Metrics for math.square on complex, imaginary part

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze13.0ms (1.3%)

Memory

-49.1MiB 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)

sample591.0ms (56.9%)

Memory

46.8MiB live, 867.2MiB allocated

Samples

376.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 183.0ms

ival-mult: 137.0ms (75% of total)

ival-add: 38.0ms (20.8% of total)

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

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

Bogosity

explain216.0ms (20.8%)

Memory

-27.2MiB live, 96.0MiB 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

24.0ms

512×

valid

Compiler

Compiled 71 to 29 computations (59.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 9.0ms (77% of total)

ival-add: 2.0ms (17.1% of total)

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

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

preprocess22.0ms (2.1%)

Memory

27.4MiB live, 27.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	37	27
2	77	25
3	210	25
4	384	25
5	405	25
0	5	7
0	8	7
1	11	5
2	17	5
3	22	5
4	28	5
0	28	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

0.6MiB live, 0.6MiB 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)

simplify3.0ms (0.3%)

Memory

3.8MiB live, 3.8MiB 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	192	(+.f64 (.f64 re im) (.f64 im re))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	11	13
2	17	13
3	22	13
4	28	13
0	28	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)

localize18.0ms (1.7%)

Memory

-15.7MiB live, 21.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 re im)
accuracy	0	(*.f64 im re)
accuracy	0.0078125	(+.f64 (.f64 re im) (.f64 im re))

Samples

13.0ms

256×

valid

Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 4.0ms (71.7% of total)

ival-add: 1.0ms (17.9% of total)

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

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

series4.0ms (0.4%)

Memory

5.9MiB live, 5.9MiB 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))

simplify2.0ms (0.2%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	9	8
2	16	8
3	18	8
0	18	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)

rewrite28.0ms (2.7%)

Memory

-8.1MiB live, 29.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	29	9
0	139	9

Stop Event

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

Counts

3 → 18

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 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 (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 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 im re))
(*.f64 im re)
(*.f64 re im)
(*.f64 im re)
(*.f64 re im)

eval2.0ms (0.1%)

Memory: 2.8MiB live, 2.8MiB allocated
Compiler: Compiled 166 to 42 computations (74.7% saved)

prune1.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	1	19

Accuracy

100.0%

Counts

19 → 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)

simplify3.0ms (0.3%)

Memory

3.1MiB live, 3.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	-128	(+.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	20	10
3	24	10
0	24	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

17.4MiB live, 17.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 im im)
accuracy	0	(*.f64 re (+.f64 im im))

Samples

9.0ms

256×

valid

Compiler

Compiled 22 to 10 computations (54.5% saved)

Precisions

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

ival-mult: 2.0ms (63.7% of total)

ival-add: 1.0ms (31.8% of total)

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

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

series6.0ms (0.6%)

Memory

-31.6MiB live, 6.6MiB 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
2.0ms	im	@	0	((* re (+ im im)) (+ im im))
2.0ms	re	@	-inf	((* re (+ im im)) (+ im im))
1.0ms	im	@	inf	((* re (+ im im)) (+ im im))
1.0ms	im	@	-inf	((* re (+ im im)) (+ im im))
0.0ms	re	@	inf	((* re (+ im im)) (+ im im))

simplify2.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	16	8
3	17	8
0	17	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)

rewrite18.0ms (1.8%)

Memory

19.1MiB live, 19.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	22	8
0	134	8

Stop Event

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

Counts

2 → 25

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

eval2.0ms (0.2%)

Memory: 4.3MiB live, 4.3MiB allocated
Compiler: Compiled 256 to 70 computations (72.7% saved)

prune1.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	1	28

Accuracy

100.0%

Counts

28 → 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)

regimes13.0ms (1.2%)

Memory

-36.1MiB live, 11.4MiB 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:

4.0ms	re
1.0ms	im
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)

simplify22.0ms (2.1%)

Memory

8.0MiB live, 46.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	5	5

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness18.0ms (1.7%)

Memory

27.6MiB live, 27.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	29	9
0	139	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)

preprocess40.0ms (3.9%)

Memory

-11.0MiB live, 64.8MiB allocated

Remove

(sort re im)

(negabs re)

(negabs im)

Compiler

Compiled 84 to 66 computations (21.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze13.0ms (1.3%)

sample591.0ms (56.9%)

explain216.0ms (20.8%)

preprocess22.0ms (2.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.3%)

localize18.0ms (1.7%)

series4.0ms (0.4%)

simplify2.0ms (0.2%)

rewrite28.0ms (2.7%)

eval2.0ms (0.1%)

prune1.0ms (0.1%)

simplify3.0ms (0.3%)

localize12.0ms (1.2%)

series6.0ms (0.6%)

simplify2.0ms (0.2%)

rewrite18.0ms (1.8%)

eval2.0ms (0.2%)

prune1.0ms (0.1%)

regimes13.0ms (1.2%)

simplify22.0ms (2.1%)

soundness18.0ms (1.7%)

preprocess40.0ms (3.9%)

end0.0ms (0%)

Profiling