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

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample739.0ms (53.9%)

Memory

18.6MiB live, 766.8MiB allocated; 171ms collecting garbage

Samples

487.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

ival-mult: 162.0ms (73.1% of total)

ival-add: 55.0ms (24.8% of total)

adjust: 2.0ms (0.9% of total)

ival-assert: 2.0ms (0.9% of total)

Bogosity

explain68.0ms (5%)

Memory

-2.9MiB live, 54.6MiB allocated; 27ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 x (+.f64 y y))`
-	-	`(+.f64 y y)`
-	-	`y`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

17.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

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

ival-add: 3.0ms (44.7% of total)

ival-mult: 3.0ms (44.7% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess276.0ms (20.2%)

Memory

24.3MiB live, 207.9MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	41	30
2	101	30
3	181	30
4	338	30
5	472	30
6	1241	30
7	3217	30
8	7707	30
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 x)

(negabs y)

(sort x y)

Compiler

Compiled 5 to 4 computations (20% saved)

eval3.0ms (0.2%)

Memory: -46.3MiB live, 0.1MiB allocated; 7ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

series6.0ms (0.4%)

Memory

11.0MiB live, 11.0MiB 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)

rewrite64.0ms (4.7%)

Memory

-4.6MiB live, 41.0MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	34
0	15	34
1	36	22
0	169	22

Stop Event

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

Counts

8 → 29

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))
x
(+.f64 y y)
y
#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
(.f64 (.f64 #s(literal 2 binary64) x) y)
(.f64 (.f64 y x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 y x))
(*.f64 #s(literal 2 binary64) x)
(.f64 y (.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(/.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 #s(literal 1 binary64) (.f64 y x) (.f64 #s(literal 1 binary64) (*.f64 y x)))
(fma.f64 (.f64 y x) #s(literal 1 binary64) (.f64 (*.f64 y x) #s(literal 1 binary64)))
(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 #s(literal 1 binary64) (.f64 y x)) (.f64 #s(literal 1 binary64) (.f64 y x)))
(+.f64 (.f64 (.f64 y x) #s(literal 1 binary64)) (.f64 (.f64 y x) #s(literal 1 binary64)))
(+.f64 (.f64 y x) (.f64 y x))
(+.f64 x x)
x
#s(literal 2 binary64)
y
#s(approx (* x (+ y y)) (*.f64 #s(literal 2 binary64) x))
#s(approx x x)
#s(approx (+ y y) #s(literal 2 binary64))
#s(approx y y)

eval3.0ms (0.2%)

Memory: 4.9MiB live, 4.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 252 to 62 computations (75.4% saved)

prune2.0ms (0.1%)

Memory

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

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	2	32

Accuracy

100.0%

Counts

32 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.7%	(+.f64 x x)
✓	100.0%	(*.f64 x (+.f64 y y))

Compiler

Compiled 8 to 7 computations (12.5% saved)

series1.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
(+.f64 x x)
x

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

Calls

6 calls:

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

rewrite23.0ms (1.7%)

Memory

25.8MiB live, 25.8MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	14
0	7	14
1	20	8
0	114	8

Stop Event

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

Counts

4 → 4

Calls

Call 1

Inputs
(+.f64 x x)
x
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))

Outputs
#s(literal 2 binary64)
x
#s(approx (+ x x) #s(literal 2 binary64))
#s(approx x x)

eval1.0ms (0%)

Memory: 1.1MiB live, 1.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 22 to 9 computations (59.1% saved)

prune1.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	5	1	6
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	5	3	8

Accuracy

100.0%

Counts

8 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.7%	(+.f64 x x)
✓	100.0%	(*.f64 x (+.f64 y y))
▶	5.0%	#s(approx (+ x x) #s(literal 2 binary64))

Compiler

Compiled 13 to 12 computations (7.7% saved)

series1.0ms (0.1%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ x x) #s(literal 2 binary64))
#s(literal 2 binary64)

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

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((+ x x) 2)
0.0ms	x	@	-inf	((+ x x) 2)
0.0ms	x	@	0	((+ x x) 2)
0.0ms	y	@	0	((+ x x) 2)
0.0ms	y	@	inf	((+ x x) 2)

rewrite43.0ms (3.1%)

Memory

-6.7MiB live, 40.3MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	6	11
1	19	7
0	113	7

Stop Event

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

Counts

3 → 3

Calls

Call 1

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

Outputs
#s(approx (+ x x) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (+ x x) #s(literal 2 binary64))

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 10 to 5 computations (50% saved)

prune1.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	2	0	2
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	2	3	5

Accuracy

100.0%

Counts

5 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.7%	(+.f64 x x)
✓	100.0%	(*.f64 x (+.f64 y y))
✓	5.0%	#s(approx (+ x x) #s(literal 2 binary64))

Compiler

Compiled 26 to 20 computations (23.1% saved)

regimes42.0ms (3.1%)

Memory

-17.0MiB live, 31.9MiB allocated; 43ms collecting garbage

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

37.0ms	x
2.0ms	(+.f64 y y)
2.0ms	y
2.0ms	(*.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)

regimes6.0ms (0.4%)

Memory

16.7MiB live, 16.7MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ x x) #s(literal 2 binary64))
(+.f64 x x)

Outputs
(+.f64 x x)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.7%	1	`(+.f64 y y)`
5.7%	1	`(*.f64 x (+.f64 y y))`
5.7%	1	`x`
5.7%	1	`y`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes7.0ms (0.5%)

Memory

-34.8MiB live, 13.3MiB allocated; 4ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ x x) #s(literal 2 binary64))

Outputs
#s(approx (+ x x) #s(literal 2 binary64))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.0%	1	`(*.f64 x (+.f64 y y))`
5.0%	1	`(+.f64 y y)`
5.0%	1	`y`
5.0%	1	`x`

Compiler

Compiled 10 to 11 computations (-10% saved)

simplify41.0ms (3%)

Memory

12.4MiB live, 56.7MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13
2	15	13
3	27	13
4	80	13
5	661	13
6	5438	13

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations2.0ms (0.2%)

Memory

5.3MiB live, 5.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess40.0ms (3%)

Memory

-11.8MiB live, 87.7MiB allocated; 12ms collecting garbage

Remove

(sort x y)

(negabs y)

(negabs x)

Compiler

Compiled 96 to 72 computations (25% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample739.0ms (53.9%)

explain68.0ms (5%)

preprocess276.0ms (20.2%)

eval3.0ms (0.2%)

prune0.0ms (0%)

series6.0ms (0.4%)

rewrite64.0ms (4.7%)

eval3.0ms (0.2%)

prune2.0ms (0.1%)

series1.0ms (0.1%)

rewrite23.0ms (1.7%)

eval1.0ms (0%)

prune1.0ms (0.1%)

series1.0ms (0.1%)

rewrite43.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes42.0ms (3.1%)

regimes6.0ms (0.4%)

regimes7.0ms (0.5%)

simplify41.0ms (3%)

derivations2.0ms (0.2%)

preprocess40.0ms (3%)

end0.0ms (0%)

Profiling