Details

analyze509.0ms (26.9%)

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
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.4%	10.1%	12
55%	30.3%	14.7%	13
59.5%	25.4%	15.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample862.0ms (45.5%)

Symmetry

(sort x y)

Results

763.0ms	8255×	body	128	valid
53.0ms	583×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify14.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary64`
33×	`distribute-rgt-in_binary64`
26×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
21×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	45	10
3	88	10
4	170	10
5	254	10
6	256	10
7	258	10
8	252	10

prune1.0ms (0.1%)

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 1))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))

series8.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`flip-+_binary64`
6×	`flip3-+_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 32

Calls

1 calls:

6.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

simplify63.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

759×	`distribute-rgt-in_binary64`
724×	`distribute-lft-in_binary64`
449×	`fma-def_binary64`
414×	`fma-neg_binary64`
258×	`unsub-neg_binary64`

Counts

68 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	908
1	269	804
2	911	798
3	3385	798
4	4092	798
5	5126	798

prune35.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	3	62

Error

Counts

62 → 3

Alt Table

Status	Error	Program
▶	29.1b	(fma.f64 y z y)
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
	30.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))

Compiler

Compiled 954 to 480 computations (49.7% saved)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	29.1b	(fma.f64 y z y)
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
▶	30.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1))
✓	0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))

series53.0ms (2.8%)

Counts

2 → 56

Calls

2 calls:

46.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1))
7.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))

rewrite30.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-div_binary64`
33×	`flip-+_binary64`
33×	`flip3-+_binary64`
32×	`frac-times_binary64`
16×	`associate-*r/_binary64`

Counts

2 → 90

Calls

2 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))
7.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1))

simplify104.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

553×	`fma-neg_binary64`
464×	`associate-+r+_binary64`
394×	`cancel-sign-sub-inv_binary64`
336×	`+-commutative_binary64`
316×	`associate--l+_binary64`

Counts

146 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3139
1	690	2791
2	2306	2741
3	4098	2735
4	4979	2735

prune73.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	168	3	171

Error

Counts

171 → 3

Alt Table

Status	Error	Program
✓	29.1b	(fma.f64 y z y)
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	30.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))

Compiler

Compiled 4403 to 1857 computations (57.8% saved)

regimes65.0ms (3.4%)

Accuracy

Total 0.0b remaining (46.1%)

Threshold costs 0.0b (46.1%)

Counts

10 → 1

Compiler

Compiled 746 to 482 computations (35.4% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	13	10
2	12	10

end51.0ms (2.7%)

Remove: (sort x y)
Compiler: Compiled 73 to 48 computations (34.2% saved)

Details

analyze509.0ms (26.9%)

sample862.0ms (45.5%)

simplify14.0ms (0.7%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite8.0ms (0.4%)

simplify63.0ms (3.3%)

prune35.0ms (1.8%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series53.0ms (2.8%)

rewrite30.0ms (1.6%)

simplify104.0ms (5.5%)

prune73.0ms (3.9%)

regimes65.0ms (3.4%)

simplify5.0ms (0.2%)

end51.0ms (2.7%)

Profiling