Metrics for math.square on complex, imaginary part

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

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 9 to 7 computations (22.2% saved)

sample609.0ms (31.7%)

Memory

36.7MiB live, 673.5MiB allocated; 204ms collecting garbage

Samples

367.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 163.0ms

ival-mult: 120.0ms (73.5% of total)

ival-add: 33.0ms (20.2% of total)

ival-true: 5.0ms (3.1% of total)

ival-assert: 3.0ms (1.8% of total)

adjust: 2.0ms (1.2% of total)

Bogosity

explain97.0ms (5%)

Memory

8.3MiB live, 98.4MiB allocated; 46ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 im re)`
-	-	`(+.f64 (.f64 re im) (.f64 im re))`
-	-	`(*.f64 re im)`
-	-	`re`
-	-	`im`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

53.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-add: 34.0ms (82.4% of total)

ival-mult: 7.0ms (17% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess303.0ms (15.8%)

Memory

-30.4MiB live, 210.7MiB allocated; 158ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	36	27
2	81	25
3	154	25
4	218	25
5	316	25
6	748	25
7	1596	25
8	3572	25
0	5	7
0	8	7
1	14	5
2	30	5
3	53	5
4	94	5
5	197	5
6	506	5
7	1248	5
8	4772	5
9	7672	5
0	8315	5

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+.f64 (.f64 re im) (.f64 im re))

Outputs
(+.f64 (.f64 re im) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))

Symmetry

(negabs im)

(negabs re)

(sort re im)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 re im) (.f64 im re))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify210.0ms (10.9%)

Memory

-33.7MiB live, 161.2MiB allocated; 13ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 im re)
cost-diff	0	(*.f64 re im)
cost-diff	2	(+.f64 (.f64 re im) (.f64 im re))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	13
2	30	13
3	53	13
4	94	13
5	197	13
6	506	13
7	1248	13
8	4772	13
9	7672	13
0	8315	13

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (.f64 re im) (.f64 im re))
(*.f64 re im)
re
im
(*.f64 im re)

Outputs
(+.f64 (.f64 re im) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(*.f64 re im)
(*.f64 im re)
re
im
(*.f64 im re)

localize15.0ms (0.8%)

Memory

31.8MiB live, 31.8MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 re im)
accuracy	0.0	(*.f64 im re)
accuracy	0.00390625	(+.f64 (.f64 re im) (.f64 im re))

Samples

10.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 3.0ms (66.2% of total)

ival-add: 1.0ms (22.1% of total)

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

adjust: 0.0ms (0% of total)

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

series22.0ms (1.2%)

Memory

-19.0MiB live, 32.7MiB allocated; 5ms collecting garbage

Counts

3 → 2

Calls

Call 1

Inputs
(+.f64 (.f64 re im) (.f64 im re))
(*.f64 re im)
(*.f64 im re)

Outputs
(* 2 (* im re))
(* im re)

Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	im	@	0	((+ (* re im) (* im re)) (* re im) (* im re))
1.0ms	re	@	inf	((+ (* re im) (* im re)) (* re im) (* im re))
1.0ms	im	@	-inf	((+ (* re im) (* im re)) (* re im) (* im re))
1.0ms	re	@	0	((+ (* re im) (* im re)) (* re im) (* im re))
1.0ms	re	@	-inf	((+ (* re im) (* im re)) (* re im) (* im re))

simplify154.0ms (8%)

Memory

6.7MiB live, 99.4MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	12	8
2	36	8
3	85	8
4	246	8
5	838	8
6	4563	8
0	8912	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
(* 2 (* im re))
(* im re)

Outputs
(* 2 (* im re))
(.f64 (.f64 im re) #s(literal 2 binary64))
(* im re)
(*.f64 im re)

rewrite32.0ms (1.7%)

Memory

-8.4MiB live, 36.0MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	32	9
0	153	9

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 22

Calls

Call 1

Inputs
(+.f64 (.f64 re im) (.f64 im re))
(*.f64 re im)
(*.f64 im re)

