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

start0.0ms (0%)

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

analyze74.0ms (4.6%)

Memory

-8.6MiB live, 40.3MiB allocated; 42ms 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)

sample809.0ms (50.5%)

Memory

20.9MiB live, 772.0MiB allocated; 165ms collecting garbage

Samples

422.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 157.0ms

ival-mult!: 106.0ms (67.5% of total)

ival-div!: 49.0ms (31.2% of total)

adjust: 2.0ms (1.3% of total)

Bogosity

explain64.0ms (4%)

Memory

-24.1MiB live, 66.2MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
22	-	1	(3.88557861083434e-109 -2.8891279977120906e-208 -7.216432436944785e-161)	`(/.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	12	0
↳	`(*.f64 x y)`	underflow	31
`/.f64`	`(/.f64 (*.f64 x y) z)`	o/n	9	0
↳	`(*.f64 x y)`	overflow	30

Confusion

	Predicted +	Predicted -
+	21	1
-	0	234

Precision

1.0

Recall

0.9545454545454546

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	21	0	1
-	0	0	234

Precision?

1.0

Recall?

0.9545454545454546

Freqs

test

number	freq
0	235
1	21

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-div!: 22.0ms (87.6% of total)

ival-mult!: 3.0ms (11.9% of total)

adjust: 0.0ms (0% of total)

preprocess21.0ms (1.3%)

Memory

36.7MiB live, 36.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	46	53
2	86	53
3	145	53
4	210	53
5	280	53
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 x)

(negabs y)

(negabs z)

(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
▶	92.0%	(/.f64 (*.f64 x y) z)

Compiler

Compiled 5 to 5 computations (0% saved)

series13.0ms (0.8%)

Memory

-21.8MiB live, 20.2MiB allocated; 7ms collecting garbage

Counts

5 → 5

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	((/ (* x y) z) (* x y) x y z)
2.0ms	y	@	-inf	((/ (* x y) z) (* x y) x y z)
2.0ms	x	@	-inf	((/ (* x y) z) (* x y) x y z)
1.0ms	x	@	0	((/ (* x y) z) (* x y) x y z)
1.0ms	y	@	inf	((/ (* x y) z) (* x y) x y z)

rewrite22.0ms (1.4%)

Memory

-24.6MiB live, 32.1MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	38
0	13	38
1	19	38
2	36	38
3	71	38
4	107	38
0	107	38

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

10 → 24

Calls

Call 1

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

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

eval2.0ms (0.1%)

Memory: 2.6MiB live, 2.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 154 to 45 computations (70.8% saved)

prune2.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Accuracy

100.0%

Counts

25 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	92.0%	(/.f64 (*.f64 x y) z)
▶	92.4%	(*.f64 (/.f64 y z) x)
▶	92.4%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 15 to 15 computations (0% saved)

series7.0ms (0.5%)

Memory

20.4MiB live, 20.4MiB allocated; 0ms collecting garbage

Counts

7 → 7

Calls

Call 1

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

Calls

9 calls:

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

rewrite11.0ms (0.7%)

Memory

-25.6MiB live, 19.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	64
0	24	64
1	36	64
2	59	64
3	110	64
4	114	64
0	114	64

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

14 → 38

Calls

Call 1

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

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

eval2.0ms (0.2%)

Memory: 6.6MiB live, 6.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 206 to 53 computations (74.3% saved)

prune4.0ms (0.2%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	32	3	35

Accuracy

100.0%

Counts

35 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	92.0%	(/.f64 (*.f64 x y) z)
✓	92.4%	(*.f64 (/.f64 y z) x)
✓	92.4%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 30 to 24 computations (20% saved)

regimes8.0ms (0.5%)

Memory

21.5MiB live, 21.5MiB 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:

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

Results

Accuracy	Segments	Branch
99.8%	3	`(*.f64 x y)`
99.8%	2	`(/.f64 (*.f64 x y) z)`
95.3%	2	`x`
96.5%	2	`y`
99.8%	2	`z`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

regimes7.0ms (0.5%)

Memory

-30.7MiB live, 15.6MiB allocated; 3ms 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:

3.0ms	(/.f64 (*.f64 x y) z)
1.0ms	z
1.0ms	y
1.0ms	(*.f64 x y)
1.0ms	x

Results

Accuracy	Segments	Branch
92.4%	1	`x`
92.4%	1	`y`
92.4%	1	`(*.f64 x y)`
92.4%	1	`(/.f64 (*.f64 x y) z)`
92.4%	1	`z`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

bsearch7.0ms (0.4%)

Memory

10.2MiB live, 10.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
6.0ms	5.7013556058804085e-8	2.0368897715210767e-5

Samples

3.0ms

96×

valid

Compiler

Compiled 68 to 83 computations (-22.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-mult!: 1.0ms (101.8% of total)

adjust: 0.0ms (0% of total)

ival-div!: 0.0ms (0% of total)

simplify8.0ms (0.5%)

Memory

14.3MiB live, 14.3MiB 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 4722366482869645/2361183241434822606848 binary64)) (.f64 (/.f64 x z) y) (.f64 (/.f64 y z) x))
(*.f64 (/.f64 x z) y)

Outputs
(if (<=.f64 z #s(literal 4722366482869645/2361183241434822606848 binary64)) (.f64 (/.f64 x z) y) (.f64 (/.f64 y z) x))
(*.f64 (/.f64 x z) y)

derivations2.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 19 to 10 computations (47.4% saved)

preprocess535.0ms (33.4%)

Memory

-25.6MiB live, 463.5MiB allocated; 204ms collecting garbage

Remove

(negabs y)

(negabs x)

(sort x y)

(negabs z)

Compiler

Compiled 266 to 200 computations (24.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze74.0ms (4.6%)

sample809.0ms (50.5%)

explain64.0ms (4%)

preprocess21.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series13.0ms (0.8%)

rewrite22.0ms (1.4%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

series7.0ms (0.5%)

rewrite11.0ms (0.7%)

eval2.0ms (0.2%)

prune4.0ms (0.2%)

regimes8.0ms (0.5%)

regimes7.0ms (0.5%)

bsearch7.0ms (0.4%)

simplify8.0ms (0.5%)

derivations2.0ms (0.1%)

preprocess535.0ms (33.4%)

end0.0ms (0%)

Profiling