Details

analyze646.0ms (14.9%)

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)

sample1.5s (33.9%)

Results

915.0ms	8256×	body	128	valid
304.0ms	2556×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify196.0ms (4.5%)

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%)

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

26.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.1b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	3.6b	(-.f64 (.f64 y y) (.f64 z z))
✓	26.0b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series51.0ms (1.2%)

Counts

3 → 84

Calls

3 calls:

33.0ms	(.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))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

6.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
5.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

simplify99.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
337×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
268×	`neg-mul-1_binary64`
187×	`distribute-rgt-neg-in_binary64`

Counts

146 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2931
1	582	2842
2	2289	2771
3	4556	2771
4	5028	2771

prune94.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	176	4	180

Error

0.0b

Counts

180 → 4

Alt Table

Status	Error	Program
✓	26.1b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.5b	(*.f64 x (neg.f64 y))
▶	29.2b	(*.f64 x y)
	31.2b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 3632 to 1621 computations (55.4% saved)

localize2.0ms (0%)

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
✓	26.1b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.5b	(*.f64 x (neg.f64 y))
✓	29.2b	(*.f64 x y)
▶	31.2b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series73.0ms (1.7%)

Counts

4 → 68

Calls

4 calls:

31.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
17.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
13.0ms	(sqrt.f64 (+.f64 y z))
13.0ms	(sqrt.f64 (-.f64 y z))

rewrite61.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
28×	`sqrt-div_binary64`
22×	`sqrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
15×	`pow1_binary64`

Counts

4 → 110

Calls

4 calls:

41.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
8.0ms	(.f64 x (.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))

simplify124.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
422×	`cancel-sign-sub-inv_binary64`
336×	`fma-neg_binary64`
277×	`distribute-rgt-in_binary64`
207×	`associate-r_binary64`

Counts

178 → 251

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	3798
1	791	3681
2	2560	3486
3	4896	3485
4	4992	3485

prune110.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	249	6	255

Error

Counts

255 → 6

Alt Table

Status	Error	Program
✓	26.1b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.5b	(*.f64 x (neg.f64 y))
✓	29.2b	(*.f64 x y)
	31.3b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z))) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))))
▶	31.2b	(.f64 x (.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))))
✓	31.2b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 5577 to 2259 computations (59.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series47.0ms (1.1%)

Counts

2 → 52

Calls

2 calls:

31.0ms

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

16.0ms

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

rewrite153.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

720×	`sqrt-div_binary64`
272×	`frac-times_binary64`
168×	`associate-*r/_binary64`
108×	`flip-+_binary64`
108×	`flip--_binary64`

Counts

2 → 240

Calls

2 calls:

28.0ms

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

20.0ms

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

simplify329.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
352×	`associate-r_binary64`
306×	`associate-l_binary64`
293×	`*-commutative_binary64`
275×	`distribute-rgt-in_binary64`

Counts

292 → 439

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	454	12478
1	925	11837
2	2756	11596
3	4894	11596
4	4994	11596

prune333.0ms (7.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	717	0	717
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	717	6	723

Error

Counts

723 → 6

Alt Table

Status	Error	Program
✓	26.1b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.5b	(*.f64 x (neg.f64 y))
✓	29.2b	(*.f64 x y)
	31.3b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z))) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))))
✓	31.2b	(.f64 x (.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))))
✓	31.2b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 29096 to 7749 computations (73.4% saved)

regimes304.0ms (7%)

Accuracy

Total 0.8b remaining (87.1%)

Threshold costs 0.8b (87.1%)

Counts

14 → 2

Compiler

Compiled 1939 to 1213 computations (37.4% saved)

bsearch24.0ms (0.6%)

Steps

Iters	Range		Point
1	-4.957508820182921e-247	4.184353912381864e-237	-4.957508820182921e-247

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (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

end168.0ms (3.9%)

Compiler: Compiled 131 to 76 computations (42% saved)

Details

analyze646.0ms (14.9%)

sample1.5s (33.9%)

simplify196.0ms (4.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series51.0ms (1.2%)

rewrite16.0ms (0.4%)

simplify99.0ms (2.3%)

prune94.0ms (2.2%)

localize2.0ms (0%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series73.0ms (1.7%)

rewrite61.0ms (1.4%)

simplify124.0ms (2.9%)

prune110.0ms (2.5%)

localize10.0ms (0.2%)

series47.0ms (1.1%)

rewrite153.0ms (3.5%)

simplify329.0ms (7.6%)

prune333.0ms (7.7%)

regimes304.0ms (7%)

bsearch24.0ms (0.6%)

simplify3.0ms (0.1%)

end168.0ms (3.9%)

Profiling