Outputs
(.f64 #s(literal 2 binary64) (.f64 im re))
(*.f64 im (+.f64 re re))
(*.f64 re (-.f64 im (neg.f64 im)))
(*.f64 re (+.f64 im im))
(/.f64 (-.f64 (pow.f64 (.f64 im re) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 im) re) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 im re) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 im re) #s(literal 2 binary64)) (.f64 (.f64 im re) (*.f64 (neg.f64 im) re)))))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (pow.f64 (.f64 im re) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (*.f64 im re) #s(literal 2 binary64)))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 (.f64 im re) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 (*.f64 im re) #s(literal 2 binary64))))
(fma.f64 im re (*.f64 (neg.f64 (neg.f64 im)) re))
(fma.f64 im re (*.f64 im re))
(fma.f64 re im (*.f64 (neg.f64 (neg.f64 im)) re))
(fma.f64 re im (*.f64 im re))
(-.f64 (/.f64 (pow.f64 (.f64 im re) #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 (.f64 im re) #s(literal 2 binary64)) #s(literal 0 binary64)))
(-.f64 (.f64 im re) (.f64 (neg.f64 re) im))
(-.f64 (.f64 im re) (.f64 (neg.f64 im) re))
(+.f64 (/.f64 (pow.f64 (.f64 im re) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 im re) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64)))))
(+.f64 (.f64 im re) (.f64 (neg.f64 (neg.f64 im)) re))
(+.f64 (.f64 im re) (.f64 im re))
(*.f64 im re)
(*.f64 re im)
(*.f64 im re)
(*.f64 re im)

eval2.0ms (0.1%)

Memory: 4.8MiB live, 4.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 229 to 55 computations (76% saved)

prune1.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	1	23

Accuracy

100.0%

Counts

23 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 re (+.f64 im im))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify166.0ms (8.6%)

Memory

13.8MiB live, 111.0MiB allocated; 14ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 im im)
cost-diff	0	(*.f64 re (+.f64 im im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	13	10
2	29	10
3	57	10
4	124	10
5	240	10
6	941	10
7	4190	10
0	8541	10

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(*.f64 re (+.f64 im im))
re
(+.f64 im im)
im

Outputs
(*.f64 re (+.f64 im im))
(.f64 (.f64 #s(literal 2 binary64) im) re)
re
(+.f64 im im)
(*.f64 #s(literal 2 binary64) im)
im

localize19.0ms (1%)

Memory

-27.8MiB live, 16.6MiB allocated; 5ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(+.f64 im im)
accuracy	0.0	(*.f64 re (+.f64 im im))

Samples

15.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-mult: 2.0ms (60.5% of total)

ival-add: 1.0ms (30.2% of total)

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

adjust: 0.0ms (0% of total)

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

series4.0ms (0.2%)

Memory

5.4MiB live, 5.3MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
(*.f64 re (+.f64 im im))
(+.f64 im im)

Outputs
(* 2 (* im re))
(* 2 im)

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	im	@	inf	((* re (+ im im)) (+ im im))
1.0ms	im	@	-inf	((* re (+ im im)) (+ im im))
0.0ms	im	@	0	((* re (+ im im)) (+ im im))
0.0ms	re	@	-inf	((* re (+ im im)) (+ im im))
0.0ms	re	@	inf	((* re (+ im im)) (+ im im))

simplify205.0ms (10.6%)

Memory

-10.3MiB live, 177.9MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	14	8
2	39	8
3	98	8
4	232	8
5	800	8
6	4710	8
0	8226	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
(* 2 (* im re))
(* 2 im)

Outputs
(* 2 (* im re))
(.f64 (.f64 im re) #s(literal 2 binary64))
(* 2 im)
(*.f64 #s(literal 2 binary64) im)

rewrite23.0ms (1.2%)

Memory

17.2MiB live, 17.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	22	8
0	137	8

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

2 → 24

Calls

Call 1

Inputs
(*.f64 re (+.f64 im im))
(+.f64 im im)

