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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze112.0ms (6.6%)

Memory

2.1MiB live, 96.0MiB allocated

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)

sample883.0ms (52%)

Memory

61.5MiB live, 1 002.4MiB allocated

Samples

645.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 281.0ms

ival-div: 173.0ms (61.5% of total)

ival-mult: 98.0ms (34.9% of total)

ival-true: 6.0ms (2.1% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain86.0ms (5%)

Memory

-30.2MiB live, 58.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
27	-	2	(-7.362113857111364e-109 -1.165828590165161e-206 -1.4660223401121044e-176)	`(/.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)`	o/n	16	0
↳	`(*.f64 x y)`	overflow	34
`/.f64`	`(/.f64 (*.f64 x y) z)`	u/n	9	0
↳	`(*.f64 x y)`	underflow	23

Confusion

	Predicted +	Predicted -
+	25	2
-	0	229

Precision

1.0

Recall

0.9259259259259259

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	25	0	2
-	0	0	229

Precision?

1.0

Recall?

0.9259259259259259

Freqs

test

number	freq
0	231
1	25

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (47.9% of total)

ival-mult: 4.0ms (47.9% of total)

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

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

preprocess22.0ms (1.3%)

Memory

35.2MiB live, 35.2MiB allocated

Algorithm

1×	egg-herbie

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
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	90.4%	(/.f64 (*.f64 x y) z)

Compiler

Compiled 5 to 5 computations (0% saved)

simplify4.0ms (0.2%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

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

localize18.0ms (1.1%)

Memory

-12.6MiB live, 29.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x y)
accuracy	6.175755439105622	(/.f64 (*.f64 x y) z)

Samples

11.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (53.6% of total)

ival-mult: 2.0ms (53.6% of total)

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

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

series7.0ms (0.4%)

Memory

18.1MiB live, 18.2MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

simplify11.0ms (0.6%)

Memory

-53.6MiB live, 3.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	8	8
2	11	8
3	12	8
0	12	8

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 2

Calls

Call 1

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

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

rewrite16.0ms (0.9%)

Memory

24.9MiB live, 24.9MiB allocated

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: 4.5MiB live, 4.5MiB allocated
Compiler: Compiled 118 to 37 computations (68.6% saved)

prune1.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

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
✓	90.4%	(/.f64 (*.f64 x y) z)
▶	91.3%	(*.f64 (/.f64 y z) x)
▶	91.4%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 15 to 15 computations (0% saved)

simplify3.0ms (0.2%)

Memory

8.9MiB live, 8.9MiB allocated

Algorithm

1×	egg-herbie

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

localize29.0ms (1.7%)

Memory

-32.1MiB live, 54.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y z)
accuracy	5.558209074333976	(*.f64 (/.f64 y z) x)
accuracy	0.0	(/.f64 x z)
accuracy	5.5349450182830555	(*.f64 (/.f64 x z) y)

Samples

19.0ms

256×

valid

Compiler

Compiled 24 to 9 computations (62.5% saved)

Precisions

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

ival-mult: 7.0ms (61.7% of total)

ival-div: 4.0ms (35.3% of total)

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

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

series11.0ms (0.6%)

Memory

24.4MiB live, 24.4MiB allocated

Counts

4 → 3

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	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	y	@	-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	z	@	0	((* (/ x z) y) (/ x z) (* (/ y z) x) (/ y z))

simplify5.0ms (0.3%)

Memory

11.0MiB live, 11.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11
2	11	11
3	12	11
0	12	11

Stop Event

1×	iter limit
1×	saturated

Counts

3 → 3

Calls

Call 1

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

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

rewrite15.0ms (0.9%)

Memory

-30.2MiB live, 13.8MiB allocated

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))

eval4.0ms (0.2%)

Memory: 8.8MiB live, 8.8MiB allocated
Compiler: Compiled 134 to 40 computations (70.1% saved)

prune4.0ms (0.2%)

Memory

9.5MiB live, 9.5MiB allocated

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
✓	90.4%	(/.f64 (*.f64 x y) z)
✓	91.3%	(*.f64 (/.f64 y z) x)
✓	91.4%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 30 to 24 computations (20% saved)

regimes24.0ms (1.4%)

Memory

-10.1MiB live, 50.8MiB allocated

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:

13.0ms	x
3.0ms	y
3.0ms	z
3.0ms	(*.f64 x y)
3.0ms	(/.f64 (*.f64 x y) z)

Results

Accuracy	Segments	Branch
99.7%	3	`(*.f64 x y)`
99.7%	2	`(/.f64 (*.f64 x y) z)`
96.2%	2	`x`
96.6%	3	`y`
99.7%	2	`z`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

regimes9.0ms (0.5%)

Memory

17.0MiB live, 17.0MiB allocated

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

Results

Accuracy	Segments	Branch
91.4%	1	`y`
91.4%	1	`x`
91.4%	1	`(*.f64 x y)`
91.4%	1	`(/.f64 (*.f64 x y) z)`
91.4%	1	`z`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

bsearch24.0ms (1.4%)

Memory

-12.2MiB live, 34.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
23.0ms	3.3971419393322486e+92	3.583413735584756e+102

Samples

9.0ms

160×

valid

Compiler

Compiled 108 to 131 computations (-21.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 2.0ms (57.2% of total)

ival-mult: 2.0ms (57.2% of total)

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

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

simplify15.0ms (0.9%)

Memory

-21.0MiB live, 25.6MiB allocated

Algorithm

1×	egg-herbie

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 349999999999999986234031631787666269758856411561201795809624659857499874646992386851180904448 binary64)) (.f64 (/.f64 x z) y) (.f64 (/.f64 y z) x))
(*.f64 (/.f64 x z) y)

Outputs
(if (<=.f64 z #s(literal 349999999999999986234031631787666269758856411561201795809624659857499874646992386851180904448 binary64)) (.f64 (/.f64 x z) y) (.f64 (/.f64 y z) x))
(*.f64 (/.f64 x z) y)

soundness10.0ms (0.6%)

Memory

17.8MiB live, 17.8MiB allocated

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

Compiler

Compiled 49 to 31 computations (36.7% saved)

preprocess384.0ms (22.6%)

Memory: -3.2MiB live, 476.6MiB allocated
Compiler: Compiled 206 to 140 computations (32% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze112.0ms (6.6%)

sample883.0ms (52%)

explain86.0ms (5%)

preprocess22.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.2%)

localize18.0ms (1.1%)

series7.0ms (0.4%)

simplify11.0ms (0.6%)

rewrite16.0ms (0.9%)

eval2.0ms (0.1%)

prune1.0ms (0.1%)

simplify3.0ms (0.2%)

localize29.0ms (1.7%)

series11.0ms (0.6%)

simplify5.0ms (0.3%)

rewrite15.0ms (0.9%)

eval4.0ms (0.2%)

prune4.0ms (0.2%)

regimes24.0ms (1.4%)

regimes9.0ms (0.5%)

bsearch24.0ms (1.4%)

simplify15.0ms (0.9%)

soundness10.0ms (0.6%)

preprocess384.0ms (22.6%)

end0.0ms (0%)

Profiling