Metrics for Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C

start8.0ms (0.6%)

Memory: -44.2MiB live, 0.0MiB allocated; 12ms collecting garbage

analyze0.0ms (0.0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0.0%	0.0%	99.9%	0.1%	0.0%	0.0%	0.0%	0
100.0%	99.9%	0.0%	0.1%	0.0%	0.0%	0.0%	1

Compiler

Compiled 7 to 7 computations (0.0% saved)

sample575.0ms (47.3%)

Memory

43.3MiB live, 797.5MiB allocated; 178ms collecting garbage

Samples

358.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 104.0ms

ival-mult!: 82.0ms (79.1% of total)

ival-sub!: 20.0ms (19.3% of total)

adjust: 2.0ms (1.9% of total)

Bogosity

preprocess19.0ms (1.6%)

Memory

16.3MiB live, 62.2MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	66	53
2	136	53
3	207	53
4	210	53

Stop Event

1×

saturated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x (*.f64 y z))

Symmetry

(sort y z)

Compiler

Compiled 10 to 10 computations (0.0% saved)

sample0.0ms (0.0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs

Outputs

series17.0ms (1.4%)

Memory

-8.4MiB live, 43.5MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	149

Stop Event

1×	iter-limit

Counts

5 → 13

Calls

Call 1

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

Outputs
#s(approx (- x (* y z)) (.f64 #s(literal -1 binary64) (.f64 y z)))
#s(approx (- x (* y z)) (-.f64 x (*.f64 y z)))
#s(approx x x)
#s(approx (- x (* y z)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (/.f64 (*.f64 y z) x)))))
#s(approx (- x (* y z)) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (/.f64 (*.f64 y z) x) #s(literal 1 binary64)))))
#s(approx (- x (* y z)) (+.f64 x (.f64 #s(literal -1 binary64) (.f64 y z))))
#s(approx (* y z) (*.f64 y z))
#s(approx y y)
#s(approx (- x (* y z)) (*.f64 y (-.f64 (/.f64 x y) z)))
#s(approx (- x (* y z)) (.f64 #s(literal -1 binary64) (.f64 y (-.f64 (.f64 #s(literal -1 binary64) (/.f64 x y)) (.f64 #s(literal -1 binary64) z)))))
#s(approx z z)
#s(approx (- x (* y z)) (*.f64 z (-.f64 (/.f64 x z) y)))
#s(approx (- x (* y z)) (.f64 #s(literal -1 binary64) (.f64 z (-.f64 (.f64 #s(literal -1 binary64) (/.f64 x z)) (.f64 #s(literal -1 binary64) y)))))

Calls

9 calls:

Time	Variable	Point
7.0ms	x	-inf
1.0ms	y	-inf
1.0ms	y	0
1.0ms	z	inf
1.0ms	z	-inf

rewrite238.0ms (19.5%)

Memory

-13.7MiB live, 211.9MiB allocated; 44ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	7	11
1	32	11
2	91	11
3	190	11
4	319	11
5	646	11
6	3324	11
0	4462	11

