Details

analyze720.0ms (20%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
34.3%	65.5%	0.1%	9
39%	60.8%	0.1%	10
41.3%	58.5%	0.1%	11
52.7%	47.2%	0.1%	12
54%	45.7%	0.2%	13
55.3%	43.8%	0.9%	14

Compiler

Compiled 19 to 10 computations (47.4% saved)

sample1.8s (49.3%)

Results

678.0ms	6025×	body	128	valid
267.0ms	839×	body	1024	valid
199.0ms	480×	body	2048	valid
147.0ms	1380×	body	128	invalid
137.0ms	563×	body	512	valid
78.0ms	314×	body	512	invalid
77.0ms	240×	body	1024	invalid
70.0ms	349×	body	256	valid
37.0ms	220×	body	256	invalid

Compiler

Compiled 56 to 29 computations (48.2% saved)

simplify256.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

7175×	`fma-neg_binary64`
753×	`unsub-neg_binary64`
515×	`distribute-lft-out_binary64`
498×	`distribute-lft-out--_binary64`
472×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	27	10
2	80	7
3	206	7
4	565	7
5	1825	7
6	2161	7
7	2289	7
8	2491	7
9	2604	7
10	2649	7
11	3904	7
12	3380	7
13	3584	7
14	3584	7
15	3996	7
16	4202	7
17	4202	7
18	4202	7
19	4304	7
20	4304	7
21	11032	7

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 y (-.f64 x z))
	18.3b	(+.f64 (-.f64 (-.f64 (.f64 x y) (.f64 y z)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 75 to 39 computations (48% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 x z))

series6.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

6.0ms

(*.f64 y (-.f64 x z))

rewrite44.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

672×	`log1p-expm1-u_binary64`
672×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
124×	`log1p-udef_binary64`
68×	`add-sqr-sqrt_binary64`

Counts

1 → 21

Calls

1 calls:

43.0ms

(*.f64 y (-.f64 x z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	129	7
2	1676	7
3	5023	7
0	0	0
1	0	0

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

172×	`fma-def_binary64`
126×	`fma-neg_binary64`
43×	`cancel-sign-sub-inv_binary64`
32×	`distribute-rgt-in_binary64`
27×	`sub-neg_binary64`

Counts

57 → 27

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	240
1	25	240
2	37	240
3	54	240
4	84	240
5	133	240
6	206	240
7	279	240
8	311	240
9	331	240
10	343	240
11	312	240

prune17.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	25	4	29

Error

Counts

29 → 4

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))
	27.9b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 z z)) y) (+.f64 x z))
	42.3b	(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)) y) (fma.f64 x x (.f64 z (+.f64 x z))))

Compiler

Compiled 333 to 152 computations (54.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 y x) (.f64 y z))

series7.0ms (0.2%)

Counts

1 → 18

Calls

1 calls:

7.0ms

(-.f64 (*.f64 y x) (*.f64 y z))

rewrite55.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

836×	`log1p-expm1-u_binary64`
836×	`expm1-log1p-u_binary64`
83×	`add-sqr-sqrt_binary64`
77×	`add-log-exp_binary64`
76×	`add-cube-cbrt_binary64`

Counts

1 → 55

Calls

1 calls:

54.0ms

(-.f64 (*.f64 y x) (*.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	158	7
2	2105	7
3	5081	7
0	0	0
1	0	0

simplify20.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

143×	`fma-def_binary64`
90×	`fma-neg_binary64`
33×	`unsub-neg_binary64`
30×	`cancel-sign-sub-inv_binary64`
28×	`distribute-rgt-in_binary64`

Counts

73 → 60

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	114
1	28	114
2	61	114
3	109	114
4	163	114
5	261	114
6	320	114
7	346	114
8	348	114
9	317	114

prune29.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
	32.5b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (-.f64 x z)))
✓	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))
▶	27.9b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 z z)) y) (+.f64 x z))

Compiler

Compiled 931 to 274 computations (70.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.3b	(-.f64 (.f64 x x) (.f64 z z))
✓	8.8b	(.f64 (-.f64 (.f64 x x) (*.f64 z z)) y)
✓	17.6b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 z z)) y) (+.f64 x z))

series60.0ms (1.7%)

Counts

3 → 96

Calls

3 calls:

31.0ms	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 z z)) y) (+.f64 x z))
21.0ms	(.f64 (-.f64 (.f64 x x) (*.f64 z z)) y)
7.0ms	(-.f64 (.f64 x x) (.f64 z z))

rewrite89.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

538×	`fma-def_binary64`
268×	`egg-rr`
247×	`fma-neg_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`

Counts

3 → 268

Calls

3 calls:

82.0ms	(-.f64 (.f64 x x) (.f64 z z))
82.0ms	(.f64 (-.f64 (.f64 x x) (*.f64 z z)) y)
82.0ms	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 z z)) y) (+.f64 x z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	232	30
2	3213	30
3	5050	30
0	0	0
1	0	0

