Metrics for Numeric.Integration.TanhSinh:simpson from integration-0.2.1

start0.0ms (0%)

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

analyze0.0ms (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%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample934.0ms (42.1%)

Memory

26.0MiB live, 1 072.2MiB allocated; 179ms collecting garbage

Samples

579.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 158.0ms

ival-add: 88.0ms (55.6% of total)

ival-mult: 59.0ms (37.3% of total)

ival-true: 6.0ms (3.8% of total)

ival-assert: 4.0ms (2.5% of total)

adjust: 2.0ms (1.3% of total)

Bogosity

explain46.0ms (2.1%)

Memory

1.3MiB live, 97.4MiB allocated; 15ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(*.f64 x (+.f64 y y))`
0	-	-	`(+.f64 y y)`
0	-	-	`y`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(*.f64 x (+.f64 y y))`	*no**	2	0

Confusion

	Predicted +	Predicted -
+	2	0
-	0	254

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	0	0	254

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	254
1	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 4.0ms (56.5% of total)

ival-add: 3.0ms (42.4% of total)

ival-true: 1.0ms (14.1% of total)

adjust: 0.0ms (0% of total)

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

preprocess270.0ms (12.2%)

Memory

-1.6MiB live, 222.9MiB allocated; 73ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	40	25
2	99	25
3	184	25
4	348	25
5	482	25
6	1397	25
7	3373	25
8	7876	25
0	4	5
0	6	5
1	13	5
2	29	5
3	57	5
4	124	5
5	240	5
6	941	5
7	4190	5
0	8541	5

Stop Event

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

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))

Outputs
(*.f64 x (+.f64 y y))
(.f64 (.f64 #s(literal 2 binary64) y) x)

Symmetry

(negabs y)

(negabs x)

(sort x y)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 x (+.f64 y y))

Compiler

Compiled 5 to 4 computations (20% saved)

series6.0ms (0.3%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Counts

4 → 4

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))
x
(+.f64 y y)
y

Outputs
#s(approx (* x (+ y y)) #s(hole binary64 (* 2 (* x y))))
#s(approx x #s(hole binary64 x))
#s(approx (+ y y) #s(hole binary64 (* 2 y)))
#s(approx y #s(hole binary64 y))

Calls

6 calls:

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

simplify180.0ms (8.1%)

Memory

28.2MiB live, 167.8MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	24	24
2	47	24
3	104	24
4	238	24
5	808	24
6	4717	24
0	8157	24

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 4

Calls

Call 1

Inputs
#s(approx (* x (+ y y)) #s(hole binary64 (* 2 (* x y))))
#s(approx x #s(hole binary64 x))
#s(approx (+ y y) #s(hole binary64 (* 2 y)))
#s(approx y #s(hole binary64 y))

Outputs
#s(approx (* x (+ y y)) #s(hole binary64 (* 2 (* x y))))
#s(approx (* x (+ y y)) (.f64 (.f64 y x) #s(literal 2 binary64)))
#s(approx x #s(hole binary64 x))
#s(approx x x)
#s(approx (+ y y) #s(hole binary64 (* 2 y)))
#s(approx (+ y y) (*.f64 #s(literal 2 binary64) y))
#s(approx y #s(hole binary64 y))
#s(approx y y)

rewrite36.0ms (1.6%)

Memory

15.0MiB live, 58.5MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	22	10
0	137	10

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

4 → 26

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))
x
(+.f64 y y)
y

Outputs
(.f64 (.f64 x #s(literal 2 binary64)) y)
(.f64 #s(literal 2 binary64) (.f64 y x))
(.f64 (.f64 #s(literal 2 binary64) y) x)
(*.f64 y (+.f64 x x))
(.f64 x (.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) x) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 x (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 y x) (.f64 y x))) (-.f64 (.f64 y x) (.f64 y x)))
(/.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (fma.f64 (.f64 y x) (.f64 y x) (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 y x) (.f64 y x)))))
(fma.f64 y x (*.f64 y x))
(fma.f64 x y (*.f64 y x))
(-.f64 (.f64 y x) (.f64 (neg.f64 y) x))
(-.f64 (.f64 y x) (.f64 (neg.f64 x) y))
(+.f64 (.f64 y x) (.f64 y x))
x
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y #s(literal 0 binary64))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y #s(literal 0 binary64))))
(+.f64 y y)
y

eval19.0ms (0.9%)

Memory: -35.9MiB live, 8.1MiB allocated; 11ms collecting garbage
Compiler: Compiled 285 to 74 computations (74% saved)

prune1.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	1	33

Accuracy

100.0%

Counts

33 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

series3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

Counts

4 → 4

Calls

Call 1

Inputs
(*.f64 y (+.f64 x x))
y
(+.f64 x x)
x

Outputs
#s(approx (* y (+ x x)) #s(hole binary64 (* 2 (* x y))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx y #s(hole binary64 y))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((* y (+ x x)) y (+ x x) x)
1.0ms	x	@	inf	((* y (+ x x)) y (+ x x) x)
0.0ms	x	@	0	((* y (+ x x)) y (+ x x) x)
0.0ms	y	@	-inf	((* y (+ x x)) y (+ x x) x)
0.0ms	y	@	inf	((* y (+ x x)) y (+ x x) x)

simplify377.0ms (17%)

