Metrics for math.abs on complex (squared)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample869.0ms (63.9%)

Memory

-7.4MiB live, 973.4MiB allocated; 370ms collecting garbage

Samples

507.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 275.0ms

ival-mult!: 179.0ms (65% of total)

ival-add!: 95.0ms (34.5% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

preprocess132.0ms (9.8%)

Memory

-4.5MiB live, 41.6MiB allocated; 4ms 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
6	4972	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 10 to 10 computations (0% saved)

series7.0ms (0.5%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms 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	Expression
1.0ms	re	@	inf	((+ (* re re) (* im im)) (* re re) re (* im im) im)
1.0ms	re	@	-inf	((+ (* re re) (* im im)) (* re re) re (* im im) im)
1.0ms	im	@	-inf	((+ (* re re) (* im im)) (* re re) re (* im im) im)
1.0ms	im	@	inf	((+ (* re re) (* im im)) (* re re) re (* im im) im)
1.0ms	re	@	0	((+ (* re re) (* im im)) (* re re) re (* im im) im)

rewrite133.0ms (9.8%)

Memory

30.2MiB live, 128.5MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	41	15
2	149	15
3	442	15
4	878	15
5	3659	15
0	8083	14
1	11144	14

Stop Event

1×	saturated
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 im im (*.f64 re re))))
(fma.f64 (neg.f64 (fabs.f64 re)) (neg.f64 (fabs.f64 re)) (*.f64 im im))
(fma.f64 (neg.f64 (fabs.f64 im)) (neg.f64 (fabs.f64 im)) (*.f64 re re))
(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))
(fma.f64 re re (*.f64 im im))
(-.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 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
(*.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

eval6.0ms (0.5%)

Memory: -37.8MiB live, 8.5MiB allocated; 3ms collecting garbage
Compiler: Compiled 232 to 134 computations (42.2% saved)

prune1.0ms (0.1%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Accuracy

100.0%

Counts

54 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 4 computations (0% saved)

series4.0ms (0.3%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	80

Stop Event

1×	iter-limit

Counts

4 → 7

Calls

Call 1

Inputs
(fma.f64 re re (*.f64 im im))
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)
#s(approx (+ (* re re) (* im im)) (pow.f64 re #s(literal 2 binary64)))
#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	Expression
1.0ms	im	@	inf	((+ (* re re) (* im im)) re (* im im) im)
1.0ms	im	@	-inf	((+ (* re re) (* im im)) re (* im im) im)
0.0ms	re	@	-inf	((+ (* re re) (* im im)) re (* im im) im)
0.0ms	re	@	inf	((+ (* re re) (* im im)) re (* im im) im)
0.0ms	im	@	0	((+ (* re re) (* im im)) re (* im im) im)

rewrite138.0ms (10.1%)

Memory

17.1MiB live, 112.6MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	11
0	7	11
1	40	11
2	148	11
3	441	11
4	877	11
5	3652	11
0	8074	11
1	11136	11

Stop Event

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

Counts

4 → 33

Calls

Call 1

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

eval4.0ms (0.3%)

Memory: 4.7MiB live, 4.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 167 to 94 computations (43.7% saved)

prune2.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	1	37

Accuracy

100.0%

Counts

37 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 11 to 10 computations (9.1% saved)

regimes6.0ms (0.4%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	im
1.0ms	re
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 11 to 15 computations (-36.4% saved)

derivations47.0ms (3.5%)

Memory

-44.3MiB live, 2.0MiB allocated; 3ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 4 to 4 computations (0% saved)

preprocess10.0ms (0.8%)

Memory

13.3MiB live, 13.3MiB allocated; 0ms collecting garbage

Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 33 to 33 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample869.0ms (63.9%)

preprocess132.0ms (9.8%)

series7.0ms (0.5%)

rewrite133.0ms (9.8%)

eval6.0ms (0.5%)

prune1.0ms (0.1%)

series4.0ms (0.3%)

rewrite138.0ms (10.1%)

eval4.0ms (0.3%)

prune2.0ms (0.1%)

regimes6.0ms (0.4%)

derivations47.0ms (3.5%)

preprocess10.0ms (0.8%)

end0.0ms (0%)

Profiling