Metrics for Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze47.0ms (3%)

Memory

-6.9MiB live, 38.9MiB allocated; 8ms collecting garbage

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
0%	0%	99.9%	0.1%	0%	0%	0%	3
50%	49.9%	49.9%	0.1%	0%	0%	0%	4
50%	49.9%	49.9%	0.1%	0%	0%	0%	5
50%	49.9%	49.9%	0.1%	0%	0%	0%	6
75%	74.9%	25%	0.1%	0%	0%	0%	7
75%	74.9%	25%	0.1%	0%	0%	0%	8
75%	74.9%	25%	0.1%	0%	0%	0%	9
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	10
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	11
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	12

Compiler

Compiled 7 to 7 computations (0% saved)

sample881.0ms (56.4%)

Memory

17.0MiB live, 721.5MiB allocated; 155ms collecting garbage

Samples

473.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-div: 93.0ms (56.8% of total)

ival-mult: 61.0ms (37.3% of total)

ival-true: 5.0ms (3.1% of total)

ival-assert: 3.0ms (1.8% of total)

adjust: 2.0ms (1.2% of total)

Bogosity

explain57.0ms (3.7%)

Memory

1.4MiB live, 100.5MiB allocated; 13ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
17	-	1	(-4.042261929437932e-264 -1.7026113743490924e-48 -2.385339300321616e-117)	`(/.f64 (*.f64 x y) z)`
0	-	0	-	`y`
0	-	0	-	`z`
0	-	0	-	`(*.f64 x y)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (*.f64 x y) z)`	u/n	11	0
↳	`(*.f64 x y)`	underflow	32
`/.f64`	`(/.f64 (*.f64 x y) z)`	o/n	5	0
↳	`(*.f64 x y)`	overflow	29

Confusion

	Predicted +	Predicted -
+	16	1
-	0	239

Precision

1.0

Recall

0.9411764705882353

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	16	0	1
-	0	0	239

Precision?

1.0

Recall?

0.9411764705882353

Freqs

test

number	freq
0	240
1	16

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

34.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 9.0ms (66.2% of total)

ival-mult: 4.0ms (29.4% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess24.0ms (1.6%)

Memory

6.4MiB live, 52.3MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
1	45	48
2	85	48
3	146	48
4	211	48
5	281	48
0	5	5
0	7	5
1	10	5
2	13	5
3	14	5
0	14	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/.f64 (*.f64 x y) z)

Outputs
(/.f64 (*.f64 x y) z)
(/.f64 (*.f64 y x) z)

Symmetry

(negabs z)

(negabs y)

(negabs x)

(sort x y)

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	93.8%	(/.f64 (*.f64 x y) z)

Compiler

Compiled 5 to 5 computations (0% saved)

simplify4.0ms (0.2%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x y)
cost-diff	0	(/.f64 (*.f64 x y) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	7	11
1	10	11
2	13	11
3	14	11
0	14	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (*.f64 x y) z)
(*.f64 x y)
x
y
z

Outputs
(/.f64 (*.f64 x y) z)
(/.f64 (*.f64 y x) z)
(*.f64 x y)
(*.f64 y x)
x
y
z

localize47.0ms (3%)

Memory

-0.8MiB live, 46.4MiB allocated; 3ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x y)
accuracy	3.971087831301351	(/.f64 (*.f64 x y) z)

Samples

43.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-div: 34.0ms (95.4% of total)

ival-mult: 2.0ms (5.6% of total)

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

adjust: 0.0ms (0% of total)

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

series7.0ms (0.5%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
(/.f64 (*.f64 x y) z)
(*.f64 x y)

Outputs
#s(approx (/ (* x y) z) #s(hole binary64 (/ (* x y) z)))
#s(approx (* x y) #s(hole binary64 (* x y)))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (* x y) z) (* x y))
1.0ms	z	@	0	((/ (* x y) z) (* x y))
1.0ms	y	@	-inf	((/ (* x y) z) (* x y))
1.0ms	x	@	inf	((/ (* x y) z) (* x y))
1.0ms	x	@	0	((/ (* x y) z) (* x y))

simplify4.0ms (0.2%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	10	18
2	13	18
3	14	18
0	14	18

