Details

analyze186.0ms (4.5%)

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
40.6%	59.3%	0.1%	7
45.2%	54.6%	0.1%	8
65.5%	34.3%	0.1%	9
78%	21.8%	0.1%	10
80%	19.5%	0.5%	11
81.7%	17.7%	0.5%	12
87.9%	11.3%	0.8%	13
88.3%	10.1%	1.6%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample979.0ms (23.6%)

Results

744.0ms	8256×	body	128	valid
21.0ms	235×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify85.0ms (2%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-neg_binary64`
504×	`div-sub_binary64`
481×	`fma-def_binary64`
326×	`times-frac_binary64`
174×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	21	10
3	37	10
4	64	10
5	113	10
6	216	10
7	415	10
8	754	10
9	1183	10
10	1537	10
11	1612	10
12	1657	10
13	1684	10
14	1694	10
15	1702	10
16	1702	10
17	1600	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))

Compiler

Compiled 30 to 18 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series17.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

17.0ms

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

rewrite111.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
728×	`fma-udef_binary64`
226×	`fma-neg_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`

Counts

1 → 69

Calls

1 calls:

109.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	167	10
2	2530	10
3	4730	10
4	4517	10
5	5108	10
0	0	0
1	0	0

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

753×	`sub-neg_binary64`
431×	`associate--l+_binary64`
342×	`fma-def_binary64`
338×	`associate--r+_binary64`
311×	`associate-+l+_binary64`

Counts

105 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1081
1	225	1075
2	827	933
3	4185	927
4	4904	927
5	5012	927

prune72.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	4	102

Error

Counts

102 → 4

Alt Table

Status	Error	Program
	0.6b	(pow.f64 (/.f64 (-.f64 z y) (-.f64 x y)) -1)
	32.9b	(+.f64 (+.f64 (/.f64 x (-.f64 z y)) (neg.f64 (.f64 (/.f64 (sqrt.f64 y) (-.f64 z y)) (/.f64 (sqrt.f64 y) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 y) (-.f64 z y))) (/.f64 (sqrt.f64 y) 1) (.f64 (/.f64 (sqrt.f64 y) (-.f64 z y)) (/.f64 (sqrt.f64 y) 1))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
▶	0.2b	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (/.f64 y (-.f64 z y))))

Compiler

Compiled 2427 to 846 computations (65.1% saved)

localize40.0ms (1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z y))
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.2b	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (/.f64 y (-.f64 z y))))

series93.0ms (2.3%)

Counts

3 → 84

Calls

3 calls:

65.0ms	(/.f64 y (-.f64 z y))
21.0ms	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (/.f64 y (-.f64 z y))))
7.0ms	(/.f64 1 (-.f64 z y))

rewrite121.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

729×	`prod-diff_binary64`
586×	`fma-udef_binary64`
234×	`fma-def_binary64`
192×	`fma-neg_binary64`
174×	`expm1-udef_binary64`

Counts

3 → 151

Calls

3 calls:

117.0ms	(/.f64 y (-.f64 z y))
117.0ms	(/.f64 1 (-.f64 z y))
117.0ms	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (/.f64 y (-.f64 z y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	214	30
2	2521	30
3	4753	30
4	4635	30
5	5102	30
0	0	0
1	0	0

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

441×	`associate--l+_binary64`
425×	`fma-def_binary64`
391×	`associate--r+_binary64`
374×	`associate-+l+_binary64`
250×	`times-frac_binary64`

Counts

235 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	2027
1	294	1991
2	1080	1737
3	4997	1737

prune119.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	209	4	213

Error

Counts

213 → 4

Alt Table

Status	Error	Program
▶	0.6b	(pow.f64 (/.f64 (-.f64 z y) (-.f64 x y)) -1)
	32.9b	(+.f64 (+.f64 (/.f64 x (-.f64 z y)) (neg.f64 (.f64 (/.f64 (sqrt.f64 y) (-.f64 z y)) (/.f64 (sqrt.f64 y) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 y) (-.f64 z y))) (/.f64 (sqrt.f64 y) 1) (.f64 (/.f64 (sqrt.f64 y) (-.f64 z y)) (/.f64 (sqrt.f64 y) 1))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	0.2b	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (/.f64 y (-.f64 z y))))

