Metrics for math.square on complex, imaginary part

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample587.0ms (30.7%)

Memory

36.4MiB live, 579.4MiB allocated; 120ms collecting garbage

Samples

364.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 187.0ms

ival-mult: 142.0ms (75.9% of total)

ival-add: 36.0ms (19.2% of total)

ival-true: 5.0ms (2.7% of total)

ival-assert: 3.0ms (1.6% of total)

adjust: 2.0ms (1.1% of total)

Bogosity

explain73.0ms (3.8%)

Memory

-28.7MiB live, 74.2MiB allocated; 12ms 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

41.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

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

ival-mult: 7.0ms (74.7% of total)

ival-add: 2.0ms (21.4% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess283.0ms (14.8%)

Memory

4.9MiB live, 189.8MiB allocated; 16ms 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)

simplify207.0ms (10.8%)

Memory

41.6MiB live, 170.6MiB allocated; 26ms 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)

localize42.0ms (2.2%)

Memory

-5.2MiB live, 48.3MiB allocated; 28ms collecting garbage

Localize:

Found 3 expressions of interest:

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

Samples

37.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 17.0ms (94.8% of total)

ival-add: 1.0ms (5.6% of total)

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

adjust: 0.0ms (0% of total)

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

series17.0ms (0.9%)

Memory

-35.6MiB live, 7.9MiB allocated; 28ms collecting garbage

Counts

3 → 3

Calls

Call 1

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

Outputs
#s(approx (+ (* re im) (* im re)) #s(hole binary64 (* 2 (* im re))))
#s(approx (* re im) #s(hole binary64 (* im re)))
#s(approx (* im re) #s(hole binary64 (* im re)))

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	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	@	-inf	((+ (* re im) (* im re)) (* re im) (* im re))
1.0ms	re	@	0	((+ (* re im) (* im re)) (* re im) (* im re))

simplify271.0ms (14.2%)

Memory

-32.4MiB live, 223.2MiB allocated; 201ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	22	25
2	50	25
3	101	25
4	273	25
5	1022	25
6	4310	25
0	8680	25

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 3

Calls

Call 1

Inputs
#s(approx (+ (* re im) (* im re)) #s(hole binary64 (* 2 (* im re))))
#s(approx (* re im) #s(hole binary64 (* im re)))
#s(approx (* im re) #s(hole binary64 (* im re)))

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

rewrite55.0ms (2.8%)

Memory

-3.5MiB live, 43.4MiB allocated; 1ms 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: 4.5MiB live, 4.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 229 to 54 computations (76.4% saved)

prune1.0ms (0%)

Memory

2.5MiB live, 2.5MiB 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)

simplify136.0ms (7.1%)

Memory

4.5MiB live, 152.8MiB allocated; 10ms 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

localize23.0ms (1.2%)

Memory

-30.5MiB live, 16.5MiB allocated; 2ms 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

19.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 12.0ms (85.1% of total)

ival-add: 1.0ms (7.1% 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, 5.4MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

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

Outputs
#s(approx (* re (+ im im)) #s(hole binary64 (* 2 (* im re))))
#s(approx (+ im im) #s(hole binary64 (* 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))
1.0ms	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))

simplify153.0ms (8%)

Memory

17.3MiB live, 156.8MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	20	18
2	45	18
3	103	18
4	237	18
5	814	18
6	4722	18
0	8082	18

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (* re (+ im im)) #s(hole binary64 (* 2 (* im re))))
#s(approx (+ im im) #s(hole binary64 (* 2 im)))

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

rewrite24.0ms (1.3%)

Memory

-25.4MiB live, 20.5MiB allocated; 3ms 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: 3.4MiB live, 3.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 249 to 67 computations (73.1% saved)

prune1.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB 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

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

11.7MiB live, 11.7MiB 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))

derivations1.0ms (0.1%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 5 to 4 computations (20% saved)

preprocess20.0ms (1%)

Memory

-20.3MiB live, 25.8MiB allocated; 2ms 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%)

sample587.0ms (30.7%)

explain73.0ms (3.8%)

preprocess283.0ms (14.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify207.0ms (10.8%)

localize42.0ms (2.2%)

series17.0ms (0.9%)

simplify271.0ms (14.2%)

rewrite55.0ms (2.8%)

eval2.0ms (0.1%)

prune1.0ms (0%)

simplify136.0ms (7.1%)

localize23.0ms (1.2%)

series4.0ms (0.2%)

simplify153.0ms (8%)

rewrite24.0ms (1.3%)

eval2.0ms (0.1%)

prune1.0ms (0.1%)

regimes4.0ms (0.2%)

simplify8.0ms (0.4%)

derivations1.0ms (0.1%)

preprocess20.0ms (1%)

end0.0ms (0%)

Profiling