Outputs
(.f64 (.f64 re #s(literal 2 binary64)) im)
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(*.f64 im (+.f64 re re))
(.f64 re (.f64 #s(literal 2 binary64) im))
(/.f64 (*.f64 #s(literal 0 binary64) re) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 im #s(literal 3 binary64))) re) (fma.f64 im im #s(literal 0 binary64)))
(/.f64 (*.f64 re #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 re (.f64 #s(literal 2 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 im im #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 (.f64 im re) (.f64 im re)) (.f64 (.f64 im re) (.f64 im re))) (-.f64 (.f64 im re) (.f64 im re)))
(/.f64 (+.f64 (pow.f64 (.f64 im re) #s(literal 3 binary64)) (pow.f64 (.f64 im re) #s(literal 3 binary64))) (fma.f64 (.f64 im re) (.f64 im re) (-.f64 (.f64 (.f64 im re) (.f64 im re)) (.f64 (.f64 im re) (.f64 im re)))))
(fma.f64 im re (*.f64 im re))
(fma.f64 re im (*.f64 im re))
(-.f64 (.f64 im re) (.f64 (neg.f64 im) re))
(-.f64 (.f64 im re) (.f64 (neg.f64 re) im))
(+.f64 (.f64 im re) (.f64 im re))
(*.f64 #s(literal 2 binary64) im)
(*.f64 im #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 im #s(literal 3 binary64)))) (neg.f64 (fma.f64 im im #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 im #s(literal 3 binary64))) (fma.f64 im im #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 im im) #s(literal 0 binary64)) (/.f64 (.f64 im im) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 im #s(literal 3 binary64)) (fma.f64 im im #s(literal 0 binary64))) (/.f64 (pow.f64 im #s(literal 3 binary64)) (fma.f64 im im #s(literal 0 binary64))))
(+.f64 im im)

eval2.0ms (0.1%)

Memory: 3.2MiB live, 3.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 249 to 67 computations (73.1% saved)

prune1.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	1	27

Accuracy

100.0%

Counts

27 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 re (+.f64 im im))

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes4.0ms (0.2%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 re (+.f64 im im))
(+.f64 (.f64 re im) (.f64 im re))

Outputs
(*.f64 re (+.f64 im im))

Calls

3 calls:

1.0ms	im
1.0ms	re
1.0ms	(+.f64 (.f64 re im) (.f64 im re))

Results

Accuracy	Segments	Branch
100.0%	1	`(+.f64 (.f64 re im) (.f64 im re))`
100.0%	1	`re`
100.0%	1	`im`

Compiler

Compiled 9 to 9 computations (0% saved)

simplify8.0ms (0.4%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 re (+.f64 im im))

Outputs
(*.f64 re (+.f64 im im))

derivations22.0ms (1.1%)

Memory

9.7MiB live, 9.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	32	9
0	153	9

Stop Event

1×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 5 to 4 computations (20% saved)

preprocess25.0ms (1.3%)

Memory

-1.6MiB live, 43.7MiB allocated; 3ms collecting garbage

Remove

(sort re im)

(negabs re)

(negabs im)

Compiler

Compiled 54 to 42 computations (22.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample609.0ms (31.7%)

explain97.0ms (5%)

preprocess303.0ms (15.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify210.0ms (10.9%)

localize15.0ms (0.8%)

series22.0ms (1.2%)

simplify154.0ms (8%)

rewrite32.0ms (1.7%)

eval2.0ms (0.1%)

prune1.0ms (0%)

simplify166.0ms (8.6%)

localize19.0ms (1%)

series4.0ms (0.2%)

simplify205.0ms (10.6%)

rewrite23.0ms (1.2%)

eval2.0ms (0.1%)

prune1.0ms (0.1%)

regimes4.0ms (0.2%)

simplify8.0ms (0.4%)

derivations22.0ms (1.1%)

preprocess25.0ms (1.3%)

end0.0ms (0%)

Profiling