Metrics for math.square on complex, imaginary part

analyze0.0ms (0%)

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 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.1s (73.5%)

Results

766.0ms	7306×	256	valid
80.0ms	950×	256	infinite

Precisions

Click to see histograms. Total time spent on operations: 384.0ms

Operation ival-mult, time spent: 324.0ms, 84.0% of total-time

Operation ival-add, time spent: 51.0ms, 13.0% of total-time

Operation const, time spent: 9.0ms, 2.0% of total-time

Bogosity

preprocess143.0ms (9.8%)

Algorithm

1×	egg-herbie

Rules

223×	`fma-define`
93×	`fma-neg`
34×	`distribute-lft-neg-in`
30×	`associate-r`
28×	`unsub-neg`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`im`
-	-	`re`
-	-	`(+.f64 (.f64 re im) (.f64 im re))`
-	-	`(*.f64 re im)`
-	-	`(*.f64 im re)`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	205
1	50	141
2	92	133
3	239	133
4	465	133
5	718	133
6	720	133

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(+.f64 (.f64 re im) (.f64 im re))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(+.f64 (.f64 re im) (.f64 im re))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(+.f64 (.f64 (neg.f64 re) im) (.f64 im (neg.f64 re)))
(fma.f64 re (neg.f64 im) (*.f64 re (neg.f64 im)))
(.f64 #s(literal 2 binary64) (.f64 re (neg.f64 im)))
(.f64 re (.f64 im #s(literal -2 binary64)))
(+.f64 (.f64 re (neg.f64 im)) (.f64 (neg.f64 im) re))
(fma.f64 re (neg.f64 im) (*.f64 re (neg.f64 im)))
(.f64 #s(literal 2 binary64) (.f64 re (neg.f64 im)))
(.f64 re (.f64 im #s(literal -2 binary64)))
(neg.f64 (+.f64 (.f64 (neg.f64 re) im) (.f64 im (neg.f64 re))))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(neg.f64 (+.f64 (.f64 re (neg.f64 im)) (.f64 (neg.f64 im) re)))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(+.f64 (.f64 im re) (.f64 re im))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))

Symmetry

(negabs re)

(negabs im)

(sort re im)

Results

45.0ms	452×	256	valid
5.0ms	60×	256	infinite

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

Operation ival-mult, time spent: 8.0ms, 71.0% of total-time

Operation ival-add, time spent: 3.0ms, 27.0% of total-time

Operation const, time spent: 1.0ms, 9.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 23 to 12 computations (47.8% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize159.0ms (10.9%)

Results

25.0ms	226×	256	valid
3.0ms	30×	256	infinite

Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

Operation ival-mult, time spent: 6.0ms, 84.0% of total-time

Operation const, time spent: 1.0ms, 14.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	0	0
Total	1	1

Accuracy

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 re (.f64 #s(literal 2 binary64) im))

Compiler

Compiled 21 to 13 computations (38.1% saved)

regimes4.0ms (0.3%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 9 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	12	19

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness42.0ms (2.9%)

Rules

223×	`fma-define`
93×	`fma-neg`
34×	`distribute-lft-neg-in`
30×	`associate-r`
28×	`unsub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	205
1	50	141
2	92	133
3	239	133
4	465	133
5	718	133
6	720	133

Stop Event

1×

saturated

Compiler

Compiled 26 to 11 computations (57.7% saved)

end0.0ms (0%)

preprocess33.0ms (2.3%)

Remove

(sort re im)

(negabs im)

(negabs re)

Compiler

Compiled 116 to 80 computations (31% saved)

analyze0.0ms (0%)

sample1.1s (73.5%)

preprocess143.0ms (9.8%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize159.0ms (10.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes4.0ms (0.3%)

simplify2.0ms (0.1%)

soundness42.0ms (2.9%)

end0.0ms (0%)

preprocess33.0ms (2.3%)

Profiling