Details

analyze659.0ms (22.9%)

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
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)

sample997.0ms (34.6%)

Symmetry

(sort x y z)

Results

957.0ms

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

39.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.7b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	37.0b	(sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))))

series38.0ms (1.3%)

Counts

1 → 36

Calls

1 calls:

37.0ms

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

rewrite44.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

642×	`log1p-expm1-u_binary64`
642×	`expm1-log1p-u_binary64`
337×	`log-prod_binary64`
135×	`expm1-udef_binary64`
135×	`log1p-udef_binary64`

Counts

1 → 28

Calls

1 calls:

43.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	156	7
2	1695	7
3	5298	7
0	0	0
1	0	0

simplify73.0ms (2.5%)

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

64 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	1977
1	667	1821
2	2790	1819
3	4938	1819
4	5002	1819

prune78.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Error

Counts

98 → 4

Alt Table

Status	Error	Program
▶	0.5b	(hypot.f64 x z)
	39.8b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
	27.0b	(hypot.f64 y z)
	33.6b	(hypot.f64 y x)

Compiler

Compiled 3050 to 1910 computations (37.4% saved)

localize2.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	0.5b	(hypot.f64 x z)
	39.8b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
▶	27.0b	(hypot.f64 y z)
	33.6b	(hypot.f64 y x)

Compiler

Compiled 68 to 44 computations (35.3% saved)

localize2.0ms (0.1%)

prune4.0ms (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

Counts

4 → 4

Alt Table

Status	Error	Program
✓	0.5b	(hypot.f64 x z)
	39.8b	(neg.f64 (fma.f64 1/2 (/.f64 (.f64 z z) x) (fma.f64 1/2 (/.f64 (.f64 y y) x) x)))
✓	27.0b	(hypot.f64 y z)
▶	33.6b	(hypot.f64 y x)

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(hypot.f64 y x)

rewrite73.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

580×	`log1p-udef_binary64`
329×	`log1p-expm1-u_binary64`
329×	`expm1-log1p-u_binary64`
294×	`add-log-exp_binary64`
293×	`add-exp-log_binary64`

Counts

1 → 39

Calls

1 calls:

72.0ms

(hypot.f64 y x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	79	4
2	869	4
3	4730	4
4	5665	4
0	0	0
1	0	0

simplify52.0ms (1.8%)

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

63 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	488
1	160	470
2	495	454
3	2157	454
4	4396	454
5	5012	454

prune29.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	69	4	73

Error

Counts

73 → 4

Alt Table

Status	Error	Program
✓	0.5b	(hypot.f64 x z)
✓	27.0b	(hypot.f64 y z)
	37.1b	(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 y y) x) x))
✓	33.6b	(hypot.f64 y x)

Compiler

Compiled 844 to 466 computations (44.8% saved)

regimes159.0ms (5.5%)

Accuracy

Total 0.4b remaining (97.4%)

Threshold costs 0.4b (97.4%)

Counts

13 → 1

Compiler

Compiled 1596 to 1100 computations (31.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end638.0ms (22.1%)

Compiler: Compiled 54 to 36 computations (33.3% saved)

Details

analyze659.0ms (22.9%)

sample997.0ms (34.6%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series38.0ms (1.3%)

rewrite44.0ms (1.5%)

simplify73.0ms (2.5%)

prune78.0ms (2.7%)

localize2.0ms (0.1%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

prune4.0ms (0.1%)

localize2.0ms (0.1%)

series10.0ms (0.4%)

rewrite73.0ms (2.5%)

simplify52.0ms (1.8%)

prune29.0ms (1%)

regimes159.0ms (5.5%)

simplify2.0ms (0.1%)

end638.0ms (22.1%)

Profiling