Details

analyze1.3s (1.6%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.7s (2.1%)

Results

1.2s	8256×	body	128	valid
425.0ms	2729×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify127.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

prune12.0ms (0%)

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
▶	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	6.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize16.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) a)
✓	5.0b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series99.0ms (0.1%)

Counts

2 → 88

Calls

2 calls:

75.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)
23.0ms	(/.f64 (-.f64 z t) a)

rewrite196.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
478×	`fma-udef_binary64`
280×	`fma-def_binary64`
194×	`fma-neg_binary64`
192×	`expm1-udef_binary64`

Counts

2 → 122

Calls

2 calls:

159.0ms	(/.f64 (-.f64 z t) a)
159.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	197	18
2	2709	18
3	4777	18
4	4727	18
5	5047	18
0	0	0
1	0	0

simplify218.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-def_binary64`
643×	`fma-neg_binary64`
172×	`cancel-sign-sub-inv_binary64`
155×	`unsub-neg_binary64`
154×	`distribute-rgt-in_binary64`

Counts

210 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	1214
1	71	944
2	154	908
3	292	774
4	563	774
5	968	774
6	1258	774
7	1393	774
8	1474	774
9	1483	774
10	1483	774
11	1410	774

prune162.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	139	4	143

Error

0.0b

Counts

143 → 4

Alt Table

Status	Error	Program
	5.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
✓	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	6.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	2.1b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

Compiler

Compiled 2789 to 681 computations (75.6% saved)

localize12.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

series54.0ms (0.1%)

Counts

1 → 60

Calls

1 calls:

54.0ms

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

rewrite83.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

499×	`log-prod_binary64`
446×	`prod-diff_binary64`
200×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

1 → 29

Calls

1 calls:

80.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	194	11
2	2576	11
3	5412	11
0	0	0
1	0	0

simplify162.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
691×	`fma-neg_binary64`
198×	`cancel-sign-sub-inv_binary64`
102×	`div-sub_binary64`
93×	`associate-r_binary64`

Counts

89 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	964
1	58	694
2	125	680
3	237	590
4	431	590
5	712	590
6	1161	590
7	1329	590
8	1418	590
9	1454	590
10	1460	590
11	1465	590
12	1465	590
13	1392	590

prune50.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	6	47

Error

0.0b

Counts

47 → 6

Alt Table

Status	Error	Program
	5.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
✓	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	6.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	3.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) 3)
	3.3b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) 2))
✓	2.1b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

Compiler

Compiled 710 to 221 computations (68.9% saved)

localize18.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) 3)
	2.0b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

series1.2min (93.1%)

Counts

2 → 120

Calls

2 calls:

1.2min	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) 3)
209.0ms	(cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x))

rewrite114.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

446×	`prod-diff_binary64`
339×	`fma-udef_binary64`
242×	`fma-def_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`

Counts

2 → 68

Calls

2 calls:

113.0ms	(cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x))
113.0ms	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	241	24
2	2999	24
3	4790	24
4	4889	24
5	4955	24
0	0	0
1	0	0

simplify187.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

786×	`associate-/l*_binary64`
662×	`associate-/r*_binary64`
434×	`fma-def_binary64`
251×	`*-commutative_binary64`
133×	`sub-neg_binary64`

Counts

188 → 202

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	622	10195
1	2299	9895
2	5927	9895

prune206.0ms (0.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	245	6	251

Error

Counts

251 → 6

Alt Table

Status	Error	Program
▶	5.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
	26.9b	(fma.f64 (*.f64 (-.f64 z t) (sqrt.f64 (/.f64 y a))) (sqrt.f64 (/.f64 y a)) x)
✓	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	6.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	3.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) 3)
✓	2.1b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

Compiler

Compiled 11539 to 5621 computations (51.3% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 a))
✓	5.0b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)

series36.0ms (0%)

Counts

2 → 96

Calls

2 calls:

28.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
9.0ms	(*.f64 (-.f64 z t) (/.f64 1 a))

rewrite93.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

568×	`prod-diff_binary64`
214×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
185×	`log-pow_binary64`

Counts

2 → 69

Calls

2 calls:

91.0ms	(*.f64 (-.f64 z t) (/.f64 1 a))
91.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	230	18
2	2816	18
3	4910	18
4	5181	18
0	0	0
1	0	0

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-def_binary64`
640×	`fma-neg_binary64`
170×	`cancel-sign-sub-inv_binary64`
154×	`distribute-rgt-in_binary64`
148×	`unsub-neg_binary64`

Counts

165 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	1192
1	74	922
2	157	920
3	296	830
4	579	830
5	963	830
6	1257	830
7	1387	830
8	1466	830
9	1475	830
10	1475	830
11	1402	830

prune84.0ms (0.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	87	6	93

Error

Counts

93 → 6

Alt Table

Status	Error	Program
✓	5.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
	26.9b	(fma.f64 (*.f64 (-.f64 z t) (sqrt.f64 (/.f64 y a))) (sqrt.f64 (/.f64 y a)) x)
✓	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	6.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	3.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) 3)
✓	2.1b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

Compiler

Compiled 1211 to 412 computations (66% saved)

regimes364.0ms (0.5%)

Accuracy

Total 1.6b remaining (98.9%)

Threshold costs 0b (0%)

Counts

21 → 3

Compiler

Compiled 2761 to 1858 computations (32.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	53
1	23	53
2	28	53
3	30	53
4	31	53
5	31	53

end84.0ms (0.1%)

Compiler: Compiled 174 to 90 computations (48.3% saved)

Details

analyze1.3s (1.6%)

sample1.7s (2.1%)

simplify127.0ms (0.2%)

prune12.0ms (0%)

localize16.0ms (0%)

series99.0ms (0.1%)

rewrite196.0ms (0.2%)

simplify218.0ms (0.3%)

prune162.0ms (0.2%)

localize12.0ms (0%)

series54.0ms (0.1%)

rewrite83.0ms (0.1%)

simplify162.0ms (0.2%)

prune50.0ms (0.1%)

localize18.0ms (0%)

series1.2min (93.1%)

rewrite114.0ms (0.1%)

simplify187.0ms (0.2%)

prune206.0ms (0.3%)

localize7.0ms (0%)

series36.0ms (0%)

rewrite93.0ms (0.1%)

simplify99.0ms (0.1%)

prune84.0ms (0.1%)

regimes364.0ms (0.5%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end84.0ms (0.1%)

Profiling