Metrics for math.log/1 on complex, imaginary part

analyze1.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
50%	50%	50%	0.1%	0%	0%	0%	2
75%	74.9%	25%	0.1%	0%	0%	0%	3
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	4
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	5
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	6
98.4%	98.3%	1.6%	0.1%	0%	0%	0%	7
99.2%	99.1%	0.8%	0.1%	0%	0%	0%	8
99.6%	99.5%	0.4%	0.1%	0%	0%	0%	9
99.8%	99.7%	0.2%	0.1%	0%	0%	0%	10
99.9%	99.8%	0.1%	0.1%	0%	0%	0%	11
100%	99.9%	0%	0.1%	0%	0%	0%	12

Compiler

Compiled 6 to 4 computations (33.3% saved)

Precisions

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

ival-atan2: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample465.0ms (77.4%)

Results

308.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-atan2: 75.0ms (87.9% of total)

const: 7.0ms (8.2% of total)

backward-pass: 3.0ms (3.5% of total)

Bogosity

preprocess12.0ms (2%)

Algorithm

2×	egg-herbie

Rules

32×	`sum3-define`
24×	`sub-neg`
16×	`fma-define`
16×	`fmsub-define`
16×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	20	24
2	28	24
3	33	24
4	57	24
5	70	24
6	85	24
7	97	24
0	3	3
0	3	3

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(atan2 im re)

Outputs
(atan2 im re)
(atan2.f64 im re)

Call 2

Inputs
(atan2 im re)
(atan2 im (neg re))
(atan2 (neg im) re)
(neg (atan2 im (neg re)))
(neg (atan2 (neg im) re))
(atan2 re im)

Outputs
(atan2 im re)
(atan2 im (neg re))
(atan2 (neg im) re)
(neg (atan2 im (neg re)))
(neg (atan2 (neg im) re))
(atan2 re im)

explain35.0ms (5.8%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`im`
-	-	`(atan2.f64 im re)`
-	-	`re`

Results

22.0ms

512×

valid

Compiler

Compiled 21 to 11 computations (47.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-atan2: 8.0ms (91.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(atan2.f64 im re)

Compiler

Compiled 5 to 3 computations (40% saved)

simplify3.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(atan2.f64 im re)

Rules

2×	`atan2-lowering-atan2.f32`
2×	`atan2-lowering-atan2.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	3	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(atan2 im re)
im
re

Outputs
(atan2 im re)
(atan2.f64 im re)
im
re

localize17.0ms (2.7%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(atan2.f64 im re)

Results

12.0ms

256×

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-atan2: 5.0ms (94.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0.1%)

Counts

1 → 24

Calls

Call 1

Inputs
#<alt (atan2 im re)>

Outputs
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	im	@	0	(atan2 im re)
0.0ms	im	@	-inf	(atan2 im re)
0.0ms	re	@	-inf	(atan2 im re)
0.0ms	im	@	inf	(atan2 im re)
0.0ms	re	@	inf	(atan2 im re)

rewrite29.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2×	`atan2-lowering-atan2.f32`
2×	`atan2-lowering-atan2.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
0	3	3

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 1

Calls

Call 1

Inputs
(atan2 im re)

Outputs
(atan2.f64 im re)

simplify4.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

2×	`atan2-lowering-atan2.f32`
2×	`atan2-lowering-atan2.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	72
0	3	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)

Outputs
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)

eval2.0ms (0.4%)

Compiler: Compiled 77 to 3 computations (96.1% saved)

prune1.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	1	26

Accuracy

100.0%

Counts

26 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(atan2.f64 im re)

Compiler

Compiled 10 to 6 computations (40% saved)

simplify10.0ms (1.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3

Stop Event

1×

saturated

Calls

Call 1

Inputs
(atan2.f64 im re)

Outputs
(atan2.f64 im re)

soundness0.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 5 to 3 computations (40% saved)

preprocess20.0ms (3.3%)

Compiler: Compiled 20 to 12 computations (40% saved)

math.log/1 on complex, imaginary part

analyze1.0ms (0.2%)

sample465.0ms (77.4%)

preprocess12.0ms (2%)

explain35.0ms (5.8%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify3.0ms (0.5%)

localize17.0ms (2.7%)

series0.0ms (0.1%)

rewrite29.0ms (4.9%)

simplify4.0ms (0.7%)

eval2.0ms (0.4%)

prune1.0ms (0.2%)

simplify10.0ms (1.6%)

soundness0.0ms (0%)

preprocess20.0ms (3.3%)

end0.0ms (0%)

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