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

1.2MiB live, 1.2MiB 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)

sample575.0ms (65.7%)

Memory

17.6MiB live, 973.2MiB allocated; 297ms collecting garbage

Samples

397.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 133.0ms

ival-mult!: 115.0ms (86.4% of total)

ival-add!: 17.0ms (12.8% of total)

adjust: 2.0ms (1.5% of total)

Bogosity

preprocess113.0ms (12.9%)

Memory

-27.0MiB live, 63.5MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	44
1	43	32
2	100	30
3	149	30
4	192	30
5	288	30
6	739	30
7	3125	30

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

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

Symmetry

(negabs re)

(negabs im)

(sort re im)

Compiler

Compiled 14 to 10 computations (28.6% saved)

series8.0ms (0.9%)

Memory

17.9MiB live, 17.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25

Stop Event

1×	iter-limit

Counts

5 → 4

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
1.0ms	im	-inf
1.0ms	re	-inf
1.0ms	re	inf
1.0ms	im	inf
1.0ms	re	0

rewrite40.0ms (4.6%)

Memory

-21.2MiB live, 41.5MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
0	39	14

Stop Event

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

Counts

5 → 14

Calls

Call 1

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

Outputs
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 im re) (.f64 im re))) (.f64 im re))
(/.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) (neg.f64 (.f64 im re)))
(+.f64 (.f64 im re) (.f64 im re))
(*.f64 im re)
(*.f64 re im)
re
im
(*.f64 im re)
(*.f64 re im)

eval6.0ms (0.7%)

Memory: 14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 158 to 40 computations (74.7% saved)

prune1.0ms (0.1%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	1	14

Accuracy

100.0%

Counts

14 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (+ (* re im) (* im re)) (.f64 #s(literal 2 binary64) (.f64 im re)))

Compiler

Compiled 13 to 9 computations (30.8% saved)

series4.0ms (0.5%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25

Stop Event

1×	iter-limit

Counts

6 → 4

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
1.0ms	re	-inf
1.0ms	im	-inf
0.0ms	re	inf
0.0ms	im	inf
0.0ms	re	0

rewrite21.0ms (2.4%)

Memory

-2.1MiB live, 46.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
0	11	22
0	48	22

Stop Event

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

Counts

6 → 17

Calls

Call 1

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

Outputs
#s(approx (+ (* re im) (* im re)) (.f64 (.f64 im re) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 im re) (.f64 im re))) (.f64 im re))
(.f64 (.f64 im re) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 im re))
(/.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) (neg.f64 (.f64 im re)))
(+.f64 (.f64 im re) (.f64 im re))
#s(literal 2 binary64)
(*.f64 im re)
(*.f64 re im)
im
re

eval5.0ms (0.6%)

Memory: -32.9MiB live, 9.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 268 to 55 computations (79.5% saved)

prune1.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	15	1	16

Accuracy

100.0%

Counts

16 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (+ (* re im) (* im re)) (.f64 (.f64 #s(literal 2 binary64) im) re))

Compiler

Compiled 13 to 9 computations (30.8% saved)

series5.0ms (0.6%)

Memory

12.6MiB live, 12.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25

Stop Event

1×	iter-limit

Counts

6 → 4

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
1.0ms	im	-inf
1.0ms	im	inf
1.0ms	re	-inf
1.0ms	im	0
0.0ms	re	inf

rewrite22.0ms (2.5%)

Memory

-3.1MiB live, 41.3MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
0	11	24
0	47	23

Stop Event

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

Counts

6 → 10

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 3.8MiB live, 3.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 138 to 30 computations (78.3% saved)

prune1.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	9	1	10
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	10	1	11

Accuracy

100.0%

Counts

11 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 13 to 8 computations (38.5% saved)

series5.0ms (0.5%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25

Stop Event

1×	iter-limit

Counts

5 → 4

Calls

Call 1

Inputs
#s(approx (+ (* re im) (* im re)) (*.f64 (+.f64 im im) re))
(*.f64 (+.f64 im im) re)
(+.f64 im im)
im
re

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

Calls

6 calls:

Time	Variable	Point
1.0ms	im	-inf
1.0ms	re	-inf
1.0ms	im	inf
0.0ms	re	inf
0.0ms	im	0

rewrite37.0ms (4.2%)

Memory

-25.2MiB live, 20.7MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
0	10	23
0	55	22

Stop Event

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

Counts

5 → 11

Calls

Call 1

Inputs
#s(approx (+ (* re im) (* im re)) (*.f64 (+.f64 im im) re))
(*.f64 (+.f64 im im) re)
(+.f64 im im)
im
re

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

eval3.0ms (0.3%)

Memory: 3.6MiB live, 3.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 168 to 49 computations (70.8% saved)

prune1.0ms (0.1%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	1	11

Accuracy

100.0%

Counts

11 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 13 to 8 computations (38.5% saved)

regimes5.0ms (0.6%)

Memory

9.2MiB live, 9.2MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (+ (* re im) (* im re)) (*.f64 (+.f64 im im) re))

Calls

3 calls:

2.0ms	re
2.0ms	im
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 55 to 26 computations (52.7% saved)

derivations2.0ms (0.2%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess20.0ms (2.3%)

Memory

-26.7MiB live, 20.8MiB allocated; 5ms collecting garbage

Remove

(sort re im)

(negabs im)

(negabs re)

Compiler

Compiled 98 to 61 computations (37.8% saved)

end0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample575.0ms (65.7%)

preprocess113.0ms (12.9%)

series8.0ms (0.9%)

rewrite40.0ms (4.6%)

eval6.0ms (0.7%)

prune1.0ms (0.1%)

series4.0ms (0.5%)

rewrite21.0ms (2.4%)

eval5.0ms (0.6%)

prune1.0ms (0.1%)

series5.0ms (0.6%)

rewrite22.0ms (2.5%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

series5.0ms (0.5%)

rewrite37.0ms (4.2%)

eval3.0ms (0.3%)

prune1.0ms (0.1%)

regimes5.0ms (0.6%)

derivations2.0ms (0.2%)

preprocess20.0ms (2.3%)

end0.0ms (0%)

Profiling