Metrics for math.abs on complex (squared)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample566.0ms (66.8%)

Memory

-31.4MiB live, 717.8MiB allocated; 253ms collecting garbage

Samples

326.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-mult!: 126.0ms (76.9% of total)

ival-add!: 36.0ms (22% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

preprocess37.0ms (4.4%)

Memory

27.9MiB live, 27.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	50	44
2	144	44
3	189	44
4	406	44
5	2058	44

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

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

Symmetry

(abs re)

(abs im)

(sort re im)

Compiler

Compiled 14 to 10 computations (28.6% saved)

series19.0ms (2.3%)

Memory

-30.7MiB live, 13.0MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	77

Stop Event

1×	iter-limit

Counts

5 → 7

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite70.0ms (8.3%)

Memory

24.8MiB live, 121.9MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	24	15
2	79	15
3	189	15
4	415	15
5	2052	15
0	4091	14

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

5 → 51

Calls

Call 1

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

Outputs
(neg.f64 (neg.f64 (fma.f64 re re (*.f64 im im))))
(fma.f64 (neg.f64 (fabs.f64 im)) (neg.f64 (fabs.f64 im)) (*.f64 re re))
(fma.f64 (neg.f64 (fabs.f64 re)) (neg.f64 (fabs.f64 re)) (*.f64 im im))
(fma.f64 re re (*.f64 im im))
(fma.f64 (fabs.f64 im) (fabs.f64 im) (*.f64 re re))
(fma.f64 (fabs.f64 re) (fabs.f64 re) (*.f64 im im))
(fma.f64 (neg.f64 im) (neg.f64 im) (*.f64 re re))
(fma.f64 (neg.f64 re) (neg.f64 re) (*.f64 im im))
(fma.f64 im im (*.f64 re re))
(-.f64 (.f64 im im) (.f64 re (neg.f64 re)))
(-.f64 (.f64 re re) (.f64 (neg.f64 im) im))
(+.f64 (.f64 im im) (.f64 re re))
(+.f64 (.f64 re re) (.f64 im im))
(*.f64 (neg.f64 (fabs.f64 re)) (neg.f64 (fabs.f64 re)))
(*.f64 re re)
(*.f64 (fabs.f64 re) (fabs.f64 re))
(*.f64 (neg.f64 re) (neg.f64 re))
(pow.f64 (pow.f64 re #s(literal 16 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 re #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 re (*.f64 re re)) re) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (fabs.f64 re)) #s(literal 2 binary64))
(pow.f64 re #s(literal 2 binary64))
(pow.f64 (fabs.f64 re) #s(literal 2 binary64))
(pow.f64 (neg.f64 re) #s(literal 2 binary64))
(pow.f64 (*.f64 re re) #s(literal 1 binary64))
(neg.f64 (*.f64 re (neg.f64 re)))
(sqrt.f64 (.f64 (.f64 re (*.f64 re re)) re))
(fabs.f64 (*.f64 re (fabs.f64 re)))
(fabs.f64 (*.f64 (fabs.f64 re) (neg.f64 re)))
(fabs.f64 (*.f64 re (neg.f64 re)))
(fabs.f64 (*.f64 re re))
re
(*.f64 (neg.f64 (fabs.f64 im)) (neg.f64 (fabs.f64 im)))
(*.f64 (fabs.f64 im) (fabs.f64 im))
(*.f64 (neg.f64 im) (neg.f64 im))
(*.f64 im im)
(pow.f64 (pow.f64 im #s(literal 16 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 im #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 (*.f64 im im) im) im) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (fabs.f64 im)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 im) #s(literal 2 binary64))
(pow.f64 (neg.f64 im) #s(literal 2 binary64))
(pow.f64 (*.f64 im im) #s(literal 1 binary64))
(pow.f64 im #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 im) im))
(sqrt.f64 (.f64 (.f64 (*.f64 im im) im) im))
(fabs.f64 (*.f64 (fabs.f64 im) (neg.f64 im)))
(fabs.f64 (*.f64 (fabs.f64 im) im))
(fabs.f64 (*.f64 (neg.f64 im) im))
(fabs.f64 (*.f64 im im))
im

eval5.0ms (0.6%)

Memory: 14.9MiB live, 14.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 512 to 134 computations (73.8% saved)

prune5.0ms (0.6%)

Memory

-40.6MiB live, 5.9MiB allocated; 4ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	2	54

Accuracy

100.0%

Counts

54 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

series5.0ms (0.6%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	77

Stop Event

1×	iter-limit

Counts

6 → 7

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite63.0ms (7.4%)

Memory

30.5MiB live, 119.7MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
0	10	20
1	29	20
2	91	20
3	175	20
4	392	20
5	2040	20
0	4078	20