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (/ (* x y) z) #s(hole binary64 (/ (* x y) z)))
#s(approx (* x y) #s(hole binary64 (* x y)))

Outputs
#s(approx (/ (* x y) z) #s(hole binary64 (/ (* x y) z)))
#s(approx (/ (* x y) z) (/.f64 (*.f64 y x) z))
#s(approx (* x y) #s(hole binary64 (* x y)))
#s(approx (* x y) (*.f64 y x))

rewrite41.0ms (2.6%)

Memory

-20.4MiB live, 26.7MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
0	7	8
1	13	8
2	30	8
3	65	8
4	101	8
0	101	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

2 → 16

Calls

Call 1

Inputs
(/.f64 (*.f64 x y) z)
(*.f64 x y)

Outputs
(*.f64 (/.f64 (neg.f64 x) z) (neg.f64 y))
(*.f64 (/.f64 (neg.f64 y) z) (neg.f64 x))
(*.f64 (/.f64 x z) y)
(*.f64 (neg.f64 x) (/.f64 (neg.f64 y) z))
(*.f64 (neg.f64 y) (/.f64 (neg.f64 x) z))
(*.f64 (/.f64 y z) x)
(*.f64 y (/.f64 x z))
(*.f64 x (/.f64 y z))
(/.f64 (*.f64 (neg.f64 x) y) (neg.f64 z))
(/.f64 (*.f64 y x) z)
(neg.f64 (*.f64 (/.f64 (neg.f64 x) z) y))
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 y x)
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 x) y))

eval2.0ms (0.1%)

Memory: 3.3MiB live, 3.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 118 to 37 computations (68.6% saved)

prune2.0ms (0.1%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	2	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Accuracy

99.9%

Counts

19 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	93.8%	(/.f64 (*.f64 x y) z)
▶	91.4%	(*.f64 (/.f64 y z) x)
▶	92.5%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 15 to 15 computations (0% saved)

simplify3.0ms (0.2%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 y z)
cost-diff	0	(*.f64 (/.f64 y z) x)
cost-diff	0	(/.f64 x z)
cost-diff	0	(*.f64 (/.f64 x z) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
0	11	22
1	17	22
2	17	22
0	17	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (/.f64 x z) y)
(/.f64 x z)
x
z
y
(*.f64 (/.f64 y z) x)
(/.f64 y z)
y
z
x

Outputs
(*.f64 (/.f64 x z) y)
(*.f64 y (/.f64 x z))
(/.f64 x z)
x
z
y
(*.f64 (/.f64 y z) x)
(*.f64 y (/.f64 x z))
(/.f64 y z)
y
z
x

localize51.0ms (3.2%)

Memory

-26.6MiB live, 37.0MiB allocated; 18ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y z)
accuracy	5.5101531438336915	(*.f64 (/.f64 y z) x)
accuracy	0.0	(/.f64 x z)
accuracy	4.800133165842796	(*.f64 (/.f64 x z) y)

Samples

46.0ms

256×

valid

Compiler

Compiled 24 to 9 computations (62.5% saved)

Precisions

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

ival-div: 4.0ms (61% of total)

ival-mult: 3.0ms (45.7% of total)

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

adjust: 0.0ms (0% of total)

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

series6.0ms (0.4%)

Memory

16.2MiB live, 16.2MiB allocated; 0ms collecting garbage

Counts

4 → 4

Calls

Call 1

Inputs
(*.f64 (/.f64 x z) y)
(/.f64 x z)
(*.f64 (/.f64 y z) x)
(/.f64 y z)

