Details

analyze690.0ms (19.6%)

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)

sample1.0s (29.6%)

Symmetry

(sort x y z)

Results

1.0s

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

37.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	0.0b	(fma.f64 z z (fma.f64 x x (*.f64 y y)))
✓	34.4b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

series75.0ms (2.1%)

Counts

3 → 96

Calls

3 calls:

54.0ms	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))
15.0ms	(fma.f64 z z (fma.f64 x x (*.f64 y y)))
6.0ms	(fma.f64 x x (*.f64 y y))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 35

Calls

3 calls:

1.0ms	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))
0.0ms	(fma.f64 x x (*.f64 y y))
0.0ms	(fma.f64 z z (fma.f64 x x (*.f64 y y)))

simplify98.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

131 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	3034
1	703	2846
2	2890	2844
3	4964	2844
4	4975	2844

prune137.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	5	141

Error

0.0b

Counts

141 → 5

Alt Table

Status	Error	Program
	29.9b	(hypot.f64 y x)
	37.3b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y)))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y))))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))))
▶	0.8b	(hypot.f64 x z)
	31.1b	(hypot.f64 y z)
✓	37.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 3835 to 2045 computations (46.7% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series15.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(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)

simplify55.0ms (1.6%)

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

prune24.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	42	5	47

Error

0.0b

Counts

47 → 5

Alt Table

Status	Error	Program
▶	29.9b	(hypot.f64 y x)
	37.3b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y)))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y))))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))))
✓	0.8b	(hypot.f64 x z)
	31.1b	(hypot.f64 y z)
✓	37.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 656 to 372 computations (43.3% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 y 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

(hypot.f64 y x)

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary64`
537×	`cancel-sign-sub-inv_binary64`
354×	`neg-mul-1_binary64`
312×	`distribute-rgt-neg-in_binary64`
310×	`distribute-lft-neg-in_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	568
1	174	541
2	511	525
3	2175	525
4	4416	525
5	5032	525

prune22.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	42	5	47

Error

0.0b

Counts

47 → 5

Alt Table

Status	Error	Program
✓	29.9b	(hypot.f64 y x)
	37.3b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y)))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y))))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))))
✓	0.8b	(hypot.f64 x z)
▶	31.1b	(hypot.f64 y z)
✓	37.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 650 to 368 computations (43.4% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(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)

simplify55.0ms (1.6%)

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

prune20.0ms (0.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	41	6	47

Error

0.0b

Counts

47 → 6

Alt Table

Status	Error	Program
	31.7b	(.f64 (.f64 (cbrt.f64 (hypot.f64 y z)) (cbrt.f64 (hypot.f64 y z))) (cbrt.f64 (hypot.f64 y z)))
✓	29.9b	(hypot.f64 y x)
	37.3b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y)))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (.f64 y y))))) (cbrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))))
✓	0.8b	(hypot.f64 x z)
✓	31.1b	(hypot.f64 y z)
✓	37.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 625 to 361 computations (42.2% saved)

regimes240.0ms (6.8%)

Accuracy

Total 0.5b remaining (98.9%)

Threshold costs 0.5b (98.9%)

Counts

16 → 1

Compiler

Compiled 1982 to 1177 computations (40.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end936.0ms (26.5%)

Compiler: Compiled 108 to 52 computations (51.9% saved)

Details

analyze690.0ms (19.6%)

sample1.0s (29.6%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series75.0ms (2.1%)

rewrite3.0ms (0.1%)

simplify98.0ms (2.8%)

prune137.0ms (3.9%)

localize2.0ms (0.1%)

series15.0ms (0.4%)

rewrite1.0ms (0%)

simplify55.0ms (1.6%)

prune24.0ms (0.7%)

localize2.0ms (0.1%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify57.0ms (1.6%)

prune22.0ms (0.6%)

localize2.0ms (0.1%)

series13.0ms (0.4%)

rewrite1.0ms (0%)

simplify55.0ms (1.6%)

prune20.0ms (0.6%)

regimes240.0ms (6.8%)

simplify2.0ms (0.1%)

end936.0ms (26.5%)

Profiling