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

analyze108.0ms (6.3%)

Memory

-16.5MiB live, 102.6MiB allocated; 60ms 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)

sample914.0ms (53.3%)

Memory

47.9MiB live, 1 452.9MiB allocated; 255ms collecting garbage

Samples

619.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 329.0ms

ival-mult: 211.0ms (64.1% of total)

ival-div: 106.0ms (32.2% of total)

ival-true: 6.0ms (1.8% of total)

ival-assert: 4.0ms (1.2% of total)

adjust: 2.0ms (0.6% of total)

Bogosity

explain130.0ms (7.6%)

Memory

-36.9MiB live, 103.8MiB allocated; 98ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
22	-	1	(1.0340215190019808e-30 1.8771651392688947e-289 -2.1556055409235232e-108)	`(/.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	13	0
↳	`(*.f64 x y)`	overflow	41
`/.f64`	`(/.f64 (*.f64 x y) z)`	u/n	8	0
↳	`(*.f64 x y)`	underflow	26

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

48.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

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

ival-mult: 4.0ms (49.3% of total)

ival-div: 3.0ms (37% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess38.0ms (2.2%)

Memory

-32.6MiB live, 59.7MiB allocated; 7ms collecting garbage

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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.2MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.9%	(/.f64 (*.f64 x y) z)

Compiler

Compiled 5 to 5 computations (0% saved)

simplify0.0ms (0%)

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

series8.0ms (0.5%)

Memory

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

Counts

5 → 5

Calls

Call 1

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

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

Calls

9 calls:

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

simplify3.0ms (0.2%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 2

Calls

Call 1

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

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

rewrite33.0ms (1.9%)

Memory

-32.6MiB live, 17.5MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	7	11
1	13	11
2	30	11
3	65	11
4	101	11
0	101	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

5 → 22

Calls

Call 1

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

eval2.0ms (0.1%)

Memory: 5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 154 to 45 computations (70.8% saved)

prune2.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB 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
✓	91.9%	(/.f64 (*.f64 x y) z)
▶	90.2%	(*.f64 (/.f64 y z) x)
▶	92.3%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 15 to 15 computations (0% saved)

simplify0.0ms (0%)

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

series7.0ms (0.4%)

Memory

17.3MiB live, 17.3MiB allocated; 0ms collecting garbage

Counts

7 → 6

Calls

Call 1

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

Outputs
(/ (* x y) z)
(/ x z)
x
y
(/ y z)
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	x	@	-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	y	@	inf	((* (/ x z) y) (/ x z) x z y (* (/ y z) x) (/ y z))

simplify3.0ms (0.2%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	9	14
2	11	14
3	12	14
0	12	14

Stop Event

1×	iter limit
1×	saturated

Counts

6 → 3

Calls

Call 1

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

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

rewrite29.0ms (1.7%)

Memory

-25.7MiB live, 16.9MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
0	11	19
1	22	19
2	47	19
3	100	19
4	116	19
5	116	19
0	116	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

7 → 34

Calls

Call 1

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

eval3.0ms (0.2%)

Memory: 9.0MiB live, 9.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 206 to 53 computations (74.3% saved)

prune3.0ms (0.2%)

Memory

8.3MiB live, 8.3MiB 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
✓	91.9%	(/.f64 (*.f64 x y) z)
✓	90.2%	(*.f64 (/.f64 y z) x)
✓	92.3%	(*.f64 (/.f64 x z) y)

Compiler

Compiled 30 to 24 computations (20% saved)

regimes8.0ms (0.4%)

Memory

18.8MiB live, 18.7MiB 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 y z) x)
(*.f64 (/.f64 x z) y)

Calls

5 calls:

2.0ms	y
1.0ms	z
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)`
99.8%	2	`(/.f64 (*.f64 x y) z)`
96.7%	2	`x`
95.0%	2	`y`
99.8%	2	`z`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

regimes22.0ms (1.3%)

Memory

-28.7MiB live, 16.4MiB allocated; 4ms 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:

18.0ms	(*.f64 x y)
1.0ms	x
1.0ms	y
1.0ms	z
1.0ms	(/.f64 (*.f64 x y) z)

Results

Accuracy	Segments	Branch
92.3%	1	`y`
92.3%	1	`x`
92.3%	1	`(*.f64 x y)`
92.3%	1	`z`
92.3%	1	`(/.f64 (*.f64 x y) z)`

Compiler

Compiled 11 to 18 computations (-63.6% saved)

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.2870932237787367e-23	6.21343524661383e-21

Compiler

Compiled 8 to 11 computations (-37.5% saved)

simplify9.0ms (0.5%)

Memory

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

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 6805647338418769/170141183460469231731687303715884105728 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 6805647338418769/170141183460469231731687303715884105728 binary64)) (.f64 (/.f64 y z) x) (*.f64 (/.f64 x z) y))
(*.f64 (/.f64 x z) y)

derivations9.0ms (0.5%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	7	11
1	13	11
2	30	11
3	65	11
4	101	11
0	101	11

Stop Event

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

Compiler

Compiled 23 to 12 computations (47.8% saved)

preprocess383.0ms (22.3%)

Memory: 14.1MiB live, 431.6MiB allocated; 107ms collecting garbage
Compiler: Compiled 246 to 160 computations (35% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze108.0ms (6.3%)

sample914.0ms (53.3%)

explain130.0ms (7.6%)

preprocess38.0ms (2.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

series8.0ms (0.5%)

simplify3.0ms (0.2%)

rewrite33.0ms (1.9%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

simplify0.0ms (0%)

series7.0ms (0.4%)

simplify3.0ms (0.2%)

rewrite29.0ms (1.7%)

eval3.0ms (0.2%)

prune3.0ms (0.2%)

regimes8.0ms (0.4%)

regimes22.0ms (1.3%)

bsearch0.0ms (0%)

simplify9.0ms (0.5%)

derivations9.0ms (0.5%)

preprocess383.0ms (22.3%)

end0.0ms (0%)

Profiling