Metrics for math.square on complex, real part

analyze4.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
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

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

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

const: 0.0ms (0% of total)

sample844.0ms (50.3%)

Results

324.0ms	4569×	0	valid
284.0ms	3687×	0	infinite

Precisions

Click to see histograms. Total time spent on operations: 207.0ms

ival-mult: 149.0ms (72.1% of total)

ival-sub: 47.0ms (22.7% of total)

const: 8.0ms (3.9% of total)

backward-pass: 4.0ms (1.9% of total)

Bogosity

preprocess233.0ms (13.9%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-define`
612×	`sub-neg`
575×	`fma-neg`
564×	`distribute-lft-in`
514×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	229
1	66	217
2	174	217
3	440	217
4	1065	217
5	2042	217
6	3011	217
7	3853	217
8	5641	217
9	6242	217
10	6355	217
11	6469	217
12	6549	217
13	6549	217
14	7930	217

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(-.f64 (.f64 re re) (.f64 im im))
(*.f64 (+.f64 re im) (-.f64 re im))
(-.f64 (.f64 re re) (.f64 im im))
(*.f64 (+.f64 re im) (-.f64 re im))
(-.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im))
(*.f64 (+.f64 re im) (-.f64 re im))
(-.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im)))
(*.f64 (+.f64 re im) (-.f64 re im))
(neg.f64 (-.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im)))
(-.f64 (.f64 im im) (.f64 re re))
(neg.f64 (-.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im))))
(-.f64 (.f64 im im) (.f64 re re))
(-.f64 (.f64 im im) (.f64 re re))

Symmetry

(abs re)

(abs im)

explain61.0ms (3.6%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
17	-	-	`(-.f64 (.f64 re re) (.f64 im im))`
0	-	-	`im`
0	-	-	`(*.f64 im im)`
0	-	-	`(*.f64 re re)`
0	-	-	`re`

Results

22.0ms	296×	256	valid
19.0ms	216×	256	infinite

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

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

ival-mult: 8.0ms (72.8% of total)

ival-sub: 3.0ms (27.3% of total)

const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize116.0ms (6.9%)

Results

11.0ms	148×	256	valid
97.0ms	108×	256	infinite

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

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

ival-mult: 6.0ms (65.3% of total)

ival-add: 2.0ms (21.8% of total)

ival-sub: 1.0ms (10.9% 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%	(*.f64 (+.f64 re im) (-.f64 re im))

Compiler

Compiled 25 to 13 computations (48% saved)

regimes7.0ms (0.4%)

Accuracy

Total -4.2b remaining (-∞%)

Threshold costs -4.2b (-∞%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(*.f64 (+.f64 re im) (-.f64 re im))

Calls

5 calls:

2.0ms	(*.f64 im im)
1.0ms	re
1.0ms	im
1.0ms	(-.f64 (.f64 re re) (.f64 im im))
1.0ms	(*.f64 re re)

Results

Accuracy	Segments	Branch
100.0%	1	`re`
100.0%	1	`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 25 to 15 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative`
2×	`sub-neg`
2×	`*-commutative`
1×	`neg-sub0`
1×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	15	31
2	20	31
3	22	31
4	23	31

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(*.f64 (+.f64 re im) (-.f64 re im))

soundness383.0ms (22.8%)

Rules

890×	`fma-define`
612×	`sub-neg`
575×	`fma-neg`
564×	`distribute-lft-in`
514×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	229
1	66	217
2	174	217
3	440	217
4	1065	217
5	2042	217
6	3011	217
7	3853	217
8	5641	217
9	6242	217
10	6355	217
11	6469	217
12	6549	217
13	6549	217
14	7930	217

Stop Event

1×	done
1×	node limit

Compiler

Compiled 25 to 13 computations (48% saved)

preprocess25.0ms (1.5%)

Remove

(abs im)

(abs re)

Compiler

Compiled 108 to 60 computations (44.4% saved)

math.square on complex, real part

analyze4.0ms (0.2%)

sample844.0ms (50.3%)

preprocess233.0ms (13.9%)

explain61.0ms (3.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize116.0ms (6.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes7.0ms (0.4%)

simplify2.0ms (0.1%)

soundness383.0ms (22.8%)

preprocess25.0ms (1.5%)

end0.0ms (0%)

Profiling