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

6 → 64

Calls

Call 1

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

Outputs
(neg.f64 (neg.f64 (fma.f64 re re (*.f64 im im))))
(fma.f64 (neg.f64 (fabs.f64 im)) (neg.f64 (fabs.f64 im)) (*.f64 re re))
(fma.f64 (neg.f64 (fabs.f64 re)) (neg.f64 (fabs.f64 re)) (*.f64 im im))
(fma.f64 (fabs.f64 re) (fabs.f64 re) (*.f64 im im))
(fma.f64 (fabs.f64 im) (fabs.f64 im) (*.f64 re re))
(fma.f64 (neg.f64 re) (neg.f64 re) (*.f64 im im))
(fma.f64 (neg.f64 im) (neg.f64 im) (*.f64 re re))
(fma.f64 re re (*.f64 im im))
(fma.f64 im im (*.f64 re re))
(-.f64 (.f64 im im) (.f64 (neg.f64 re) re))
(-.f64 (.f64 re re) (.f64 (neg.f64 im) im))
(+.f64 (.f64 im im) (.f64 re re))
(+.f64 (.f64 re re) (.f64 im im))
im
(*.f64 (neg.f64 (fabs.f64 re)) (neg.f64 (fabs.f64 re)))
(*.f64 (fabs.f64 re) (fabs.f64 re))
(*.f64 (neg.f64 re) (neg.f64 re))
(*.f64 re re)
(pow.f64 (pow.f64 re #s(literal 16 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 re #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 (*.f64 re re) re) re) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (fabs.f64 re)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 re) #s(literal 2 binary64))
(pow.f64 (neg.f64 re) #s(literal 2 binary64))
(pow.f64 (*.f64 re re) #s(literal 1 binary64))
(pow.f64 re #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 re) re))
(sqrt.f64 (.f64 (.f64 (*.f64 re re) re) re))
(fabs.f64 (*.f64 (fabs.f64 re) (neg.f64 re)))
(fabs.f64 (*.f64 (fabs.f64 re) re))
(fabs.f64 (*.f64 (neg.f64 re) re))
(fabs.f64 (*.f64 re re))
re
(neg.f64 (neg.f64 (fma.f64 re re (*.f64 im im))))
(fma.f64 (neg.f64 (fabs.f64 im)) (neg.f64 (fabs.f64 im)) (*.f64 re re))
(fma.f64 (neg.f64 (fabs.f64 re)) (neg.f64 (fabs.f64 re)) (*.f64 im im))
(fma.f64 (fabs.f64 re) (fabs.f64 re) (*.f64 im im))
(fma.f64 (fabs.f64 im) (fabs.f64 im) (*.f64 re re))
(fma.f64 (neg.f64 re) (neg.f64 re) (*.f64 im im))
(fma.f64 (neg.f64 im) (neg.f64 im) (*.f64 re re))
(fma.f64 re re (*.f64 im im))
(fma.f64 im im (*.f64 re re))
(-.f64 (.f64 im im) (.f64 (neg.f64 re) re))
(-.f64 (.f64 re re) (.f64 (neg.f64 im) im))
(+.f64 (.f64 im im) (.f64 re re))
(+.f64 (.f64 re re) (.f64 im im))
(*.f64 (neg.f64 (fabs.f64 im)) (neg.f64 (fabs.f64 im)))
(*.f64 (fabs.f64 im) (fabs.f64 im))
(*.f64 (neg.f64 im) (neg.f64 im))
(*.f64 im im)
(pow.f64 (pow.f64 im #s(literal 16 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 im #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 (*.f64 im im) im) im) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (fabs.f64 im)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 im) #s(literal 2 binary64))
(pow.f64 (neg.f64 im) #s(literal 2 binary64))
(pow.f64 (*.f64 im im) #s(literal 1 binary64))
(pow.f64 im #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 im) im))
(sqrt.f64 (.f64 (.f64 (*.f64 im im) im) im))
(fabs.f64 (*.f64 (fabs.f64 im) (neg.f64 im)))
(fabs.f64 (*.f64 (fabs.f64 im) im))
(fabs.f64 (*.f64 (neg.f64 im) im))
(fabs.f64 (*.f64 im im))

eval5.0ms (0.6%)

Memory: 12.6MiB live, 12.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 490 to 136 computations (72.2% saved)

prune14.0ms (1.7%)

Memory

-41.9MiB live, 10.0MiB allocated; 9ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	54	2	56

Accuracy

100.0%

Counts

56 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes7.0ms (0.8%)

Memory

19.7MiB live, 19.7MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	re
1.0ms	im
1.0ms	(+.f64 (.f64 re re) (.f64 im im))
1.0ms	(*.f64 im im)
1.0ms	(*.f64 re re)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 im im)`
100.0%	1	`(*.f64 re re)`
100.0%	1	`(+.f64 (.f64 re re) (.f64 im im))`
100.0%	1	`re`
100.0%	1	`im`

Compiler

Compiled 34 to 22 computations (35.3% saved)

derivations20.0ms (2.4%)

Memory

-24.6MiB live, 21.7MiB allocated; 3ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 6 to 4 computations (33.3% saved)

preprocess30.0ms (3.6%)

Memory: 12.2MiB live, 58.5MiB allocated; 3ms collecting garbage
Compiler: Compiled 49 to 33 computations (32.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample566.0ms (66.8%)

preprocess37.0ms (4.4%)

series19.0ms (2.3%)

rewrite70.0ms (8.3%)

eval5.0ms (0.6%)

prune5.0ms (0.6%)

series5.0ms (0.6%)

rewrite63.0ms (7.4%)

eval5.0ms (0.6%)

prune14.0ms (1.7%)

regimes7.0ms (0.8%)

derivations20.0ms (2.4%)

preprocess30.0ms (3.6%)

end0.0ms (0%)

Profiling