Details

analyze544.0ms (18%)

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
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (46.7%)

Results

891.0ms	8256×	body	128	valid
265.0ms	2681×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify192.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

767×	`unsub-neg_binary64`
741×	`*-commutative_binary64`
699×	`fma-def_binary64`
598×	`fma-neg_binary64`
465×	`distribute-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	19	15
2	29	15
3	57	15
4	118	15
5	278	15
6	529	15
7	1007	15
8	1781	15
9	2585	15
10	2834	15
11	3141	15
12	3371	15
13	3485	15
14	3485	15
15	4444	15
16	4284	15
17	4604	15
18	4604	15
19	5103	15

prune2.0ms (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

24.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	24.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	2.8b	(-.f64 (.f64 y y) (.f64 z z))
✓	26.7b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series49.0ms (1.6%)

Counts

3 → 84

Calls

3 calls:

32.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
12.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
6.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite135.0ms (4.5%)

Algorithm

2×	batch-egg-rewrite

Rules

665×	`prod-diff_binary64`
465×	`fma-udef_binary64`
406×	`fma-def_binary64`
257×	`fma-neg_binary64`
227×	`egg-rr`

Counts

3 → 227

Calls

3 calls:

127.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
127.0ms	(-.f64 (.f64 y y) (.f64 z z))
127.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	196	37
2	2367	35
3	4789	35
4	4782	35
5	4938	35
0	0	0
1	0	0

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-/l*_binary64`
591×	`associate-/r*_binary64`
472×	`fma-def_binary64`
305×	`fma-neg_binary64`
264×	`cancel-sign-sub-inv_binary64`

Counts

311 → 311

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1894
1	429	1872
2	1491	1838
3	4802	1838
4	5097	1838

prune147.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	308	3	311
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	308	4	312

Error

0.2b

Counts

312 → 4

Alt Table

Status	Error	Program
	32.9b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	24.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
▶	28.3b	(*.f64 x (neg.f64 y))
	30.2b	(*.f64 x y)

Compiler

Compiled 6799 to 2654 computations (61% saved)

localize6.0ms (0.2%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.2b

Counts

4 → 4

Alt Table

Status	Error	Program
	32.9b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	24.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	28.3b	(*.f64 x (neg.f64 y))
▶	30.2b	(*.f64 x y)

Compiler

Compiled 60 to 39 computations (35% saved)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.2b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	32.9b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	24.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	28.3b	(*.f64 x (neg.f64 y))
✓	30.2b	(*.f64 x y)

Compiler

Compiled 54 to 35 computations (35.2% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series30.0ms (1%)

Counts

2 → 28

Calls

2 calls:

15.0ms	(sqrt.f64 (+.f64 y z))
15.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

rewrite57.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

868×	`log1p-expm1-u_binary64`
868×	`expm1-log1p-u_binary64`
534×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`

Counts

2 → 44

Calls

2 calls:

56.0ms	(sqrt.f64 (+.f64 y z))
56.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	173	18
2	2190	18
3	6356	18
0	0	0
1	0	0

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
591×	`fma-neg_binary64`
322×	`fma-def_binary64`
319×	`associate-/r*_binary64`
311×	`associate-/l*_binary64`

Counts

72 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	805
1	308	789
2	978	761
3	4715	760
4	5184	760

prune42.0ms (1.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	89	4	93

Error

0.2b

Counts

93 → 4

Alt Table

Status	Error	Program
✓	32.9b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	24.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	28.3b	(*.f64 x (neg.f64 y))
✓	30.2b	(*.f64 x y)

Compiler

Compiled 1778 to 974 computations (45.2% saved)

regimes160.0ms (5.3%)

Accuracy

Total 0.6b remaining (82.7%)

Threshold costs 0.6b (82.7%)

Counts

7 → 2

Compiler

Compiled 743 to 508 computations (31.6% saved)

bsearch38.0ms (1.2%)

Steps

Iters	Range		Point
2	-3.772512675547034e-242	6.924855485400472e-277	-2.783211035485618e-291

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	17	16
2	24	16
3	29	16
4	32	16
5	33	16
6	33	16

end49.0ms (1.6%)

Compiler: Compiled 68 to 44 computations (35.3% saved)

Details

analyze544.0ms (18%)

sample1.4s (46.7%)

simplify192.0ms (6.3%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series49.0ms (1.6%)

rewrite135.0ms (4.5%)

simplify82.0ms (2.7%)

prune147.0ms (4.9%)

localize6.0ms (0.2%)

prune2.0ms (0.1%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series30.0ms (1%)

rewrite57.0ms (1.9%)

simplify55.0ms (1.8%)

prune42.0ms (1.4%)

regimes160.0ms (5.3%)

bsearch38.0ms (1.2%)

simplify3.0ms (0.1%)

end49.0ms (1.6%)

Profiling