Details

analyze1.7s (28.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.2s (36.1%)

Results

1.7s	8256×	body	128	valid
406.0ms	2140×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

prune6.0ms (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
▶	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series36.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

36.0ms

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

rewrite68.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
197×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Counts

1 → 29

Calls

1 calls:

67.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2368	11
3	5028	11
0	0	0
1	0	0

simplify122.0ms (2%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
716×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`
109×	`distribute-lft-in_binary64`

Counts

77 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	69	561
2	152	552
3	273	552
4	527	480
5	936	480
6	1333	480
7	1453	480
8	1489	480
9	1533	480
10	1543	480
11	1543	480
12	1458	480

prune47.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)
	30.0b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 y x) (/.f64 z t)) (.f64 (-.f64 y x) (/.f64 z t))) (.f64 x x)) (-.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x))
	41.4b	(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 z t)) 3) (pow.f64 x 3)) (fma.f64 (.f64 (-.f64 y x) (/.f64 z t)) (.f64 (-.f64 y x) (/.f64 z t)) (-.f64 (.f64 x x) (.f64 (.f64 (-.f64 y x) (/.f64 z t)) x))))
	34.2b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	4.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 780 to 244 computations (68.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	0.0b	(*.f64 (-.f64 y x) z)
✓	5.8b	(/.f64 (*.f64 (-.f64 y x) z) t)

series48.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

21.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
18.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
8.0ms	(*.f64 (-.f64 y x) z)

rewrite75.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

578×	`log-prod_binary64`
367×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
196×	`fma-neg_binary64`

Counts

3 → 139

Calls

3 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	205	30
2	3002	28
3	5851	28
0	0	0
1	0	0

simplify131.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

975×	`fma-def_binary64`
730×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`
121×	`unsub-neg_binary64`

Counts

271 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	1701
1	99	1260
2	202	1260
3	375	1188
4	712	1188
5	1137	1188
6	1439	1188
7	1515	1188
8	1542	1188
9	1548	1188
10	1553	1188
11	1553	1188
12	1468	1188

prune100.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	4	0	4
Picked	1	0	1
Done	0	1	1
Total	165	5	170

Error

0.0b

Counts

170 → 5

Alt Table

Status	Error	Program
▶	1.4b	(+.f64 x (-.f64 (/.f64 y (/.f64 t z)) (/.f64 x (/.f64 t z))))
	7.0b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.9b	(+.f64 x (/.f64 (fma.f64 y z (*.f64 (neg.f64 x) z)) t))

Compiler

Compiled 2494 to 717 computations (71.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (-.f64 (/.f64 y (/.f64 t z)) (/.f64 x (/.f64 t z))))
✓	0.0b	(-.f64 (/.f64 y (/.f64 t z)) (/.f64 x (/.f64 t z)))
✓	3.7b	(/.f64 y (/.f64 t z))
✓	4.1b	(/.f64 x (/.f64 t z))

series76.0ms (1.2%)

Counts

4 → 168

Calls

4 calls:

25.0ms	(-.f64 (/.f64 y (/.f64 t z)) (/.f64 x (/.f64 t z)))
24.0ms	(+.f64 x (-.f64 (/.f64 y (/.f64 t z)) (/.f64 x (/.f64 t z))))
15.0ms	(/.f64 y (/.f64 t z))
12.0ms	(/.f64 x (/.f64 t z))

rewrite104.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

453×	`fma-neg_binary64`
243×	`egg-rr`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`

Counts

4 → 243

Calls

4 calls:

100.0ms	(+.f64 x (-.f64 (/.f64 y (/.f64 t z)) (/.f64 x (/.f64 t z))))
100.0ms	(-.f64 (/.f64 y (/.f64 t z)) (/.f64 x (/.f64 t z)))
100.0ms	(/.f64 y (/.f64 t z))
100.0ms	(/.f64 x (/.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	246	37
2	4041	37
3	5263	37
0	0	0
1	0	0

simplify147.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
742×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
160×	`distribute-rgt-in_binary64`
123×	`unsub-neg_binary64`

