Details

analyze6.0ms (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)

sample1.2s (42.8%)

Results

447.0ms	2072×	body	512	valid
435.0ms	4746×	body	128	valid
188.0ms	1010×	body	256	valid
113.0ms	428×	body	1024	valid
0.0ms	2×	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

14.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.8b	(-.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))
✓	3.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite82.0ms (2.9%)

Algorithm

1×	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:

79.0ms	(/.f64 1 (+.f64 x 1))
79.0ms	(-.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

simplify105.0ms (3.7%)

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

prune132.0ms (4.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	4	164

Error

0.4b

Counts

164 → 4

Alt Table

Status	Error	Program
	33.0b	(/.f64 -1 (pow.f64 x 2))
	32.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 x) -2) (pow.f64 x -2)) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 x)))
	28.6b	(+.f64 (fma.f64 (/.f64 1 (fma.f64 x x -1)) (+.f64 x -1) (/.f64 -1 x)) (fma.f64 (/.f64 -1 x) 1 (/.f64 1 x)))
▶	14.0b	(/.f64 (/.f64 (-.f64 x (+.f64 1 x)) (+.f64 1 x)) x)

Compiler

Compiled 3457 to 2576 computations (25.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (+.f64 1 x)) (+.f64 1 x))
✓	0.0b	(/.f64 (/.f64 (-.f64 x (+.f64 1 x)) (+.f64 1 x)) x)
✓	3.1b	(-.f64 x (+.f64 1 x))

series6.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 (-.f64 x (+.f64 1 x)) (+.f64 1 x))
2.0ms	(/.f64 (/.f64 (-.f64 x (+.f64 1 x)) (+.f64 1 x)) x)
1.0ms	(-.f64 x (+.f64 1 x))

rewrite127.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

623×	`prod-diff_binary64`
480×	`fma-udef_binary64`
327×	`fma-def_binary64`
254×	`fma-neg_binary64`
195×	`egg-rr`

Counts

3 → 195

Calls

3 calls:

124.0ms	(/.f64 (-.f64 x (+.f64 1 x)) (+.f64 1 x))
124.0ms	(/.f64 (/.f64 (-.f64 x (+.f64 1 x)) (+.f64 1 x)) x)
123.0ms	(-.f64 x (+.f64 1 x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	36
1	169	30
2	2628	30
3	4831	30
4	4850	30
5	5002	30

simplify78.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

666×	`sub-neg_binary64`
633×	`fma-def_binary64`
532×	`fma-neg_binary64`
350×	`cancel-sign-sub-inv_binary64`
266×	`times-frac_binary64`

Counts

231 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	384
1	99	378
2	242	378
3	608	375
4	1602	375
5	4182	375
6	4828	375
7	5223	375

prune146.0ms (5.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	223	4	227

Error

0.0b

Counts

227 → 4

Alt Table

Status	Error	Program
	33.0b	(/.f64 -1 (pow.f64 x 2))
	14.8b	(/.f64 (+.f64 (/.f64 x (+.f64 x 1)) -1) x)
▶	0.1b	(/.f64 (/.f64 -1 (+.f64 1 x)) x)
	14.8b	(-.f64 (/.f64 (-.f64 x 1) (fma.f64 x x x)) (/.f64 x (fma.f64 x x x)))

Compiler

Compiled 4075 to 2827 computations (30.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -1 (+.f64 1 x))
✓	0.1b	(/.f64 (/.f64 -1 (+.f64 1 x)) x)

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite47.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

761×	`log1p-expm1-u_binary64`
761×	`expm1-log1p-u_binary64`
128×	`log1p-udef_binary64`
105×	`prod-diff_binary64`
73×	`add-sqr-sqrt_binary64`

Counts

2 → 63

Calls

2 calls:

46.0ms	(/.f64 -1 (+.f64 1 x))
46.0ms	(/.f64 (/.f64 -1 (+.f64 1 x)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	151	17
2	1942	17
3	5123	17

simplify75.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

666×	`sub-neg_binary64`
633×	`fma-def_binary64`
532×	`fma-neg_binary64`
350×	`cancel-sign-sub-inv_binary64`
266×	`times-frac_binary64`

Counts

87 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	372
1	99	366
2	242	366
3	608	363
4	1602	363
5	4182	363
6	4828	363
7	5223	363

prune54.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	89	6	95

Error

Counts

95 → 6

Alt Table

Status	Error	Program
	33.0b	(/.f64 -1 (pow.f64 x 2))
	14.8b	(/.f64 (+.f64 (/.f64 x (+.f64 x 1)) -1) x)
▶	0.9b	(*.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2))
✓	0.1b	(/.f64 (/.f64 -1 (+.f64 1 x)) x)
	31.1b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x) 3))
	32.2b	(*.f64 (/.f64 -1 (sqrt.f64 x)) (/.f64 (/.f64 1 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 1194 to 895 computations (25% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (/.f64 -1 (+.f64 1 x)) x)
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2))
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2)
✓	14.4b	(cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x))

series60.0ms (2.1%)

Counts

3 → 36

Calls

3 calls:

36.0ms

(pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2)

16.0ms

(cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x))

8.0ms

(*.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2))

rewrite88.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

438×	`log-prod_binary64`
319×	`prod-diff_binary64`
168×	`pow1/3_binary64`
164×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`

Counts

3 → 109

Calls

3 calls:

86.0ms

(*.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2))

86.0ms

(pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2)

86.0ms

(cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	215	37
2	2447	31
3	4929	31
4	5367	31

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-def_binary64`
433×	`associate-r_binary64`
379×	`associate-l_binary64`
378×	`sub-neg_binary64`
339×	`cancel-sign-sub-inv_binary64`

Counts

145 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1332
1	442	1314
2	1271	1122
3	4634	1074
4	5173	1074

prune244.0ms (8.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	338	5	343

Error

Counts

343 → 5

Alt Table

Status	Error	Program
✓	0.9b	(*.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2))
	0.4b	(/.f64 -1 (fma.f64 x x x))
	1.2b	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -1 (+.f64 1 x)) x)) 2))
✓	0.1b	(/.f64 (/.f64 -1 (+.f64 1 x)) x)
	32.2b	(*.f64 (/.f64 -1 (sqrt.f64 x)) (/.f64 (/.f64 1 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 8243 to 6334 computations (23.2% saved)

regimes190.0ms (6.7%)

Accuracy

Total 0.1b remaining (81.9%)

Threshold costs 0.1b (81.9%)

Counts

105 → 1

Compiler

Compiled 2978 to 2354 computations (21% 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

end70.0ms (2.5%)

Compiler: Compiled 84 to 62 computations (26.2% 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	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

Details

analyze6.0ms (0.2%)

sample1.2s (42.8%)

simplify10.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite82.0ms (2.9%)

simplify105.0ms (3.7%)

prune132.0ms (4.6%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite127.0ms (4.5%)

simplify78.0ms (2.8%)

prune146.0ms (5.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite47.0ms (1.7%)

simplify75.0ms (2.6%)

prune54.0ms (1.9%)

localize11.0ms (0.4%)

series60.0ms (2.1%)

rewrite88.0ms (3.1%)

simplify66.0ms (2.3%)

prune244.0ms (8.6%)

regimes190.0ms (6.7%)

simplify2.0ms (0.1%)

end70.0ms (2.5%)

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