Metrics for math.abs on complex (squared)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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)

sample759.0ms (55%)

Memory

-12.7MiB live, 1 292.6MiB allocated; 424ms collecting garbage

Samples

374.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-mult!: 129.0ms (85.4% of total)

ival-add!: 21.0ms (13.9% of total)

adjust: 1.0ms (0.7% of total)

Bogosity

preprocess136.0ms (9.8%)

Memory

-1.2MiB live, 44.4MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	51	44
2	161	44
3	214	44
4	465	44
5	2496	44
6	6215	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)

series4.0ms (0.3%)

Memory

10.2MiB live, 10.2MiB allocated; 0ms 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)) #s(hole binary64 (pow im 2)))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (+ (pow im 2) (pow re 2))))
#s(approx (* re re) #s(hole binary64 (pow re 2)))
#s(approx re #s(hole binary64 re))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))))
#s(approx im #s(hole binary64 im))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))))

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)

rewrite92.0ms (6.7%)

Memory

14.4MiB live, 114.9MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	96
0	28	96
1	144	96
0	1639	88
1	5872	88

Stop Event

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

Counts

12 → 140

Calls

Call 1

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

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

eval15.0ms (1.1%)

Memory: -17.5MiB live, 28.8MiB allocated; 5ms collecting garbage
Compiler: Compiled 657 to 254 computations (61.3% saved)

prune3.0ms (0.2%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Accuracy

100.0%

Counts

136 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 re re (*.f64 im im))
▶	99.4%	#s(approx (+ (* re re) (* im im)) (*.f64 im im))

Compiler

Compiled 11 to 11 computations (0% saved)

series3.0ms (0.2%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Counts

5 → 7

Calls

Call 1

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

Outputs
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (pow im 2)))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (+ (pow im 2) (pow re 2))))
#s(approx re #s(hole binary64 re))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (pow re 2)))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))))
#s(approx im #s(hole binary64 im))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))))

Calls

6 calls:

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

rewrite84.0ms (6.1%)

Memory

-4.9MiB live, 93.2MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	101
0	27	100
1	138	100
0	1633	98
1	5867	98

Stop Event

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

Counts

12 → 109

Calls

Call 1

Inputs
#s(approx (+ (* re re) (* im im)) (*.f64 im im))
(*.f64 im im)
im
(fma.f64 re re (*.f64 im im))
re
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (pow im 2)))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (+ (pow im 2) (pow re 2))))
#s(approx re #s(hole binary64 re))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (pow re 2)))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))))
#s(approx im #s(hole binary64 im))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))))

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

eval11.0ms (0.8%)

Memory: 23.6MiB live, 23.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 659 to 217 computations (67.1% saved)

prune7.0ms (0.5%)

Memory

-39.0MiB live, 7.9MiB allocated; 3ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	134	3	137

Accuracy

100.0%

Counts

137 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 re re (*.f64 im im))
▶	15.6%	#s(approx (+ (* re re) (* im im)) (*.f64 re re))
✓	99.4%	#s(approx (+ (* re re) (* im im)) (*.f64 im im))

Compiler

Compiled 18 to 18 computations (0% saved)

series2.0ms (0.2%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Counts

3 → 6

Calls

Call 1

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

Outputs
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (pow im 2)))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (+ (pow im 2) (pow re 2))))
#s(approx (* re re) #s(hole binary64 (pow re 2)))
#s(approx re #s(hole binary64 re))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow re 2) (+ 1 (/ (pow im 2) (pow re 2))))))
#s(approx (+ (* re re) (* im im)) #s(hole binary64 (* (pow im 2) (+ 1 (/ (pow re 2) (pow im 2))))))

Calls

6 calls:

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

rewrite77.0ms (5.6%)

Memory

8.0MiB live, 100.6MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	93
0	25	93
1	137	93
0	1632	85
1	5867	85

Stop Event

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

Counts

9 → 40

Calls

Call 1

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

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

eval3.0ms (0.2%)

Memory: 7.3MiB live, 7.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 173 to 104 computations (39.9% saved)

prune2.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	36	3	39

Accuracy

100.0%

Counts

39 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 re re (*.f64 im im))
✓	15.6%	#s(approx (+ (* re re) (* im im)) (*.f64 re re))
✓	99.4%	#s(approx (+ (* re re) (* im im)) (*.f64 im im))

Compiler

Compiled 35 to 29 computations (17.1% saved)

regimes8.0ms (0.6%)

Memory

16.3MiB live, 16.3MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

2.0ms	im
2.0ms	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)

regimes50.0ms (3.6%)

Memory

-31.6MiB live, 20.2MiB allocated; 5ms collecting garbage

Accuracy

Total -53.6b remaining (-13832.8%)

Threshold costs -53.6b (-13832.8%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

45.0ms	re
1.0ms	im
1.0ms	(+.f64 (.f64 re re) (.f64 im im))
1.0ms	(*.f64 re re)
1.0ms	(*.f64 im im)

Results

Accuracy	Segments	Branch
99.4%	1	`(*.f64 im im)`
99.4%	1	`(*.f64 re re)`
99.4%	1	`(+.f64 (.f64 re re) (.f64 im im))`
99.4%	1	`re`
99.4%	1	`im`

Compiler

Compiled 11 to 15 computations (-36.4% saved)

derivations14.0ms (1%)

Memory

16.8MiB live, 16.9MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 9 to 8 computations (11.1% saved)

preprocess109.0ms (7.9%)

Memory: -0.9MiB live, 46.2MiB allocated; 2ms collecting garbage
Compiler: Compiled 80 to 79 computations (1.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample759.0ms (55%)

preprocess136.0ms (9.8%)

series4.0ms (0.3%)

rewrite92.0ms (6.7%)

eval15.0ms (1.1%)

prune3.0ms (0.2%)

series3.0ms (0.2%)

rewrite84.0ms (6.1%)

eval11.0ms (0.8%)

prune7.0ms (0.5%)

series2.0ms (0.2%)

rewrite77.0ms (5.6%)

eval3.0ms (0.2%)

prune2.0ms (0.1%)

regimes8.0ms (0.6%)

regimes50.0ms (3.6%)

derivations14.0ms (1%)

preprocess109.0ms (7.9%)

end0.0ms (0%)

Profiling