Compiler

Compiled 4982 to 1813 computations (63.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series92.0ms (2.2%)

Counts

2 → 72

Calls

2 calls:

74.0ms	(pow.f64 (/.f64 (-.f64 z y) (-.f64 x y)) -1)
17.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

rewrite163.0ms (3.9%)

Algorithm

2×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
282×	`egg-rr`
193×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
105×	`log1p-expm1-u_binary64`

Counts

2 → 282

Calls

2 calls:

151.0ms	(/.f64 (-.f64 z y) (-.f64 x y))
150.0ms	(pow.f64 (/.f64 (-.f64 z y) (-.f64 x y)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	209	20
2	2918	20
3	5111	20
0	0	0
1	0	0

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

440×	`sub-neg_binary64`
385×	`times-frac_binary64`
276×	`associate-/l*_binary64`
236×	`+-commutative_binary64`
234×	`associate-+r+_binary64`

Counts

354 → 356

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	3611
1	886	3548
2	4142	3473
3	5187	3473

prune296.0ms (7.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	355	1	356
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	357	3	360

Error

Counts

360 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
▶	0.6b	(pow.f64 (-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)
✓	0.2b	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (/.f64 y (-.f64 z y))))

Compiler

Compiled 15948 to 4638 computations (70.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series101.0ms (2.4%)

Counts

4 → 111

Calls

4 calls:

58.0ms	(pow.f64 (-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)
20.0ms	(-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y)))
15.0ms	(/.f64 z (-.f64 x y))
8.0ms	(/.f64 y (-.f64 x y))

rewrite91.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

525×	`fma-def_binary64`
283×	`fma-neg_binary64`
254×	`egg-rr`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`

Counts

4 → 254

Calls

4 calls:

86.0ms	(/.f64 z (-.f64 x y))
86.0ms	(-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y)))
86.0ms	(/.f64 y (-.f64 x y))
86.0ms	(pow.f64 (-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	237	37
2	3511	37
3	4956	37
0	0	0
1	0	0

simplify258.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

559×	`times-frac_binary64`
398×	`associate-/l*_binary64`
364×	`associate-/r*_binary64`
256×	`associate-+l+_binary64`
204×	`associate--r+_binary64`

Counts

365 → 363

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	335	4704
1	1180	4615
2	5237	4615

prune543.0ms (13.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	363	0	363
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	363	3	366

Error

Counts

366 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	0.6b	(pow.f64 (-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y))) -1)
✓	0.2b	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (/.f64 y (-.f64 z y))))

Compiler

Compiled 10557 to 4130 computations (60.9% saved)

regimes495.0ms (11.9%)

Accuracy

Total 0.0b remaining (64%)

Threshold costs 0.0b (64%)

Counts

92 → 1

Compiler

Compiled 5953 to 3763 computations (36.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	28	37
2	33	37
3	36	37
4	37	37
5	35	37

end56.0ms (1.4%)

Compiler: Compiled 98 to 46 computations (53.1% saved)

Details

analyze186.0ms (4.5%)

sample979.0ms (23.6%)

simplify85.0ms (2%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series17.0ms (0.4%)

rewrite111.0ms (2.7%)

simplify66.0ms (1.6%)

prune72.0ms (1.7%)

localize40.0ms (1%)

series93.0ms (2.3%)

rewrite121.0ms (2.9%)

simplify54.0ms (1.3%)

prune119.0ms (2.9%)

localize6.0ms (0.1%)

series92.0ms (2.2%)

rewrite163.0ms (3.9%)

simplify92.0ms (2.2%)

prune296.0ms (7.1%)

localize8.0ms (0.2%)

series101.0ms (2.4%)

rewrite91.0ms (2.2%)

simplify258.0ms (6.2%)

prune543.0ms (13.1%)

regimes495.0ms (11.9%)

simplify3.0ms (0.1%)

end56.0ms (1.4%)

Profiling