Details

analyze419.0ms (17.7%)

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
46.8%	44.5%	8.7%	10
51.5%	39%	9.5%	11
57.3%	32.6%	10.1%	12
63.8%	21.6%	14.7%	13
66.2%	18.7%	15.1%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.0s (43.8%)

Symmetry

(sort x y)

Results

919.0ms	8256×	body	128	valid
65.0ms	613×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`
1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	16	7
3	18	7
4	18	7

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) z)

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

6.0ms

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

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
3×	`associate-r_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 23

Calls

1 calls:

4.0ms

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

simplify98.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
448×	`associate-+l+_binary64`
431×	`fma-neg_binary64`
402×	`associate-+r+_binary64`
300×	`distribute-rgt-out_binary64`

Counts

59 → 41

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	490
1	115	460
2	370	460
3	930	460
4	1654	460
5	2723	460
6	3208	460
7	4769	460
8	4995	460
9	4860	460

prune16.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Error

0.0b

Counts

42 → 3

Alt Table

Status	Error	Program
	31.0b	(.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))
▶	0.0b	(+.f64 (.f64 y z) (.f64 z x))
✓	0.0b	(*.f64 (+.f64 x y) z)

Compiler

Compiled 494 to 150 computations (69.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.5%)

Counts

1 → 18

Calls

1 calls:

11.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`+-commutative_binary64`
1×	`flip-+_binary64`
1×	`*-un-lft-identity_binary64`
1×	`flip3-+_binary64`

Counts

1 → 14

Calls

1 calls:

3.0ms

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

simplify77.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

801×	`unsub-neg_binary64`
588×	`distribute-rgt-out_binary64`
339×	`distribute-rgt-in_binary64`
307×	`distribute-lft-in_binary64`
288×	`associate-l_binary64`

Counts

32 → 28

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	296
1	115	272
2	397	271
3	1233	271
4	2569	268
5	3818	268
6	4353	268
7	5317	268

prune15.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	28	3	31

Error

Counts

31 → 3

Alt Table

Status	Error	Program
	31.0b	(.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))
▶	0.0b	(fma.f64 y z (*.f64 z x))
✓	0.0b	(*.f64 (+.f64 x y) z)

Compiler

Compiled 393 to 113 computations (71.2% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 y z (*.f64 z x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y z (*.f64 z x))

simplify79.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
773×	`distribute-rgt-in_binary64`
765×	`distribute-lft-in_binary64`
405×	`*-commutative_binary64`
380×	`distribute-rgt-out_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	346
1	25	331
2	78	331
3	295	331
4	778	331
5	2919	331
6	3117	331
7	3288	331
8	3563	331
9	4329	331
10	4791	331

prune9.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	23	3	26

Error

Counts

26 → 3

Alt Table

Status	Error	Program
▶	31.0b	(.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))
✓	0.0b	(fma.f64 y z (*.f64 z x))
✓	0.0b	(*.f64 (+.f64 x y) z)

Compiler

Compiled 261 to 74 computations (71.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x y) z)
✓	0.2b	(.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))
✓	3.3b	(sqrt.f64 (*.f64 (+.f64 x y) z))

series254.0ms (10.7%)

Counts

2 → 40

Calls

2 calls:

207.0ms	(sqrt.f64 (*.f64 (+.f64 x y) z))
47.0ms	(.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
21×	`pow-prod-down_binary64`
16×	`associate-*l/_binary64`
14×	`sqrt-div_binary64`

Counts

2 → 74

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))
7.0ms	(sqrt.f64 (*.f64 (+.f64 x y) z))

simplify80.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
746×	`times-frac_binary64`
724×	`unswap-sqr_binary64`
240×	`*-commutative_binary64`
174×	`distribute-rgt-in_binary64`

Counts

114 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	127	1390
1	264	1336
2	846	1296
3	2092	1277
4	4408	1214
5	5266	1214

prune76.0ms (3.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	232	3	235

Error

Counts

235 → 3

Alt Table

Status	Error	Program
✓	31.0b	(.f64 (sqrt.f64 (.f64 (+.f64 x y) z)) (sqrt.f64 (*.f64 (+.f64 x y) z)))
✓	0.0b	(fma.f64 y z (*.f64 z x))
✓	0.0b	(*.f64 (+.f64 x y) z)

Compiler

Compiled 4560 to 979 computations (78.5% saved)

regimes68.0ms (2.9%)

Accuracy

Total 0.0b remaining (64.2%)

Threshold costs 0.0b (64.2%)

Counts

10 → 1

Compiler

Compiled 692 to 449 computations (35.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end51.0ms (2.2%)

Remove: (sort x y)
Compiler: Compiled 69 to 37 computations (46.4% saved)

Details

analyze419.0ms (17.7%)

sample1.0s (43.8%)

simplify10.0ms (0.4%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify98.0ms (4.2%)

prune16.0ms (0.7%)

localize5.0ms (0.2%)

series11.0ms (0.5%)

rewrite3.0ms (0.1%)

simplify77.0ms (3.3%)

prune15.0ms (0.6%)

localize4.0ms (0.2%)

series8.0ms (0.3%)

rewrite1.0ms (0%)

simplify79.0ms (3.3%)

prune9.0ms (0.4%)

localize6.0ms (0.2%)

series254.0ms (10.7%)

rewrite23.0ms (1%)

simplify80.0ms (3.4%)

prune76.0ms (3.2%)

regimes68.0ms (2.9%)

simplify2.0ms (0.1%)

end51.0ms (2.2%)

Profiling