Metrics for math.abs on complex

analyze1.0ms (0.1%)

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
0%	0%	99.9%	0.1%	0%	0%	0%	2
100%	99.9%	0%	0.1%	0%	0%	0%	3

Compiler

Compiled 11 to 7 computations (36.4% saved)

Precisions

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

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

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

const: 0.0ms (0% of total)

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

sample869.0ms (69.3%)

Results

638.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 255.0ms

ival-mult: 126.0ms (49.4% of total)

ival-sqrt: 69.0ms (27.1% of total)

ival-add: 49.0ms (19.2% of total)

const: 8.0ms (3.1% of total)

backward-pass: 3.0ms (1.2% of total)

Bogosity

preprocess52.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

52×	`fma-neg`
45×	`fma-define`
15×	`distribute-lft-neg-in`
15×	`neg-sub0`
14×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	99
1	51	99
2	98	99
3	185	99
4	282	99
5	321	99
6	331	99

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im))))
(hypot.f64 re im)
(neg.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im))))
(neg.f64 (hypot.f64 re im))
(neg.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im)))))
(neg.f64 (hypot.f64 re im))
(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
(hypot.f64 re im)

Symmetry

(abs re)

(abs im)

(sort re im)

explain176.0ms (14%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
122	-	-	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
0	-	-	`im`
0	-	-	`(*.f64 im im)`
0	-	-	`(*.f64 re re)`
0	-	-	`re`
0	-	-	`(+.f64 (.f64 re re) (.f64 im im))`

Results

149.0ms

512×

256

valid

Compiler

Compiled 62 to 20 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-mult: 112.0ms (93.7% of total)

ival-sqrt: 4.0ms (3.3% of total)

ival-add: 3.0ms (2.5% of total)

const: 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%	(hypot.f64 re im)

Compiler

Compiled 5 to 3 computations (40% saved)

localize38.0ms (3%)

Results

32.0ms

256×

256

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

composed: 19.0ms (51.8% of total)

ival-mult: 11.0ms (30% of total)

ival-sqrt: 6.0ms (16.4% of total)

ival-add: 1.0ms (2.7% of total)

const: 0.0ms (0% of total)

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%	(hypot.f64 re im)

Compiler

Compiled 18 to 10 computations (44.4% saved)

regimes32.0ms (2.6%)

Accuracy

Total -28.4b remaining (-∞%)

Threshold costs -28.4b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(hypot.f64 re im)
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Outputs
(hypot.f64 re im)

Calls

6 calls:

26.0ms	im
1.0ms	re
1.0ms	(+.f64 (.f64 re re) (.f64 im im))
1.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
1.0ms	(*.f64 im im)

Results

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

Compiler

Compiled 35 to 21 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 re im)

Outputs
(hypot.f64 re im)

soundness21.0ms (1.7%)

Rules

52×	`fma-neg`
45×	`fma-define`
15×	`distribute-lft-neg-in`
15×	`neg-sub0`
14×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	99
1	51	99
2	98	99
3	185	99
4	282	99
5	321	99
6	331	99

Stop Event

1×	done
1×	saturated

Compiler

Compiled 18 to 10 computations (44.4% saved)

preprocess61.0ms (4.9%)

Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 90 to 54 computations (40% saved)

math.abs on complex

analyze1.0ms (0.1%)

sample869.0ms (69.3%)

preprocess52.0ms (4.1%)

explain176.0ms (14%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize38.0ms (3%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes32.0ms (2.6%)

simplify2.0ms (0.1%)

soundness21.0ms (1.7%)

preprocess61.0ms (4.9%)

end0.0ms (0%)

Profiling