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

5 → 29

Calls

Call 1

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

Outputs
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (.f64 (neg.f64 y) z))) (*.f64 (neg.f64 y) z))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (.f64 (neg.f64 y) z))) (*.f64 (neg.f64 y) z))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 z y) x)) x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 y) z) x)) x)
(/.f64 (-.f64 (.f64 (.f64 (neg.f64 y) z) (.f64 (neg.f64 y) z)) (.f64 (neg.f64 x) (neg.f64 x))) (+.f64 (*.f64 (neg.f64 y) z) (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (neg.f64 y) z) #s(literal 3 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (fma.f64 (.f64 (neg.f64 y) z) (.f64 (neg.f64 y) z) (fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (*.f64 (neg.f64 y) z) (neg.f64 x)))))
(/.f64 (-.f64 (.f64 (.f64 (neg.f64 y) z) (.f64 (neg.f64 y) z)) (.f64 x x)) (-.f64 (*.f64 (neg.f64 y) z) x))
(/.f64 (+.f64 (pow.f64 (.f64 (neg.f64 y) z) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 (neg.f64 y) z) (.f64 (neg.f64 y) z) (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 y) z) x))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (neg.f64 y) z) (.f64 (neg.f64 y) z))) (-.f64 x (*.f64 (neg.f64 y) z)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 y) z) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 (neg.f64 y) z) (.f64 (neg.f64 y) z)) (.f64 x (.f64 (neg.f64 y) z)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 z y) (.f64 z y))) (+.f64 x (*.f64 z y)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 z y) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (.f64 z y) (.f64 z y) (.f64 x (*.f64 z y)))))
(neg.f64 (-.f64 (*.f64 z y) x))
(fma.f64 (neg.f64 z) y x)
(fma.f64 (neg.f64 y) z x)
(fma.f64 z (neg.f64 y) x)
(fma.f64 y (neg.f64 z) x)
(-.f64 (*.f64 (neg.f64 y) z) (neg.f64 x))
(-.f64 x (*.f64 z y))
(+.f64 (*.f64 (neg.f64 y) z) x)
(+.f64 x (*.f64 (neg.f64 y) z))
x
(*.f64 (neg.f64 z) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 z))
(*.f64 z y)
(*.f64 y z)
(neg.f64 (*.f64 (neg.f64 y) z))
y
z

eval4.0ms (0.3%)

Memory: 12.3MiB live, 12.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 483 to 127 computations (73.7% saved)

prune2.0ms (0.2%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	2	39

Accuracy

100.0%

Counts

39 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (neg.f64 z) y x)
✓	100.0%	(-.f64 x (*.f64 y z))

Compiler

Compiled 10 to 10 computations (0.0% saved)

sample0.0ms (0.0%)

Memory

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

Calls

Call 1

Inputs

Outputs

series9.0ms (0.8%)

Memory

-23.5MiB live, 21.4MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	135

Stop Event

1×	iter-limit

Counts

5 → 12

Calls

Call 1

Inputs
(fma.f64 (neg.f64 z) y x)
(neg.f64 z)
z
y
x

Outputs
#s(approx (+ (* (neg z) y) x) (.f64 #s(literal -1 binary64) (.f64 y z)))
#s(approx (+ (* (neg z) y) x) (+.f64 x (.f64 #s(literal -1 binary64) (.f64 y z))))
#s(approx x x)
#s(approx (+ (* (neg z) y) x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (/.f64 (*.f64 y z) x)))))
#s(approx (+ (* (neg z) y) x) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (/.f64 (*.f64 y z) x) #s(literal 1 binary64)))))
#s(approx y y)
#s(approx (+ (* (neg z) y) x) (*.f64 y (fma.f64 #s(literal -1 binary64) z (/.f64 x y))))
#s(approx (+ (* (neg z) y) x) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 z (*.f64 #s(literal -1 binary64) (/.f64 x y))))))
#s(approx (neg z) (*.f64 #s(literal -1 binary64) z))
#s(approx z z)
#s(approx (+ (* (neg z) y) x) (*.f64 z (fma.f64 #s(literal -1 binary64) y (/.f64 x z))))
#s(approx (+ (* (neg z) y) x) (.f64 #s(literal -1 binary64) (.f64 z (+.f64 y (*.f64 #s(literal -1 binary64) (/.f64 x z))))))

Calls

9 calls:

Time	Variable	Point
1.0ms	z	0
0.0ms	z	-inf
0.0ms	x	-inf
0.0ms	z	inf
0.0ms	y	inf

rewrite230.0ms (19.0%)

Memory

23.6MiB live, 209.2MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
0	8	10
1	31	10
2	74	10
3	207	10
4	329	10
5	645	10
6	3323	10
0	4461	10

