Details

analyze465.0ms (18.9%)

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
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)

sample263.0ms (10.7%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
3.0ms	28×	body	128	invalid
2.0ms	57×	body	128	nan

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify193.0ms (7.8%)

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

23.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.6b	(-.f64 (.f64 y y) (.f64 z z))
✓	23.1b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series25.0ms (1%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
7.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`sqrt-prod_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 35

Calls

2 calls:

3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

simplify70.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-/l*_binary64`
396×	`associate-/r*_binary64`
360×	`associate-l_binary64`
298×	`fma-def_binary64`
245×	`fma-neg_binary64`

Counts

83 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1406
1	328	1361
2	1155	1328
3	4926	1328
4	5018	1328

prune53.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Error

0.0b

Counts

98 → 4

Alt Table

Status	Error	Program
	32.2b	(*.f64 x (neg.f64 y))
▶	27.9b	(*.f64 x y)
✓	23.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 1849 to 893 computations (51.7% saved)

localize2.0ms (0.1%)

prune3.0ms (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

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
	32.2b	(*.f64 x (neg.f64 y))
✓	27.9b	(*.f64 x y)
✓	23.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
▶	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 y z))
✓	0.0b	(sqrt.f64 (+.f64 y z))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

series75.0ms (3%)

Counts

3 → 36

Calls

3 calls:

28.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
25.0ms	(sqrt.f64 (+.f64 y z))
22.0ms	(sqrt.f64 (-.f64 y z))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`sqrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
16×	`sqrt-div_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

9.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
3.0ms	(sqrt.f64 (-.f64 y z))
2.0ms	(sqrt.f64 (+.f64 y z))

simplify101.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

737×	`times-frac_binary64`
547×	`fma-neg_binary64`
511×	`fma-def_binary64`
365×	`associate-/l*_binary64`
273×	`cancel-sign-sub-inv_binary64`

Counts

118 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	2287
1	526	2233
2	1567	2119
3	4933	2118
4	5329	2118

prune75.0ms (3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	174	4	178

Error

0.0b

Counts

178 → 4

Alt Table

Status	Error	Program
▶	32.2b	(*.f64 x (neg.f64 y))
✓	27.9b	(*.f64 x y)
✓	23.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 3664 to 1498 computations (59.1% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	32.2b	(*.f64 x (neg.f64 y))
✓	27.9b	(*.f64 x y)
✓	23.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 40 to 26 computations (35% saved)

regimes166.0ms (6.8%)

Accuracy

Total 0.4b remaining (76.5%)

Threshold costs 0.4b (76.5%)

Counts

6 → 2

Compiler

Compiled 615 to 420 computations (31.7% saved)

bsearch11.0ms (0.4%)

Steps

Iters	Range		Point
1	-1.5520177427993868e-290	1.760306478871254e-297	-3.4846515832014294e-305

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	28	29
2	38	29
3	46	29
4	50	29
5	51	29
6	51	29

end1.0ms (0%)

Compiler: Compiled 22 to 14 computations (36.4% saved)

sample906.0ms (36.9%)

Algorithm

1×

intervals

Results

400.0ms	8000×	body	128	valid
82.0ms	1869×	body	128	nan
30.0ms	693×	body	128	invalid

Compiler

Compiled 79 to 52 computations (34.2% saved)

Details

analyze465.0ms (18.9%)

sample263.0ms (10.7%)

simplify193.0ms (7.8%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series25.0ms (1%)

rewrite7.0ms (0.3%)

simplify70.0ms (2.8%)

prune53.0ms (2.2%)

localize2.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series75.0ms (3%)

rewrite19.0ms (0.8%)

simplify101.0ms (4.1%)

prune75.0ms (3%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

regimes166.0ms (6.8%)

bsearch11.0ms (0.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample906.0ms (36.9%)

Profiling