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)

sample696.0ms (59.6%)

Memory

18.2MiB live, 757.6MiB allocated

Samples

446.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 279.0ms

ival-mult: 196.0ms (70.2% of total)

ival-add: 75.0ms (26.9% of total)

ival-true: 6.0ms (2.1% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain104.0ms (8.9%)

Memory

-20.9MiB live, 97.6MiB 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

52.0ms

512×

valid

Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-add: 30.0ms (80.8% of total)

ival-mult: 7.0ms (18.9% of total)

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

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

preprocess56.0ms (4.8%)

Memory

25.6MiB live, 62.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	46	27
2	108	25
3	291	25
4	438	25
5	459	25
0	5	7
0	8	7
1	14	5
2	36	5
3	73	5
4	211	5
5	417	5
6	466	5
0	466	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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

simplify20.0ms (1.7%)

Memory

-41.5MiB live, 10.7MiB 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	36	13
3	73	13
4	211	13
5	417	13
6	466	13
0	466	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)

localize15.0ms (1.3%)

Memory

16.6MiB live, 16.6MiB 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 32 to 12 computations (62.5% saved)

Precisions

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

ival-mult: 3.0ms (66% of total)

ival-add: 1.0ms (22% of total)

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

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

series4.0ms (0.4%)

Memory

7.2MiB live, 7.2MiB 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))

simplify15.0ms (1.3%)

Memory

-18.8MiB live, 17.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	12	8
2	31	8
3	55	8
4	86	8
5	232	8
6	455	8
7	479	8
0	479	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)

rewrite38.0ms (3.2%)

Memory

2.7MiB live, 40.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	32	9
0	170	9

Stop Event

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

Counts

3 → 29

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 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (.f64 im re) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64)))))
(*.f64 im (+.f64 re re))
(*.f64 re (-.f64 im (neg.f64 im)))
(*.f64 re (+.f64 im im))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (pow.f64 (*.f64 im re) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.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 (neg.f64 (*.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 (neg.f64 (*.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) (neg.f64 (.f64 (neg.f64 im) re)))
(+.f64 (.f64 im re) (.f64 im re))
(*.f64 im re)
(*.f64 re im)
(*.f64 im re)
(*.f64 re im)

eval3.0ms (0.2%)

Memory: 4.4MiB live, 4.4MiB allocated
Compiler: Compiled 298 to 67 computations (77.5% saved)

prune1.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB allocated

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	1	30

Accuracy

100.0%

Counts

30 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify13.0ms (1.1%)

Memory

16.8MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

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	88	10
5	234	10
6	450	10
7	477	10
0	477	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize15.0ms (1.3%)

Memory

-10.2MiB live, 28.0MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

10.0ms

256×

valid

Compiler

Compiled 22 to 10 computations (54.5% saved)

Precisions

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

ival-add: 3.0ms (60.6% of total)

ival-mult: 2.0ms (40.4% of total)

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

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

series3.0ms (0.3%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

6 calls:

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

simplify12.0ms (1.1%)

Memory

16.7MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	15	8
2	30	8
3	52	8
4	83	8
5	229	8
6	474	8
7	496	8
0	496	8

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 2

Calls

Call 1

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

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

rewrite36.0ms (3.1%)

Memory

-43.0MiB live, 41.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	22	8
0	147	8

Stop Event

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

Counts

2 → 28

Calls

Call 1

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

Outputs
(.f64 (.f64 im #s(literal 2 binary64)) re)
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 (.f64 #s(literal 2 binary64) re) im)
(*.f64 re (+.f64 im im))
(.f64 im (.f64 #s(literal 2 binary64) re))
(/.f64 (*.f64 #s(literal 0 binary64) im) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 re #s(literal 3 binary64))) im) (fma.f64 re re #s(literal 0 binary64)))
(/.f64 (*.f64 im #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 im (.f64 #s(literal 2 binary64) (pow.f64 re #s(literal 3 binary64)))) (fma.f64 re re #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 (.f64 re im) (.f64 re im)) (.f64 (.f64 re im) (.f64 re im))) (-.f64 (.f64 re im) (.f64 re im)))
(/.f64 (+.f64 (pow.f64 (.f64 re im) #s(literal 3 binary64)) (pow.f64 (.f64 re im) #s(literal 3 binary64))) (fma.f64 (.f64 re im) (.f64 re im) (-.f64 (.f64 (.f64 re im) (.f64 re im)) (.f64 (.f64 re im) (.f64 re im)))))
(fma.f64 re im (*.f64 re im))
(fma.f64 im re (*.f64 re im))
(-.f64 (.f64 re im) (.f64 (neg.f64 re) im))
(-.f64 (.f64 re im) (.f64 (neg.f64 im) re))
(+.f64 (.f64 re im) (.f64 re im))
(*.f64 #s(literal 2 binary64) re)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 re #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 re re #s(literal 0 binary64))))
(*.f64 re #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 re re #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 re #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) re))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 re #s(literal 3 binary64)))) (neg.f64 (fma.f64 re re #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 re #s(literal 3 binary64))) (fma.f64 re re #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 re re) #s(literal 0 binary64)) (/.f64 (.f64 re re) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 re #s(literal 3 binary64)) (fma.f64 re re #s(literal 0 binary64))) (/.f64 (pow.f64 re #s(literal 3 binary64)) (fma.f64 re re #s(literal 0 binary64))))
(+.f64 re re)

eval5.0ms (0.4%)

Memory: 5.9MiB live, 5.9MiB allocated
Compiler: Compiled 291 to 79 computations (72.9% saved)

prune1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	1	31

Accuracy

100.0%

Counts

31 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes4.0ms (0.3%)

Memory

6.8MiB live, 6.8MiB allocated

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts

2 → 1

Calls

Call 1

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

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

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 (0.8%)

Memory

15.1MiB live, 15.1MiB 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 im (+.f64 re re))

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

soundness73.0ms (6.2%)

Memory

-11.1MiB live, 26.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	32	9
0	170	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)

preprocess43.0ms (3.7%)

Memory

4.2MiB live, 40.6MiB 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	46	27
2	108	25
3	291	25
4	438	25
5	459	25
0	5	7
0	8	7
1	14	5
2	36	5
3	73	5
4	211	5
5	417	5
6	466	5
0	466	5

Iter	Nodes	Cost
0	15	43
1	46	27
2	108	25
3	291	25
4	438	25
5	459	25
0	5	7
0	8	7
1	14	5
2	36	5
3	73	5
4	211	5
5	417	5
6	466	5
0	466	5

start0.0ms (0%)

analyze0.0ms (0%)

sample696.0ms (59.6%)

explain104.0ms (8.9%)

preprocess56.0ms (4.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify20.0ms (1.7%)

localize15.0ms (1.3%)

series4.0ms (0.4%)

simplify15.0ms (1.3%)

rewrite38.0ms (3.2%)

eval3.0ms (0.2%)

prune1.0ms (0.1%)

simplify13.0ms (1.1%)

localize15.0ms (1.3%)

series3.0ms (0.3%)

simplify12.0ms (1.1%)

rewrite36.0ms (3.1%)

eval5.0ms (0.4%)

prune1.0ms (0.1%)

regimes4.0ms (0.3%)

simplify9.0ms (0.8%)

soundness73.0ms (6.2%)

preprocess43.0ms (3.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	43
1	46	27
2	108	25
3	291	25
4	438	25
5	459	25
0	5	7
0	8	7
1	14	5
2	36	5
3	73	5
4	211	5
5	417	5
6	466	5
0	466	5