Metrics for Data.HyperLogLog.Config:hll from hyperloglog-0.3.4

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 8 to 5 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.0s (70.8%)

Results

786.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 165.0ms

ival-mult: 156.0ms (94.6% of total)

const: 7.0ms (4.2% of total)

backward-pass: 2.0ms (1.2% of total)

Bogosity

preprocess22.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

86×	`associate-r`
58×	`unsub-neg`
54×	`distribute-lft-in`
50×	`distribute-lft-neg-in`
36×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	50	32
2	110	32
3	240	32
4	353	32
5	380	32
6	386	32
0	4	5
1	8	5
2	9	5
0	9	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (* x y) y)

Outputs
(* (* x y) y)
(.f64 x (.f64 y y))

Call 2

Inputs
(* (* x y) y)
(* (* (neg x) y) y)
(* (* x (neg y)) (neg y))
(neg (* (* (neg x) y) y))
(neg (* (* x (neg y)) (neg y)))
(* (* y x) x)

Outputs
(* (* x y) y)
(* x (* y y))
(* (* (neg x) y) y)
(* x (* y (neg y)))
(* (* x (neg y)) (neg y))
(* x (* y y))
(neg (* (* (neg x) y) y))
(* x (* y y))
(neg (* (* x (neg y)) (neg y)))
(* x (* y (neg y)))
(* (* y x) x)
(* y (* x x))

Symmetry

(abs y)

(negabs x)

explain43.0ms (2.9%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(.f64 (.f64 x y) y)`
-	-	`(*.f64 x y)`
-	-	`x`
-	-	`y`

Results

25.0ms

512×

valid

Compiler

Compiled 33 to 14 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 8.0ms (92.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.f64 (.f64 x y) y)
▶	89.6%	(.f64 x (.f64 y y))

Compiler

Compiled 14 to 8 computations (42.9% saved)

localize40.0ms (2.7%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(.f64 (.f64 x y) y)
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(.f64 x (.f64 y y))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	99.8%	(.f64 (.f64 x y) y)
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	89.6%	(.f64 x (.f64 y y))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
6×	`*-commutative`
2×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
0	9	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x (* y y))
x
(* y y)
y
(* (* x y) y)
(* x y)

Outputs
(* x (* y y))
(.f64 y (.f64 x y))
x
(* y y)
(*.f64 y y)
y
(* (* x y) y)
(.f64 y (.f64 x y))
(* x y)
(*.f64 x y)

Results

21.0ms

256×

valid

Compiler

Compiled 23 to 7 computations (69.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 9.0ms (91.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series13.0ms (0.9%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (* x (* y y))>
#<alt (* y y)>
#<alt (* (* x y) y)>
#<alt (* x y)>

Outputs
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>

Calls

21 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	(* x y)
1.0ms	x	@	0	(* x (* y y))
1.0ms	y	@	inf	(* x (* y y))
0.0ms	y	@	inf	(* x y)
0.0ms	x	@	inf	(* x (* y y))

rewrite162.0ms (11.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2136×	`pow-lowering-pow.f64`
2136×	`pow-lowering-pow.f32`
1592×	`-lowering-.f32`
1592×	`-lowering-.f64`
1412×	`prod-exp`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	11	18
2	18	18
3	34	18
4	90	18
5	279	10
6	1692	4
7	1717	4
8	1840	4
9	3080	4
0	8467	4

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 11

Calls

Call 1

Inputs
(* x (* y y))
(* y y)
(* (* x y) y)
(* x y)

Outputs
x
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
y
x
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
x
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))

simplify9.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	348
1	9	348
2	11	348
0	11	348

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

Calls

Call 1

Inputs
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

Outputs
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)

eval8.0ms (0.5%)

Compiler: Compiled 455 to 22 computations (95.2% saved)

prune2.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	93	4	97

Accuracy

99.9%

Counts

97 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(.f64 (.f64 x y) y)
✓	89.6%	(.f64 x (.f64 y y))
▶	30.2%	(*.f64 x y)
▶	5.0%	x

Compiler

Compiled 22 to 13 computations (40.9% saved)

localize56.0ms (3.8%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x y)
✓	accuracy	100.0%	(*.f64 x y)

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* x y)
y

Outputs
x
(* x y)
(*.f64 x y)
y

Results

45.0ms

256×

valid

Compiler

Compiled 9 to 4 computations (55.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (76.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0.1%)

Counts

1 → 24

Calls

Call 1

Inputs
#<alt (* x y)>

Outputs
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* x y)
0.0ms	y	@	inf	(* x y)
0.0ms	x	@	inf	(* x y)
0.0ms	x	@	-inf	(* x y)
0.0ms	y	@	-inf	(* x y)

rewrite9.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	4	3
0	4	3

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* x y)

Outputs
(*.f64 x y)
(*.f64 y x)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	72
1	4	72
0	4	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

Outputs
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)

eval2.0ms (0.2%)

Compiler: Compiled 80 to 4 computations (95% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	26	4	30

Accuracy

99.9%

Counts

30 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(.f64 (.f64 x y) y)
✓	89.6%	(.f64 x (.f64 y y))
✓	30.2%	(*.f64 x y)
✓	5.0%	x

Compiler

Compiled 38 to 19 computations (50% saved)

regimes6.0ms (0.4%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(*.f64 x y)
(.f64 x (.f64 y y))
(.f64 (.f64 x y) y)

Outputs
(.f64 (.f64 x y) y)

Calls

3 calls:

2.0ms	y
2.0ms	x
1.0ms	(.f64 (.f64 x y) y)

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`(.f64 (.f64 x y) y)`

Compiler

Compiled 13 to 8 computations (38.5% saved)

regimes7.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(*.f64 x y)
(.f64 x (.f64 y y))

Outputs
(.f64 x (.f64 y y))

Calls

2 calls:

5.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
89.6%	1	`x`
89.6%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 x y)

Outputs
(*.f64 x y)

Calls

2 calls:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
30.2%	1	`y`
30.2%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes1.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

0.0ms	x
0.0ms	y

Results

Accuracy	Segments	Branch
5.0%	1	`y`
5.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 16 to 6 computations (62.5% saved)

preprocess33.0ms (2.3%)

Remove

(negabs x)

(abs y)

Compiler

Compiled 186 to 100 computations (46.2% saved)

Data.HyperLogLog.Config:hll from hyperloglog-0.3.4

analyze0.0ms (0%)

sample1.0s (70.8%)

preprocess22.0ms (1.5%)

explain43.0ms (2.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize40.0ms (2.7%)

series13.0ms (0.9%)

rewrite162.0ms (11.1%)

simplify9.0ms (0.6%)

eval8.0ms (0.5%)

prune2.0ms (0.2%)

localize56.0ms (3.8%)

series1.0ms (0.1%)

rewrite9.0ms (0.6%)

simplify4.0ms (0.3%)

eval2.0ms (0.2%)

prune2.0ms (0.1%)

regimes6.0ms (0.4%)

regimes7.0ms (0.5%)

regimes3.0ms (0.2%)

regimes1.0ms (0.1%)

soundness1.0ms (0%)

preprocess33.0ms (2.3%)

end0.0ms (0%)

Profiling