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)

sample799.0ms (15%)

Memory

-23.6MiB live, 807.0MiB allocated; 354ms collecting garbage

Samples

569.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-mult: 161.0ms (78.3% of total)

ival-add: 34.0ms (16.5% of total)

ival-true: 5.0ms (2.4% of total)

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

adjust: 2.0ms (1% of total)

Bogosity

explain71.0ms (1.3%)

Memory

6.2MiB live, 100.6MiB allocated; 4ms 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

21.0ms

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 (71.2% of total)

ival-add: 2.0ms (20.3% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess644.0ms (12.1%)

Memory

-1.2MiB live, 419.9MiB allocated; 69ms collecting garbage

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	218	25
5	316	25
6	748	25
7	1595	25
8	3576	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	1247	5
8	4777	5
9	7671	5
0	8314	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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

simplify599.0ms (11.2%)

Memory

33.5MiB live, 396.1MiB allocated; 69ms collecting garbage

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	94	13
5	197	13
6	506	13
7	1247	13
8	4777	13
9	7671	13
0	8314	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)

localize14.0ms (0.3%)

Memory

20.2MiB live, 20.2MiB 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	0.0078125	(+.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 (65% of total)

ival-add: 1.0ms (21.7% of total)

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

adjust: 0.0ms (0% of total)

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

series32.0ms (0.6%)

Memory

-65.5MiB live, 5.5MiB allocated; 9ms 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
28.0ms	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))

simplify1.1s (21.3%)

Memory

24.5MiB live, 769.8MiB allocated; 147ms collecting garbage

Algorithm

1×	egg-herbie

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	837	8
6	4569	8
0	8905	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)

rewrite30.0ms (0.6%)

Memory

36.3MiB live, 36.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	32	9
0	152	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%)

Memory: 5.5MiB live, 5.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 229 to 55 computations (76% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB 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 im (+.f64 re re))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify1.1s (21.2%)

Memory

-17.6MiB live, 790.6MiB allocated; 152ms collecting garbage

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	124	10
5	240	10
6	940	10
7	4194	10
0	8532	10

Stop Event

1×	iter limit
1×	node limit
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 (0.3%)

Memory

-14.9MiB live, 28.8MiB allocated; 6ms collecting garbage

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

9.0ms

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 (61.1% of total)

ival-add: 1.0ms (30.6% of total)

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

adjust: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

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))

simplify759.0ms (14.2%)

Memory

-10.6MiB live, 506.1MiB allocated; 123ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	15	8
2	39	8
3	96	8
4	230	8
5	794	8
6	4714	8
0	8249	8

Stop Event

1×	iter limit
1×	node limit

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)

rewrite27.0ms (0.5%)

Memory

-17.2MiB live, 29.0MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	22	8
0	136	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 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 re #s(literal 2 binary64))
(/.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)

eval2.0ms (0%)

Memory: 6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 249 to 67 computations (73.1% saved)

prune1.0ms (0%)

Memory

4.2MiB live, 4.2MiB 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 im (+.f64 re re))

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes4.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

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

Compiler

Compiled 9 to 9 computations (0% saved)

simplify13.0ms (0.2%)

Memory

-23.1MiB live, 20.9MiB allocated; 5ms collecting garbage

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))

derivations22.0ms (0.4%)

Memory

32.6MiB live, 32.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	32	9
0	152	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)

preprocess27.0ms (0.5%)

Memory

-8.8MiB live, 36.4MiB allocated; 5ms 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%)

sample799.0ms (15%)

explain71.0ms (1.3%)

preprocess644.0ms (12.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify599.0ms (11.2%)

localize14.0ms (0.3%)

series32.0ms (0.6%)

simplify1.1s (21.3%)

rewrite30.0ms (0.6%)

eval2.0ms (0%)

prune1.0ms (0%)

simplify1.1s (21.2%)

localize15.0ms (0.3%)

series4.0ms (0.1%)

simplify759.0ms (14.2%)

rewrite27.0ms (0.5%)

eval2.0ms (0%)

prune1.0ms (0%)

regimes4.0ms (0.1%)

simplify13.0ms (0.2%)

derivations22.0ms (0.4%)

preprocess27.0ms (0.5%)

end0.0ms (0%)

Profiling