Metrics for math.square on complex, imaginary part

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

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)

sample688.0ms (68.9%)

Memory

-0.0MiB live, 781.4MiB allocated

Samples

487.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 204.0ms

ival-mult: 160.0ms (78.4% of total)

ival-add: 35.0ms (17.2% of total)

ival-true: 6.0ms (2.9% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain88.0ms (8.8%)

Memory

-4.5MiB live, 93.4MiB allocated

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

48.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

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

ival-mult: 7.0ms (73.7% of total)

ival-add: 2.0ms (21% of total)

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

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

preprocess21.0ms (2.1%)

Memory

28.0MiB live, 28.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	36	27
2	81	25
3	154	25
4	206	25
5	230	25
0	5	7
0	8	7
1	14	5
2	30	5
3	53	5
4	89	5
5	143	5
6	177	5
7	197	5
8	212	5
0	212	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

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)

simplify14.0ms (1.4%)

Memory

-40.3MiB live, 6.7MiB allocated

Algorithm

1×	egg-herbie

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	89	13
5	143	13
6	177	13
7	197	13
8	212	13
0	212	13

Stop Event

1×	iter limit
1×	saturated
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)

localize14.0ms (1.4%)

Memory

28.8MiB live, 28.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 re im)
accuracy	0.0	(*.f64 im re)
accuracy	0.01171875	(+.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 (66.5% of total)

ival-add: 1.0ms (22.2% of total)

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

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

series4.0ms (0.4%)

Memory

8.4MiB live, 8.4MiB allocated

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
1.0ms	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))

simplify10.0ms (1%)

Memory

-34.6MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	12	8
2	31	8
3	46	8
4	64	8
5	98	8
6	168	8
7	193	8
8	213	8
9	223	8
0	223	8

Stop Event

1×	iter limit
1×	saturated

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)

rewrite26.0ms (2.6%)

Memory

41.6MiB live, 41.6MiB allocated

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)

eval8.0ms (0.8%)

Memory: -43.7MiB live, 6.7MiB allocated
Compiler: Compiled 229 to 55 computations (76% saved)

prune1.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated

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)

simplify7.0ms (0.7%)

Memory

4.6MiB live, 4.6MiB allocated

Algorithm

1×	egg-herbie

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	48	10
4	66	10
5	100	10
6	164	10
7	189	10
8	209	10
9	219	10
0	219	10

Stop Event

1×	iter limit
1×	saturated
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

localize12.0ms (1.2%)

Memory

14.8MiB live, 14.8MiB allocated

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

8.0ms

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 (65.4% of total)

ival-add: 1.0ms (32.7% of total)

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

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

series3.0ms (0.3%)

Memory

7.6MiB live, 7.6MiB allocated

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	@	0	((* re (+ im im)) (+ im im))

simplify6.0ms (0.6%)

Memory

8.4MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	14	8
2	30	8
3	44	8
4	62	8
5	96	8
6	166	8
7	191	8
8	211	8
9	221	8
0	221	8

Stop Event

1×	iter limit
1×	saturated

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)

rewrite32.0ms (3.2%)

Memory

-34.2MiB live, 12.3MiB allocated

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 (0.2%)

Memory: 3.0MiB live, 3.0MiB allocated
Compiler: Compiled 249 to 67 computations (73.1% saved)

prune1.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated

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 (0.4%)

Memory

8.2MiB live, 8.2MiB allocated

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	`re`
100.0%	1	`im`
100.0%	1	`(+.f64 (.f64 re im) (.f64 im re))`

Compiler

Compiled 9 to 9 computations (0% saved)

simplify9.0ms (0.9%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

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))

soundness21.0ms (2.1%)

Memory

-20.5MiB live, 25.9MiB allocated

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 17 to 11 computations (35.3% saved)

preprocess26.0ms (2.6%)

Memory

6.7MiB live, 51.5MiB allocated

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

Iter	Nodes	Cost
0	15	43
1	36	27
2	81	25
3	154	25
4	206	25
5	230	25
0	5	7
0	8	7
1	14	5
2	30	5
3	53	5
4	89	5
5	143	5
6	177	5
7	197	5
8	212	5
0	212	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	13	10
2	29	10
3	48	10
4	66	10
5	100	10
6	164	10
7	189	10
8	209	10
9	219	10
0	219	10

Iter	Nodes	Cost
0	15	43
1	36	27
2	81	25
3	154	25
4	206	25
5	230	25
0	5	7
0	8	7
1	14	5
2	30	5
3	53	5
4	89	5
5	143	5
6	177	5
7	197	5
8	212	5
0	212	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	13	10
2	29	10
3	48	10
4	66	10
5	100	10
6	164	10
7	189	10
8	209	10
9	219	10
0	219	10

start0.0ms (0%)

analyze0.0ms (0%)

sample688.0ms (68.9%)

explain88.0ms (8.8%)

preprocess21.0ms (2.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify14.0ms (1.4%)

localize14.0ms (1.4%)

series4.0ms (0.4%)

simplify10.0ms (1%)

rewrite26.0ms (2.6%)

eval8.0ms (0.8%)

prune1.0ms (0.1%)

simplify7.0ms (0.7%)

localize12.0ms (1.2%)

series3.0ms (0.3%)

simplify6.0ms (0.6%)

rewrite32.0ms (3.2%)

eval2.0ms (0.2%)

prune1.0ms (0.1%)

regimes4.0ms (0.4%)

simplify9.0ms (0.9%)

soundness21.0ms (2.1%)

preprocess26.0ms (2.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	43
1	36	27
2	81	25
3	154	25
4	206	25
5	230	25
0	5	7
0	8	7
1	14	5
2	30	5
3	53	5
4	89	5
5	143	5
6	177	5
7	197	5
8	212	5
0	212	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	13	10
2	29	10
3	48	10
4	66	10
5	100	10
6	164	10
7	189	10
8	209	10
9	219	10
0	219	10