Metrics for math.abs on complex (squared)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample631.0ms (17.4%)

Memory

3.3MiB live, 452.0MiB allocated; 276ms collecting garbage

Samples

432.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 276.0ms

ival-mult!: 259.0ms (93.7% of total)

ival-add!: 16.0ms (5.8% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

preprocess154.0ms (4.2%)

Memory

-20.5MiB live, 23.7MiB allocated; 10ms 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)

series97.0ms (2.7%)

Memory

1.3MiB live, 48.1MiB allocated; 9ms collecting garbage

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	re	@	0	((+ (* 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)

rewrite1.3s (35.7%)

Memory

4.5MiB live, 673.3MiB allocated; 279ms collecting garbage

Counts

5 → 63

Calls

Call 1

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

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

eval6.0ms (0.2%)

Memory: 7.6MiB live, 7.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 334 to 159 computations (52.4% saved)

prune2.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	1	66

Accuracy

100.0%

Counts

66 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 4 computations (0% saved)

series115.0ms (3.2%)

Memory

-9.4MiB live, 37.5MiB allocated; 14ms collecting garbage

Counts

4 → 7

Calls

Call 1

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

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	Expression
1.0ms	re	@	-inf	((+ (* im im) (* re re)) im (* re re) re)
1.0ms	re	@	inf	((+ (* im im) (* re re)) im (* re re) re)
0.0ms	im	@	-inf	((+ (* im im) (* re re)) im (* re re) re)
0.0ms	im	@	inf	((+ (* im im) (* re re)) im (* re re) re)
0.0ms	re	@	0	((+ (* im im) (* re re)) im (* re re) re)

rewrite1.3s (35.7%)

Memory

38.3MiB live, 310.6MiB allocated; 68ms collecting garbage

Counts

4 → 40

Calls

Call 1

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

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

eval5.0ms (0.1%)

Memory: 3.9MiB live, 3.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 220 to 111 computations (49.5% saved)

prune2.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	1	44

Accuracy

100.0%

Counts

44 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 11 to 10 computations (9.1% saved)

regimes8.0ms (0.2%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	re
2.0ms	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 11 to 15 computations (-36.4% saved)

derivations0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 4 to 4 computations (0% saved)

preprocess12.0ms (0.3%)

Memory

9.1MiB live, 9.1MiB 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%)

sample631.0ms (17.4%)

preprocess154.0ms (4.2%)

series97.0ms (2.7%)

rewrite1.3s (35.7%)

eval6.0ms (0.2%)

prune2.0ms (0.1%)

series115.0ms (3.2%)

rewrite1.3s (35.7%)

eval5.0ms (0.1%)

prune2.0ms (0.1%)

regimes8.0ms (0.2%)

derivations0.0ms (0%)

preprocess12.0ms (0.3%)

end0.0ms (0%)

Profiling