Memory

-26.1MiB live, 261.8MiB allocated; 163ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	22	24
2	47	24
3	105	24
4	239	24
5	813	24
6	4725	24
0	8098	24

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 4

Calls

Call 1

Inputs
#s(approx (* y (+ x x)) #s(hole binary64 (* 2 (* x y))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx y #s(hole binary64 y))

Outputs
#s(approx (* y (+ x x)) #s(hole binary64 (* 2 (* x y))))
#s(approx (* y (+ x x)) (.f64 (.f64 x y) #s(literal 2 binary64)))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (+ x x) (*.f64 #s(literal 2 binary64) x))
#s(approx x #s(hole binary64 x))
#s(approx x x)
#s(approx y #s(hole binary64 y))
#s(approx y y)

rewrite220.0ms (9.9%)

Memory

-24.5MiB live, 61.8MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	22	10
0	137	10

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

4 → 26

Calls

Call 1

Inputs
(*.f64 y (+.f64 x x))
y
(+.f64 x x)
x

Outputs
(.f64 (.f64 y #s(literal 2 binary64)) x)
(.f64 #s(literal 2 binary64) (.f64 x y))
(.f64 (.f64 #s(literal 2 binary64) x) y)
(*.f64 x (+.f64 y y))
(.f64 y (.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) y) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 y #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 y (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (.f64 x y))) (-.f64 (.f64 x y) (.f64 x y)))
(/.f64 (+.f64 (pow.f64 (.f64 x y) #s(literal 3 binary64)) (pow.f64 (.f64 x y) #s(literal 3 binary64))) (fma.f64 (.f64 x y) (.f64 x y) (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (.f64 x y)))))
(fma.f64 x y (*.f64 x y))
(fma.f64 y x (*.f64 x y))
(-.f64 (.f64 x y) (.f64 (neg.f64 x) y))
(-.f64 (.f64 x y) (.f64 (neg.f64 y) x))
(+.f64 (.f64 x y) (.f64 x y))
y
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 x x)
x

eval4.0ms (0.2%)

Memory: 15.7MiB live, 15.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 285 to 74 computations (74% saved)

prune2.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	1	33

Accuracy

100.0%

Counts

33 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 y (+.f64 x x))

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.3%)

Memory

-15.6MiB live, 27.2MiB allocated; 2ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))
(*.f64 y (+.f64 x x))

Outputs
(*.f64 y (+.f64 x x))

Calls

4 calls:

3.0ms	(+.f64 y y)
1.0ms	y
1.0ms	x
1.0ms	(*.f64 x (+.f64 y y))

Results

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

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes4.0ms (0.2%)

Memory

19.9MiB live, 19.9MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))

Outputs
(*.f64 x (+.f64 y y))

Calls

4 calls:

1.0ms	(*.f64 x (+.f64 y y))
1.0ms	y
1.0ms	x
1.0ms	(+.f64 y y)

Results

Accuracy	Segments	Branch
99.3%	1	`(+.f64 y y)`
99.3%	1	`(*.f64 x (+.f64 y y))`
99.3%	1	`x`
99.3%	1	`y`

Compiler

Compiled 10 to 11 computations (-10% saved)

simplify14.0ms (0.6%)

Memory

-21.8MiB live, 39.5MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 y (+.f64 x x))
(*.f64 x (+.f64 y y))

Outputs
(*.f64 y (+.f64 x x))
(*.f64 x (+.f64 y y))

derivations1.0ms (0%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 10 to 6 computations (40% saved)

preprocess91.0ms (4.1%)

Memory

30.1MiB live, 122.9MiB allocated; 10ms collecting garbage

Remove

(negabs y)

(sort x y)

(negabs x)

Compiler

Compiled 110 to 84 computations (23.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample934.0ms (42.1%)

explain46.0ms (2.1%)

preprocess270.0ms (12.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series6.0ms (0.3%)

simplify180.0ms (8.1%)

rewrite36.0ms (1.6%)

eval19.0ms (0.9%)

prune1.0ms (0.1%)

series3.0ms (0.1%)

simplify377.0ms (17%)

rewrite220.0ms (9.9%)

eval4.0ms (0.2%)

prune2.0ms (0.1%)

regimes7.0ms (0.3%)

regimes4.0ms (0.2%)

simplify14.0ms (0.6%)

derivations1.0ms (0%)

preprocess91.0ms (4.1%)

end0.0ms (0%)

Profiling