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

5 → 25

Calls

Call 1

Inputs
(fma.f64 (neg.f64 z) y x)
(neg.f64 z)
z
y
x

Outputs
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 y z) x)) x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y (neg.f64 z)) x)) x)
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (.f64 y (neg.f64 z)))) (*.f64 y (neg.f64 z)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (neg.f64 z)))) (*.f64 y (neg.f64 z)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (+.f64 x (*.f64 y z)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 y z) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (.f64 y z) (.f64 y z) (.f64 x (*.f64 y z)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y (neg.f64 z)) (.f64 y (neg.f64 z)))) (-.f64 x (*.f64 y (neg.f64 z))))
(/.f64 (-.f64 (.f64 (.f64 y (neg.f64 z)) (.f64 y (neg.f64 z))) (.f64 (neg.f64 x) (neg.f64 x))) (+.f64 (*.f64 y (neg.f64 z)) (neg.f64 x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 y (neg.f64 z)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 y (neg.f64 z)) (.f64 y (neg.f64 z))) (.f64 x (.f64 y (neg.f64 z))))))
(/.f64 (-.f64 (pow.f64 (.f64 y (neg.f64 z)) #s(literal 3 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (fma.f64 (.f64 y (neg.f64 z)) (.f64 y (neg.f64 z)) (fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (*.f64 y (neg.f64 z)) (neg.f64 x)))))
(/.f64 (-.f64 (.f64 (.f64 y (neg.f64 z)) (.f64 y (neg.f64 z))) (.f64 x x)) (-.f64 (*.f64 y (neg.f64 z)) x))
(/.f64 (+.f64 (pow.f64 (.f64 y (neg.f64 z)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 y (neg.f64 z)) (.f64 y (neg.f64 z)) (-.f64 (.f64 x x) (.f64 (.f64 y (neg.f64 z)) x))))
(neg.f64 (-.f64 (*.f64 y z) x))
(fma.f64 (neg.f64 y) z x)
(fma.f64 y (neg.f64 z) x)
(fma.f64 (neg.f64 z) y x)
(fma.f64 z (neg.f64 y) x)
(-.f64 (*.f64 y (neg.f64 z)) (neg.f64 x))
(-.f64 x (*.f64 y z))
(+.f64 (*.f64 y (neg.f64 z)) x)
(+.f64 x (*.f64 y (neg.f64 z)))
(neg.f64 z)
z
y
x

eval3.0ms (0.2%)

Memory: 7.4MiB live, 7.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 442 to 114 computations (74.2% saved)

prune1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	31	2	33

Accuracy

100.0%

Counts

33 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (neg.f64 z) y x)
✓	100.0%	(-.f64 x (*.f64 y z))

Compiler

Compiled 10 to 10 computations (0.0% saved)

regimes47.0ms (3.9%)

Memory

-0.7MiB live, 45.2MiB allocated; 4ms collecting garbage

Counts

1 → 1

2 → 1

Calls

Call 1

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

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

Call 2

Inputs
(-.f64 x (*.f64 y z))
(fma.f64 (neg.f64 z) y x)

Outputs
(fma.f64 (neg.f64 z) y x)

Calls

10 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 y z)`
100.0%	1	`(-.f64 x (*.f64 y z))`
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(*.f64 y z)`
100.0%	1	`(-.f64 x (*.f64 y z))`
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`

Compiler

Compiled 32 to 43 computations (-34.4% saved)

derivations45.0ms (3.7%)

Memory

-39.2MiB live, 21.6MiB allocated; 35ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 10 to 7 computations (30.0% saved)

preprocess17.0ms (1.4%)

Memory: 5.0MiB live, 49.3MiB allocated; 7ms collecting garbage
Compiler: Compiled 35 to 32 computations (8.6% saved)

end0.0ms (0.0%)

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

start8.0ms (0.6%)

analyze0.0ms (0.0%)

sample575.0ms (47.3%)

preprocess19.0ms (1.6%)

sample0.0ms (0.0%)

series17.0ms (1.4%)

rewrite238.0ms (19.5%)

eval4.0ms (0.3%)

prune2.0ms (0.2%)

sample0.0ms (0.0%)

series9.0ms (0.8%)

rewrite230.0ms (19.0%)

eval3.0ms (0.2%)

prune1.0ms (0.1%)

regimes47.0ms (3.9%)

derivations45.0ms (3.7%)

preprocess17.0ms (1.4%)

end0.0ms (0.0%)

Profiling