Details

analyze714.0ms (16.4%)

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
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.5s (33.7%)

Results

1.1s	8256×	body	128	valid
187.0ms	1233×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	3.0b	(*.f64 (/.f64 x y) z)

series38.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

19.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
13.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)

rewrite76.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

334×	`fma-def_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
202×	`fma-neg_binary64`
199×	`log-div_binary64`

Counts

3 → 176

Calls

3 calls:

72.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
72.0ms	(/.f64 (+.f64 x 4) y)
72.0ms	(*.f64 (/.f64 x y) z)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	236	27
2	3339	27
3	5221	27

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
180×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Counts

272 → 193

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	1102
1	76	1102
2	174	952
3	335	860
4	580	790
5	1196	790
6	1420	790
7	1487	790
8	1499	790
9	1499	790
10	1398	790

prune130.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	190	5	195

Error

Counts

195 → 5

Alt Table

Status	Error	Program
	33.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 (/.f64 (*.f64 x z) (sqrt.f64 y)) (sqrt.f64 y))))
	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x))))
	32.6b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 4115 to 1974 computations (52% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x)))
	0.0b	(/.f64 (+.f64 x 4) y)
✓	3.4b	(/.f64 z (/.f64 y x))

series32.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x)))
13.0ms	(/.f64 z (/.f64 y x))

rewrite86.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

425×	`fma-def_binary64`
256×	`fma-neg_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
182×	`egg-rr`

Counts

2 → 182

Calls

2 calls:

81.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 z (/.f64 y x)))
81.0ms	(/.f64 z (/.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	245	23
2	3790	23
3	5138	23

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
180×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Counts

254 → 196

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	880
1	76	880
2	174	730
3	335	638
4	580	631
5	1196	631
6	1420	631
7	1487	631
8	1499	631
9	1499	631
10	1398	631

prune153.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	235	4	239

Error

Counts

239 → 4

Alt Table

Status	Error	Program
	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (/.f64 (/.f64 y x) z) -1)))
	32.6b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 5365 to 2370 computations (55.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (/.f64 (/.f64 y x) z) -1))
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.4b	(pow.f64 (/.f64 (/.f64 y x) z) -1)
✓	3.4b	(/.f64 (/.f64 y x) z)

series93.0ms (2.1%)

Counts

3 → 108

Calls

3 calls:

41.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (/.f64 (/.f64 y x) z) -1))
34.0ms	(pow.f64 (/.f64 (/.f64 y x) z) -1)
17.0ms	(/.f64 (/.f64 y x) z)

rewrite86.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

342×	`fma-def_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
223×	`fma-neg_binary64`
194×	`egg-rr`

Counts

3 → 194

Calls

3 calls:

82.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (/.f64 (/.f64 y x) z) -1))
81.0ms	(pow.f64 (/.f64 (/.f64 y x) z) -1)
81.0ms	(/.f64 (/.f64 y x) z)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	281	30
2	3918	30
3	5164	30

simplify92.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-neg_binary64`
336×	`fma-def_binary64`
186×	`distribute-rgt-in_binary64`
183×	`cancel-sign-sub-inv_binary64`
161×	`unsub-neg_binary64`

Counts

302 → 209

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	1132
1	79	1132
2	176	982
3	337	890
4	585	883
5	1202	883
6	1420	883
7	1487	883
8	1499	883
9	1499	883
10	1398	883

prune155.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	247	4	251

Error

Counts

251 → 4

Alt Table

Status	Error	Program
▶	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (/.f64 (/.f64 y x) z) -1)))
	32.6b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 5323 to 2565 computations (51.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series15.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

rewrite115.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`prod-diff_binary64`
209×	`fma-def_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
169×	`egg-rr`

Counts

1 → 169

Calls

1 calls:

108.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	180	11
2	2479	11
3	4868	11
4	5139	11

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-neg_binary64`
291×	`fma-def_binary64`
275×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`
164×	`div-sub_binary64`

Counts

205 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	619
1	67	619
2	139	469
3	286	379
4	566	379
5	1039	379
6	1297	379
7	1478	379
8	1489	379
9	1497	379
10	1497	379
11	1396	379

prune166.0ms (3.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	180	4	184

Error

Counts

184 → 4

Alt Table

Status	Error	Program
✓	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (/.f64 (/.f64 y x) z) -1)))
	32.6b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 8321 to 4482 computations (46.1% saved)

regimes471.0ms (10.8%)

Accuracy

Total 0.2b remaining (94.3%)

Threshold costs 0.2b (94.3%)

Counts

30 → 3

Compiler

Compiled 2072 to 1436 computations (30.7% saved)

bsearch24.0ms (0.5%)

Steps

Iters	Range		Point
7	2.512129695118171e+67	3.2725002446697765e+69	3.883658016843068e+67
1	-2.0192965836964857e+34	-1.671665335275408e+31	-5.829815448466412e+32

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
8×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	63
1	46	61
2	61	61
3	76	61
4	86	61
5	94	61
6	102	61
7	106	61
8	107	61
9	106	61

end75.0ms (1.7%)

Compiler: Compiled 145 to 93 computations (35.9% saved)

Details

analyze714.0ms (16.4%)

sample1.5s (33.7%)

simplify63.0ms (1.4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series38.0ms (0.9%)

rewrite76.0ms (1.7%)

simplify93.0ms (2.1%)

prune130.0ms (3%)

localize8.0ms (0.2%)

series32.0ms (0.7%)

rewrite86.0ms (2%)

simplify85.0ms (1.9%)

prune153.0ms (3.5%)

localize10.0ms (0.2%)

series93.0ms (2.1%)

rewrite86.0ms (2%)

simplify92.0ms (2.1%)

prune155.0ms (3.6%)

localize6.0ms (0.1%)

series15.0ms (0.4%)

rewrite115.0ms (2.6%)

simplify80.0ms (1.8%)

prune166.0ms (3.8%)

regimes471.0ms (10.8%)

bsearch24.0ms (0.5%)

simplify5.0ms (0.1%)

end75.0ms (1.7%)

Profiling