Outputs
#s(approx (* (/ x z) y) #s(hole binary64 (/ (* x y) z)))
#s(approx (/ x z) #s(hole binary64 (/ x z)))
#s(approx (* (/ y z) x) #s(hole binary64 (/ (* x y) z)))
#s(approx (/ y z) #s(hole binary64 (/ y z)))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	-inf	((* (/ x z) y) (/ x z) (* (/ y z) x) (/ y z))
1.0ms	x	@	-inf	((* (/ x z) y) (/ x z) (* (/ y z) x) (/ y z))
1.0ms	x	@	0	((* (/ x z) y) (/ x z) (* (/ y z) x) (/ y z))
1.0ms	y	@	-inf	((* (/ x z) y) (/ x z) (* (/ y z) x) (/ y z))
1.0ms	x	@	inf	((* (/ x z) y) (/ x z) (* (/ y z) x) (/ y z))

simplify4.0ms (0.3%)

Memory

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	18	36
0	18	36

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 4

Calls

Call 1

Inputs
#s(approx (* (/ x z) y) #s(hole binary64 (/ (* x y) z)))
#s(approx (/ x z) #s(hole binary64 (/ x z)))
#s(approx (* (/ y z) x) #s(hole binary64 (/ (* x y) z)))
#s(approx (/ y z) #s(hole binary64 (/ y z)))

Outputs
#s(approx (* (/ x z) y) #s(hole binary64 (/ (* x y) z)))
#s(approx (* (/ x z) y) (*.f64 (/.f64 x z) y))
#s(approx (/ x z) #s(hole binary64 (/ x z)))
#s(approx (/ x z) (/.f64 x z))
#s(approx (* (/ y z) x) #s(hole binary64 (/ (* x y) z)))
#s(approx (* (/ x z) y) (*.f64 (/.f64 x z) y))
#s(approx (/ y z) #s(hole binary64 (/ y z)))
#s(approx (/ y z) (/.f64 y z))

rewrite13.0ms (0.8%)

Memory

-36.2MiB live, 8.3MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
0	11	16
1	22	16
2	47	16
3	100	16
4	116	16
5	116	16
0	116	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

4 → 28

Calls

Call 1

Inputs
(*.f64 (/.f64 x z) y)
(/.f64 x z)
(*.f64 (/.f64 y z) x)
(/.f64 y z)

Outputs
(*.f64 (/.f64 (neg.f64 x) z) (neg.f64 y))
(*.f64 (/.f64 (neg.f64 y) z) (neg.f64 x))
(*.f64 (neg.f64 x) (/.f64 (neg.f64 y) z))
(*.f64 (neg.f64 y) (/.f64 (neg.f64 x) z))
(*.f64 (/.f64 y z) x)
(*.f64 y (/.f64 x z))
(*.f64 (/.f64 x z) y)
(*.f64 x (/.f64 y z))
(/.f64 (*.f64 y x) z)
(/.f64 (*.f64 (neg.f64 x) y) (neg.f64 z))
(neg.f64 (*.f64 (/.f64 (neg.f64 x) z) y))
(/.f64 (neg.f64 x) (neg.f64 z))
(/.f64 x z)
(neg.f64 (/.f64 (neg.f64 x) z))
(*.f64 (/.f64 (neg.f64 x) z) (neg.f64 y))
(*.f64 (/.f64 (neg.f64 y) z) (neg.f64 x))
(*.f64 (neg.f64 x) (/.f64 (neg.f64 y) z))
(*.f64 (neg.f64 y) (/.f64 (neg.f64 x) z))
(*.f64 (/.f64 y z) x)
(*.f64 y (/.f64 x z))
(*.f64 (/.f64 x z) y)
(*.f64 x (/.f64 y z))
(/.f64 (*.f64 y x) z)
(/.f64 (*.f64 (neg.f64 x) y) (neg.f64 z))
(neg.f64 (*.f64 (/.f64 (neg.f64 x) z) y))
(/.f64 (neg.f64 y) (neg.f64 z))
(/.f64 y z)
(neg.f64 (/.f64 (neg.f64 y) z))

eval2.0ms (0.1%)

