 1 x)) (*.f64 x (+.f64 1 x)))
	31.1b	(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))

Compiler

Compiled 498 to 377 computations (24.3% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 -1 x) (-.f64 1 (*.f64 x x)))
✓	5.5b	(.f64 (/.f64 (/.f64 -1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 (/.f64 -1 x) (-.f64 1 (*.f64 x x)))
3.0ms	(.f64 (/.f64 (/.f64 -1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))

rewrite72.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

349×	`prod-diff_binary64`
252×	`fma-def_binary64`
236×	`log-div_binary64`
189×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`

Counts

2 → 137

Calls

2 calls:

68.0ms	(/.f64 (/.f64 -1 x) (-.f64 1 (*.f64 x x)))
68.0ms	(.f64 (/.f64 (/.f64 -1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	223	23
2	2970	23
3	5093	23
0	0	0
1	0	0

simplify81.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

598×	`cancel-sign-sub-inv_binary64`
472×	`associate-/r*_binary64`
349×	`sub-neg_binary64`
338×	`div-sub_binary64`
322×	`fma-def_binary64`

Counts

161 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	414
1	123	406
2	316	405
3	808	405
4	2084	405
5	4178	405
6	4920	405
7	4931	405

prune117.0ms (4.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	4	165
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	164	5	169

Error

0.0b

Counts

169 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f64 (/.f64 -1 x) (+.f64 x 1))
	37.1b	(*.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 1 x))
	1.0b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 x) (+.f64 x 1))) 3)
	0.2b	(/.f64 (/.f64 (-.f64 1 x) (neg.f64 x)) (-.f64 1 (*.f64 x x)))
	24.4b	(/.f64 (neg.f64 (-.f64 1 (.f64 x x))) (.f64 (.f64 x (-.f64 1 (.f64 x x))) (+.f64 x 1)))

Compiler

Compiled 3411 to 2185 computations (35.9% saved)

regimes170.0ms (7%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Counts

100 → 1

Compiler

Compiled 2852 to 2154 computations (24.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	9	10

end66.0ms (2.7%)

Compiler: Compiled 77 to 56 computations (27.3% saved)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Iter	Nodes	Cost
0	11	21
1	270	21
2	131	21
0	5	7
1	115	7
2	73	7
0	11	25
1	270	25
2	131	25
0	9	19
1	223	19
2	131	19
0	0	0
1	0	0

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Iter	Nodes	Cost
0	11	21
1	270	21
2	131	21
0	5	7
1	115	7
2	73	7
0	11	25
1	270	25
2	131	25
0	9	19
1	223	19
2	131	19
0	0	0
1	0	0

Details

analyze5.0ms (0.2%)

sample1.1s (44.9%)

simplify10.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite63.0ms (2.6%)

simplify78.0ms (3.2%)

prune117.0ms (4.9%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite77.0ms (3.2%)

simplify90.0ms (3.7%)

prune148.0ms (6.1%)

localize9.0ms (0.4%)

series7.0ms (0.3%)

rewrite85.0ms (3.5%)

simplify78.0ms (3.2%)

prune19.0ms (0.8%)

localize7.0ms (0.3%)

series6.0ms (0.2%)

rewrite72.0ms (3%)

simplify81.0ms (3.3%)

prune117.0ms (4.8%)

regimes170.0ms (7%)

simplify2.0ms (0.1%)

end66.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Iter	Nodes	Cost
0	11	21
1	270	21
2	131	21
0	5	7
1	115	7
2	73	7
0	11	25
1	270	25
2	131	25
0	9	19
1	223	19
2	131	19
0	0	0
1	0	0