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-neg_binary64`
648×	`associate-l_binary64`
447×	`associate-r_binary64`
364×	`cancel-sign-sub-inv_binary64`
355×	`fma-def_binary64`

Counts

364 → 287

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	888
1	58	888
2	102	888
3	238	888
4	765	888
5	2899	888
6	4532	888
7	5009	888

prune130.0ms (3.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	287	4	291

Error

Counts

291 → 4

Alt Table

Status	Error	Program
▶	32.5b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (-.f64 x z)))
✓	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))
✓	27.9b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 z z)) y) (+.f64 x z))

Compiler

Compiled 6332 to 1557 computations (75.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (-.f64 x z)))
✓	0.2b	(*.f64 (sqrt.f64 y) (-.f64 x z))

series31.0ms (0.9%)

Counts

2 → 56

Calls

2 calls:

20.0ms	(*.f64 (sqrt.f64 y) (-.f64 x z))
11.0ms	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (-.f64 x z)))

rewrite52.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

843×	`log1p-expm1-u_binary64`
843×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
80×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

51.0ms	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (-.f64 x z)))
51.0ms	(*.f64 (sqrt.f64 y) (-.f64 x z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	169	16
2	2142	16
3	5862	16
0	0	0
1	0	0

simplify46.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

315×	`fma-def_binary64`
218×	`fma-neg_binary64`
73×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-in_binary64`
42×	`sub-neg_binary64`

Counts

97 → 52

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	416
1	42	416
2	62	416
3	90	416
4	141	416
5	222	416
6	339	416
7	454	416
8	499	416
9	539	416
10	551	416
11	516	416

prune18.0ms (0.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	52	4	56

Error

Counts

56 → 4

Alt Table

Status	Error	Program
✓	32.5b	(.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (-.f64 x z)))
✓	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))
✓	27.9b	(/.f64 (.f64 (-.f64 (.f64 x x) (*.f64 z z)) y) (+.f64 x z))

Compiler

Compiled 593 to 220 computations (62.9% saved)

regimes49.0ms (1.3%)

Accuracy

Total 0.0b remaining (76.1%)

Threshold costs 0.0b (76.1%)

Counts

12 → 1

Compiler

Compiled 592 to 368 computations (37.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	14	10
2	24	10
3	30	10
4	34	10
5	35	10
6	35	10

end55.0ms (1.5%)

Compiler: Compiled 66 to 39 computations (40.9% saved)

Iter	Nodes	Cost
0	11	240
1	25	240
2	37	240
3	54	240
4	84	240
5	133	240
6	206	240
7	279	240
8	311	240
9	331	240
10	343	240
11	312	240

Iter	Nodes	Cost
0	13	114
1	28	114
2	61	114
3	109	114
4	163	114
5	261	114
6	320	114
7	346	114
8	348	114
9	317	114

Iter	Nodes	Cost
0	16	416
1	42	416
2	62	416
3	90	416
4	141	416
5	222	416
6	339	416
7	454	416
8	499	416
9	539	416
10	551	416
11	516	416

Iter	Nodes	Cost
0	11	240
1	25	240
2	37	240
3	54	240
4	84	240
5	133	240
6	206	240
7	279	240
8	311	240
9	331	240
10	343	240
11	312	240

Iter	Nodes	Cost
0	13	114
1	28	114
2	61	114
3	109	114
4	163	114
5	261	114
6	320	114
7	346	114
8	348	114
9	317	114

Iter	Nodes	Cost
0	16	416
1	42	416
2	62	416
3	90	416
4	141	416
5	222	416
6	339	416
7	454	416
8	499	416
9	539	416
10	551	416
11	516	416

Details

analyze720.0ms (20%)

sample1.8s (49.3%)

simplify256.0ms (7.1%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite44.0ms (1.2%)

simplify30.0ms (0.8%)

prune17.0ms (0.5%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite55.0ms (1.5%)

simplify20.0ms (0.6%)

prune29.0ms (0.8%)

localize7.0ms (0.2%)

series60.0ms (1.7%)

rewrite89.0ms (2.5%)

simplify87.0ms (2.4%)

prune130.0ms (3.6%)

localize6.0ms (0.2%)

series31.0ms (0.9%)

rewrite52.0ms (1.4%)

simplify46.0ms (1.3%)

prune18.0ms (0.5%)

regimes49.0ms (1.3%)

simplify2.0ms (0.1%)

end55.0ms (1.5%)

Profiling

Iter	Nodes	Cost
0	11	240
1	25	240
2	37	240
3	54	240
4	84	240
5	133	240
6	206	240
7	279	240
8	311	240
9	331	240
10	343	240
11	312	240

Iter	Nodes	Cost
0	13	114
1	28	114
2	61	114
3	109	114
4	163	114
5	261	114
6	320	114
7	346	114
8	348	114
9	317	114

Iter	Nodes	Cost
0	16	416
1	42	416
2	62	416
3	90	416
4	141	416
5	222	416
6	339	416
7	454	416
8	499	416
9	539	416
10	551	416
11	516	416