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

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated

analyze33.0ms (2.1%)

Memory

22.2MiB live, 57.5MiB 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)

sample797.0ms (50.9%)

Memory

-143.5MiB live, 797.9MiB allocated

Samples

533.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 156.0ms

ival-mult: 88.0ms (56.3% of total)

ival-div: 59.0ms (37.7% of total)

ival-true: 7.0ms (4.5% of total)

ival-assert: 3.0ms (1.9% of total)

Bogosity

explain66.0ms (4.2%)

Memory

-20.8MiB live, 117.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
14	-	2	(8.51986052656213e-87 4.382334274510994e-228 -8.058620278310881e-290)	`(/.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	8	0
↳	`(*.f64 x y)`	underflow	25
`/.f64`	`(/.f64 (*.f64 x y) z)`	o/n	4	0
↳	`(*.f64 x y)`	overflow	30

Confusion

	Predicted +	Predicted -
+	12	2
-	0	242

Precision

1.0

Recall

0.8571428571428571

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	12	0	2
-	0	0	242

Precision?

1.0

Recall?

0.8571428571428571

Freqs

test

number	freq
0	244
1	12

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 13.0ms (74.6% of total)

ival-div: 3.0ms (17.2% of total)

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

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

preprocess46.0ms (2.9%)

Memory

-10.8MiB live, 28.0MiB 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

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.2%	(/.f64 (*.f64 x y) z)

Compiler

Compiled 5 to 5 computations (0% saved)

simplify4.0ms (0.2%)

Memory

3.4MiB live, 3.4MiB 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

localize13.0ms (0.8%)

Memory

15.4MiB live, 15.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x y)
accuracy	3.069794423563597	(/.f64 (*.f64 x y) z)

Samples

10.0ms

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)

series30.0ms (1.9%)

Memory

-23.9MiB live, 14.3MiB 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
23.0ms	z	@	-inf	((/ (* x y) z) (* x y))
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))

simplify3.0ms (0.2%)

Memory

6.6MiB live, 6.6MiB 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)

rewrite15.0ms (1%)

Memory

24.3MiB live, 24.3MiB 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: 2.9MiB live, 2.9MiB allocated
Compiler: Compiled 118 to 37 computations (68.6% saved)

prune24.0ms (1.6%)

Memory

-35.1MiB live, 3.7MiB 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

100.0%

Counts

19 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	95.2%	(/.f64 (*.f64 x y) z)
▶	90.2%	(*.f64 (/.f64 y z) x)
▶	93.2%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 15 to 15 computations (0% saved)

simplify4.0ms (0.2%)

Memory

5.5MiB live, 5.5MiB 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

localize18.0ms (1.2%)

Memory

25.7MiB live, 25.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y z)
accuracy	6.296034006074278	(*.f64 (/.f64 y z) x)
accuracy	0.0	(/.f64 x z)
accuracy	4.366727222182724	(*.f64 (/.f64 x z) y)

Samples

14.0ms

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 (59.1% of total)

ival-mult: 3.0ms (44.3% of total)

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

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

series74.0ms (4.7%)

Memory

-28.2MiB live, 9.2MiB 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
69.0ms	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))

simplify3.0ms (0.2%)

Memory

3.5MiB live, 3.5MiB 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)

rewrite9.0ms (0.6%)

Memory

8.9MiB live, 8.9MiB 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))

eval2.0ms (0.1%)

Memory: 4.4MiB live, 4.4MiB allocated
Compiler: Compiled 134 to 40 computations (70.1% saved)

prune2.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB 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

100.0%

Counts

23 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	95.2%	(/.f64 (*.f64 x y) z)
✓	90.2%	(*.f64 (/.f64 y z) x)
✓	93.2%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 30 to 24 computations (20% saved)

regimes11.0ms (0.7%)

Memory

-17.2MiB live, 21.1MiB 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 y z) x)
(*.f64 (/.f64 x z) y)

Calls

5 calls:

4.0ms	x
2.0ms	z
2.0ms	y
2.0ms	(*.f64 x y)
1.0ms	(/.f64 (*.f64 x y) z)

Results

Accuracy	Segments	Branch
95.2%	1	`x`
98.3%	2	`y`
99.7%	2	`z`
99.7%	2	`(/.f64 (*.f64 x y) z)`
98.3%	2	`(*.f64 x y)`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

regimes6.0ms (0.4%)

Memory

15.5MiB live, 15.5MiB 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:

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

Results

Accuracy	Segments	Branch
93.2%	1	`x`
93.2%	1	`y`
93.2%	1	`(*.f64 x y)`
93.2%	1	`z`
93.2%	1	`(/.f64 (*.f64 x y) z)`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.3775089278300193e+25	1.190228593263791e+29

Compiler

Compiled 8 to 11 computations (-37.5% saved)

simplify9.0ms (0.6%)

Memory

13.8MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (.f64 x y) z) #s(literal 20000000000000001811939328 binary64)) (.f64 (/.f64 y z) x) (*.f64 (/.f64 x z) y))
(*.f64 (/.f64 x z) y)

Outputs
(if (<=.f64 (/.f64 (.f64 x y) z) #s(literal 20000000000000001811939328 binary64)) (.f64 (/.f64 y z) x) (*.f64 (/.f64 x z) y))
(*.f64 (/.f64 x z) y)

soundness31.0ms (2%)

Memory

-28.3MiB live, 9.4MiB 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 53 to 33 computations (37.7% saved)

preprocess364.0ms (23.2%)

Memory: 7.6MiB live, 279.1MiB allocated
Compiler: Compiled 246 to 160 computations (35% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze33.0ms (2.1%)

sample797.0ms (50.9%)

explain66.0ms (4.2%)

preprocess46.0ms (2.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.2%)

localize13.0ms (0.8%)

series30.0ms (1.9%)

simplify3.0ms (0.2%)

rewrite15.0ms (1%)

eval2.0ms (0.1%)

prune24.0ms (1.6%)

simplify4.0ms (0.2%)

localize18.0ms (1.2%)

series74.0ms (4.7%)

simplify3.0ms (0.2%)

rewrite9.0ms (0.6%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

regimes11.0ms (0.7%)

regimes6.0ms (0.4%)

bsearch0.0ms (0%)

simplify9.0ms (0.6%)

soundness31.0ms (2%)

preprocess364.0ms (23.2%)

end0.0ms (0%)

Profiling