Memory: 4.4MiB live, 4.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 134 to 40 computations (70.1% saved)

prune2.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	20	3	23

Accuracy

99.9%

Counts

23 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	93.8%	(/.f64 (*.f64 x y) z)
✓	91.4%	(*.f64 (/.f64 y z) x)
✓	92.5%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 30 to 24 computations (20% saved)

regimes8.0ms (0.5%)

Memory

20.1MiB live, 20.1MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

Inputs
(*.f64 (/.f64 x z) y)
(*.f64 (/.f64 y z) x)
(/.f64 (*.f64 x y) z)

Outputs
(*.f64 (/.f64 x z) y)
(*.f64 (/.f64 y z) x)

Calls

5 calls:

1.0ms	z
1.0ms	y
1.0ms	x
1.0ms	(*.f64 x y)
1.0ms	(/.f64 (*.f64 x y) z)

Results

Accuracy	Segments	Branch
99.8%	3	`(*.f64 x y)`
99.7%	2	`(/.f64 (*.f64 x y) z)`
95.7%	2	`x`
97.9%	2	`y`
99.8%	2	`z`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

regimes6.0ms (0.4%)

Memory

-29.5MiB live, 16.2MiB allocated; 2ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 x z) y)

Outputs
(*.f64 (/.f64 x z) y)

Calls

5 calls:

2.0ms	x
1.0ms	z
1.0ms	y
1.0ms	(*.f64 x y)
1.0ms	(/.f64 (*.f64 x y) z)

Results

Accuracy	Segments	Branch
92.5%	1	`x`
92.5%	1	`y`
92.5%	1	`(*.f64 x y)`
92.5%	1	`(/.f64 (*.f64 x y) z)`
92.5%	1	`z`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

bsearch9.0ms (0.6%)

Memory

19.4MiB live, 19.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
8.0ms	1.0049206496264065e-28	9.15761157628155e-26

Samples

4.0ms

112×

valid

Compiler

Compiled 78 to 95 computations (-21.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (64.5% of total)

ival-mult: 1.0ms (64.5% of total)

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

adjust: 0.0ms (0% of total)

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

simplify9.0ms (0.6%)

Memory

24.2MiB live, 24.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 z #s(literal 3920052866929211/43556142965880123323311949751266331066368 binary64)) (.f64 (/.f64 x z) y) (.f64 (/.f64 y z) x))
(*.f64 (/.f64 x z) y)

Outputs
(if (<=.f64 z #s(literal 3920052866929211/43556142965880123323311949751266331066368 binary64)) (.f64 (/.f64 x z) y) (.f64 (/.f64 y z) x))
(*.f64 (/.f64 x z) y)

derivations4.0ms (0.3%)

Memory

-43.7MiB live, 2.7MiB allocated; 5ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 19 to 10 computations (47.4% saved)

preprocess329.0ms (21.1%)

Memory: 16.4MiB live, 398.3MiB allocated; 51ms collecting garbage
Compiler: Compiled 206 to 140 computations (32% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze47.0ms (3%)

sample881.0ms (56.4%)

explain57.0ms (3.7%)

preprocess24.0ms (1.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.2%)

localize47.0ms (3%)

series7.0ms (0.5%)

simplify4.0ms (0.2%)

rewrite41.0ms (2.6%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

simplify3.0ms (0.2%)

localize51.0ms (3.2%)

series6.0ms (0.4%)

simplify4.0ms (0.3%)

rewrite13.0ms (0.8%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

regimes8.0ms (0.5%)

regimes6.0ms (0.4%)

bsearch9.0ms (0.6%)

simplify9.0ms (0.6%)

derivations4.0ms (0.3%)

preprocess329.0ms (21.1%)

end0.0ms (0%)

Profiling