Details

analyze3.0ms (0.1%)

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
99.9%	0%	0.1%	4

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample772.0ms (41.1%)

Infinites

0% of outputs are infinite.

Symmetry

(sort x y z)

Results

714.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify7.0ms (0.4%)

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 (0.2%)

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

36.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.7b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize28.0ms (1.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	36.7b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

series65.0ms (3.4%)

Counts

2 → 60

Calls

2 calls:

55.0ms	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))
9.0ms	(fma.f64 x x (*.f64 y y))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 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))

simplify91.0ms (4.9%)

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

85 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	2486
1	694	2327
2	2830	2325
3	4984	2325
4	5047	2325

prune94.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Error

0.0b

Counts

116 → 3

Alt Table

Status	Error	Program
▶	29.4b	(hypot.f64 y z)
	31.1b	(hypot.f64 y x)
✓	36.7b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 3424 to 1946 computations (43.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.7%)

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)

simplify56.0ms (3%)

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

prune32.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	42	3	45

Error

0.0b

Counts

45 → 3

Alt Table

Status	Error	Program
✓	29.4b	(hypot.f64 y z)
▶	31.1b	(hypot.f64 y x)
✓	36.7b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 572 to 344 computations (39.9% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(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)

simplify54.0ms (2.9%)

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

prune20.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	42	3	45

Error

0.0b

Counts

45 → 3

Alt Table

Status	Error	Program
✓	29.4b	(hypot.f64 y z)
✓	31.1b	(hypot.f64 y x)
✓	36.7b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 566 to 340 computations (39.9% saved)

regimes145.0ms (7.7%)

Accuracy

Total 0.3b remaining (59.4%)

Threshold costs 0.3b (59.4%)

Counts

12 → 1

Compiler

Compiled 1256 to 860 computations (31.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end473.0ms (25.2%)

Compiler: Compiled 49 to 31 computations (36.7% saved)

Details

analyze3.0ms (0.1%)

sample772.0ms (41.1%)

simplify7.0ms (0.4%)

prune3.0ms (0.2%)

localize28.0ms (1.5%)

series65.0ms (3.4%)

rewrite2.0ms (0.1%)

simplify91.0ms (4.9%)

prune94.0ms (5%)

localize3.0ms (0.1%)

series13.0ms (0.7%)

rewrite1.0ms (0%)

simplify56.0ms (3%)

prune32.0ms (1.7%)

localize2.0ms (0.1%)

series13.0ms (0.7%)

rewrite1.0ms (0%)

simplify54.0ms (2.9%)

prune20.0ms (1.1%)

regimes145.0ms (7.7%)

simplify2.0ms (0.1%)

end473.0ms (25.2%)

Profiling