Counts

411 → 260

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	1875
1	88	1524
2	195	1524
3	355	1524
4	682	1452
5	1139	1452
6	1437	1452
7	1518	1452
8	1545	1452
9	1551	1452
10	1556	1452
11	1556	1452
12	1471	1452

prune167.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	260	5	265

Error

Counts

265 → 5

Alt Table

Status	Error	Program
	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
▶	1.4b	(+.f64 x (-.f64 (/.f64 y (/.f64 t z)) (pow.f64 (/.f64 (/.f64 t z) x) -1)))
	7.0b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.9b	(+.f64 x (/.f64 (fma.f64 y z (*.f64 (neg.f64 x) z)) t))

Compiler

Compiled 4863 to 1200 computations (75.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y (/.f64 t z)) (pow.f64 (/.f64 (/.f64 t z) x) -1))
✓	0.5b	(pow.f64 (/.f64 (/.f64 t z) x) -1)
	3.7b	(/.f64 y (/.f64 t z))
✓	4.0b	(/.f64 (/.f64 t z) x)

series101.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

50.0ms	(-.f64 (/.f64 y (/.f64 t z)) (pow.f64 (/.f64 (/.f64 t z) x) -1))
35.0ms	(pow.f64 (/.f64 (/.f64 t z) x) -1)
15.0ms	(/.f64 (/.f64 t z) x)

rewrite121.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

339×	`fma-neg_binary64`
323×	`fma-def_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
223×	`egg-rr`

Counts

3 → 223

Calls

3 calls:

115.0ms	(-.f64 (/.f64 y (/.f64 t z)) (pow.f64 (/.f64 (/.f64 t z) x) -1))
115.0ms	(pow.f64 (/.f64 (/.f64 t z) x) -1)
115.0ms	(/.f64 (/.f64 t z) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	251	30
2	3570	30
3	4968	30
4	5050	30
0	0	0
1	0	0

simplify106.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-def_binary64`
378×	`fma-neg_binary64`
161×	`cancel-sign-sub-inv_binary64`
118×	`associate-/l*_binary64`
118×	`unsub-neg_binary64`

Counts

343 → 235

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	1098
1	64	972
2	145	972
3	284	972
4	489	972
5	796	972
6	1038	972
7	1082	972
8	1128	972
9	1134	972
10	1139	972
11	1139	972
12	1066	972

prune193.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	279	5	284

Error

Counts

284 → 5

Alt Table

Status	Error	Program
	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
✓	1.4b	(+.f64 x (-.f64 (/.f64 y (/.f64 t z)) (pow.f64 (/.f64 (/.f64 t z) x) -1)))
	7.0b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.9b	(+.f64 x (/.f64 (fma.f64 y z (*.f64 (neg.f64 x) z)) t))

Compiler

Compiled 6126 to 1647 computations (73.1% saved)

regimes280.0ms (4.6%)

Accuracy

Total 1.9b remaining (99.5%)

Threshold costs 0b (0%)

Counts

60 → 1

Compiler

Compiled 4751 to 2853 computations (39.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
9×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`
7×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	41	15
3	61	15
4	73	15
5	78	15
6	81	15
7	82	15
8	78	15

end130.0ms (2.1%)

Compiler: Compiled 100 to 61 computations (39% saved)

Details

analyze1.7s (28.3%)

sample2.2s (36.1%)

simplify80.0ms (1.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

series36.0ms (0.6%)

rewrite68.0ms (1.1%)

simplify122.0ms (2%)

prune47.0ms (0.8%)

localize11.0ms (0.2%)

series48.0ms (0.8%)

rewrite75.0ms (1.2%)

simplify131.0ms (2.1%)

prune100.0ms (1.6%)

localize9.0ms (0.1%)

series76.0ms (1.2%)

rewrite104.0ms (1.7%)

simplify147.0ms (2.4%)

prune167.0ms (2.7%)

localize10.0ms (0.2%)

series101.0ms (1.6%)

rewrite121.0ms (2%)

simplify106.0ms (1.7%)

prune193.0ms (3.2%)

regimes280.0ms (4.6%)

simplify7.0ms (0.1%)

end130.0ms (2.1%)

Profiling