Metrics for math.square on complex, imaginary part

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample988.0ms (66.6%)

Memory

-30.0MiB live, 871.6MiB allocated

Samples

509.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 282.0ms

ival-mult: 235.0ms (83.3% of total)

ival-add: 37.0ms (13.1% of total)

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

ival-assert: 4.0ms (1.4% of total)

Bogosity

explain67.0ms (4.5%)

Memory

-5.6MiB live, 161.5MiB 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

35.0ms

512×

valid

Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-add: 12.0ms (61.6% of total)

ival-mult: 7.0ms (35.9% of total)

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

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

preprocess21.0ms (1.4%)

Memory

2.8MiB live, 41.4MiB 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: 0.4MiB live, 0.4MiB 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)

simplify3.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB 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)

localize172.0ms (11.6%)

Memory

-19.8MiB live, 18.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 re im)
accuracy	0	(*.f64 im re)
accuracy	0.00390625	(+.f64 (.f64 re im) (.f64 im re))

Samples

167.0ms

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 (66.5% 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 (0.3%)

Memory

5.1MiB live, 5.1MiB 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 (0.1%)

Memory

2.0MiB live, 2.0MiB 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)

rewrite70.0ms (4.7%)

Memory

3.2MiB live, 38.2MiB 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: 4.6MiB live, 4.5MiB allocated
Compiler: Compiled 166 to 42 computations (74.7% saved)

prune1.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB 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 (0.2%)

Memory

6.6MiB live, 6.6MiB 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

localize20.0ms (1.4%)

Memory

5.1MiB live, 44.1MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

11.0ms

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 (61.3% of total)

ival-add: 1.0ms (30.7% of total)

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

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

series5.0ms (0.4%)

Memory

-22.4MiB live, 15.7MiB 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
3.0ms	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))

simplify2.0ms (0.2%)

Memory

9.4MiB live, 9.4MiB 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)

rewrite20.0ms (1.4%)

Memory

0.8MiB live, 37.9MiB 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)

eval3.0ms (0.2%)

Memory: 7.8MiB live, 7.8MiB allocated
Compiler: Compiled 256 to 70 computations (72.7% saved)

prune1.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB 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)

regimes5.0ms (0.3%)

Memory

7.9MiB live, 7.9MiB 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	(+.f64 (.f64 re im) (.f64 im re))
1.0ms	im
1.0ms	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)

simplify33.0ms (2.2%)

Memory

-27.9MiB live, 58.6MiB 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 (1.2%)

Memory

21.2MiB live, 21.2MiB 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)

preprocess41.0ms (2.8%)

Memory

-8.5MiB live, 67.7MiB 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%)

analyze0.0ms (0%)

sample988.0ms (66.6%)

explain67.0ms (4.5%)

preprocess21.0ms (1.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.2%)

localize172.0ms (11.6%)

series4.0ms (0.3%)

simplify2.0ms (0.1%)

rewrite70.0ms (4.7%)

eval2.0ms (0.1%)

prune1.0ms (0.1%)

simplify3.0ms (0.2%)

localize20.0ms (1.4%)

series5.0ms (0.4%)

simplify2.0ms (0.2%)

rewrite20.0ms (1.4%)

eval3.0ms (0.2%)

prune1.0ms (0.1%)

regimes5.0ms (0.3%)

simplify33.0ms (2.2%)

soundness18.0ms (1.2%)

preprocess41.0ms (2.8%)

end0.0ms (0%)

Profiling