Details

analyze681.0ms (23.2%)

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
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample990.0ms (33.7%)

Symmetry

(sort x y z)

Results

940.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	14
2	25	14
3	29	14
4	29	14

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

35.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.4b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	33.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

series62.0ms (2.1%)

Counts

1 → 36

Calls

1 calls:

62.0ms

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

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

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

simplify86.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

704×	`cancel-sign-sub-inv_binary64`
387×	`fma-neg_binary64`
324×	`sub-neg_binary64`
203×	`fma-def_binary64`
180×	`distribute-neg-in_binary64`

Counts

51 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	2211
1	688	2064
2	2820	2062
3	4970	2062
4	5033	2062

prune71.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Error

0.0b

Counts

93 → 3

Alt Table

Status	Error	Program
✓	35.4b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))
▶	0.5b	(hypot.f64 x z)
	32.7b	(hypot.f64 y z)

Compiler

Compiled 3122 to 1857 computations (40.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 x z)

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

(hypot.f64 x z)

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
534×	`cancel-sign-sub-inv_binary64`
273×	`associate-/r/_binary64`
262×	`distribute-rgt-neg-in_binary64`
259×	`distribute-lft-neg-in_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	550
1	178	541
2	505	525
3	2143	525
4	4483	525
5	5070	525

prune26.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Error

0.0b

Counts

45 → 4

Alt Table

Status	Error	Program
✓	35.4b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))
▶	1.0b	(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))
✓	0.5b	(hypot.f64 x z)
	32.7b	(hypot.f64 y z)

Compiler

Compiled 596 to 356 computations (40.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x z)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))

series12.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
16×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 53

Calls

1 calls:

5.0ms

(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))

simplify81.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-neg_binary64`
534×	`cancel-sign-sub-inv_binary64`
315×	`neg-mul-1_binary64`
262×	`distribute-rgt-neg-in_binary64`
259×	`distribute-lft-neg-in_binary64`

Counts

77 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	923
1	226	885
2	647	856
3	2475	824
4	4347	824
5	4965	824
6	4933	824

prune77.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	173	4	177

Error

0.0b

Counts

177 → 4

Alt Table

Status	Error	Program
✓	35.4b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))
✓	1.0b	(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))
✓	0.5b	(hypot.f64 x z)
▶	32.7b	(hypot.f64 y z)

Compiler

Compiled 2840 to 1253 computations (55.9% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 y z)

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

(hypot.f64 y z)

simplify56.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-neg_binary64`
527×	`cancel-sign-sub-inv_binary64`
291×	`distribute-rgt-neg-in_binary64`
290×	`distribute-lft-neg-in_binary64`
281×	`associate-/r/_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	574
1	175	541
2	506	525
3	2149	525
4	4655	525
5	5014	525

prune22.0ms (0.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	42	4	46

Error

0.0b

Counts

46 → 4

Alt Table

Status	Error	Program
✓	35.4b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))
✓	1.0b	(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))
✓	0.5b	(hypot.f64 x z)
✓	32.7b	(hypot.f64 y z)

Compiler

Compiled 578 to 346 computations (40.1% saved)

regimes162.0ms (5.5%)

Accuracy

Total 0.3b remaining (69.1%)

Threshold costs 0.3b (69.1%)

Counts

14 → 1

Compiler

Compiled 1453 to 1016 computations (30.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end486.0ms (16.5%)

Compiler: Compiled 61 to 37 computations (39.3% saved)

Details

analyze681.0ms (23.2%)

sample990.0ms (33.7%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series62.0ms (2.1%)

rewrite2.0ms (0.1%)

simplify86.0ms (2.9%)

prune71.0ms (2.4%)

localize2.0ms (0.1%)

series11.0ms (0.4%)

rewrite1.0ms (0%)

simplify57.0ms (1.9%)

prune26.0ms (0.9%)

localize4.0ms (0.1%)

series12.0ms (0.4%)

rewrite15.0ms (0.5%)

simplify81.0ms (2.8%)

prune77.0ms (2.6%)

localize2.0ms (0.1%)

series11.0ms (0.4%)

rewrite1.0ms (0%)

simplify56.0ms (1.9%)

prune22.0ms (0.7%)

regimes162.0ms (5.5%)

simplify2.0ms (0.1%)

end486.0ms (16.5%)

Profiling