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)

sample509.0ms (62.7%)

Memory

-29.4MiB live, 631.4MiB allocated; 134ms collecting garbage

Samples

277.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 128.0ms

ival-mult!: 93.0ms (72.5% of total)

ival-add!: 34.0ms (26.5% of total)

adjust: 1.0ms (0.8% of total)

Bogosity

preprocess89.0ms (10.9%)

Memory

2.5MiB live, 50.1MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 1 (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

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(*.f64 x (+.f64 y y))

Symmetry

(negabs x)

(negabs y)

(sort x y)

Compiler

Compiled 8 to 8 computations (0% saved)

series6.0ms (0.7%)

Memory

11.6MiB live, 11.6MiB 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)

rewrite36.0ms (4.5%)

Memory

11.2MiB live, 57.7MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	34
0	16	34
1	37	22
0	170	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 x 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 x x))
(*.f64 x #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) #s(literal 2 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 (fma.f64 y y #s(literal 0 binary64)) #s(literal 2 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 x x))
#s(approx x x)
#s(approx (+ y y) #s(literal 2 binary64))
#s(approx y y)

eval2.0ms (0.3%)

Memory: 5.1MiB live, 5.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 108 to 60 computations (44.4% saved)

prune1.0ms (0.2%)

Memory

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

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Accuracy

100.0%

Counts

29 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.2%	(+.f64 x x)
✓	99.6%	(*.f64 x (+.f64 y y))

Compiler

Compiled 6 to 7 computations (-16.7% saved)

series1.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB 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)

rewrite24.0ms (2.9%)

Memory

-17.8MiB live, 32.7MiB allocated; 4ms 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)

eval8.0ms (0.9%)

Memory: 12.6MiB live, 12.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 8 to 8 computations (0% saved)

prune1.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	3	3	6

Accuracy

100.0%

Counts

6 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.2%	(+.f64 x x)
✓	99.6%	(*.f64 x (+.f64 y y))
▶	5.1%	#s(approx (+ x x) #s(literal 2 binary64))

Compiler

Compiled 10 to 12 computations (-20% saved)

series1.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB 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)

rewrite26.0ms (3.2%)

Memory

-13.7MiB live, 33.5MiB allocated; 1ms 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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.2%	(+.f64 x x)
✓	99.6%	(*.f64 x (+.f64 y y))
✓	5.1%	#s(approx (+ x x) #s(literal 2 binary64))

Compiler

Compiled 18 to 20 computations (-11.1% saved)

regimes8.0ms (0.9%)

Memory

-28.9MiB live, 18.4MiB allocated; 2ms 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:

2.0ms	(+.f64 y y)
2.0ms	x
2.0ms	y
1.0ms	(*.f64 x (+.f64 y y))

Results

Accuracy	Segments	Branch
99.6%	1	`(+.f64 y y)`
99.6%	1	`(*.f64 x (+.f64 y y))`
99.6%	1	`x`
99.6%	1	`y`

Compiler

Compiled 8 to 11 computations (-37.5% saved)

regimes7.0ms (0.9%)

Memory

18.3MiB live, 18.3MiB 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:

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

Results

Accuracy	Segments	Branch
6.2%	1	`(+.f64 y y)`
6.2%	1	`(*.f64 x (+.f64 y y))`
6.2%	1	`x`
6.2%	1	`y`

Compiler

Compiled 8 to 11 computations (-37.5% saved)

regimes4.0ms (0.5%)

Memory

12.4MiB live, 12.4MiB allocated; 0ms 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:

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

Results

Accuracy	Segments	Branch
5.1%	1	`x`
5.1%	1	`(*.f64 x (+.f64 y y))`
5.1%	1	`(+.f64 y y)`
5.1%	1	`y`

Compiler

Compiled 8 to 11 computations (-37.5% saved)

derivations3.0ms (0.4%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 8 to 8 computations (0% saved)

preprocess85.0ms (10.5%)

Memory: -16.7MiB live, 171.9MiB allocated; 12ms collecting garbage
Remove: (sort x y)
Compiler: Compiled 96 to 116 computations (-20.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample509.0ms (62.7%)

preprocess89.0ms (10.9%)

series6.0ms (0.7%)

rewrite36.0ms (4.5%)

eval2.0ms (0.3%)

prune1.0ms (0.2%)

series1.0ms (0.1%)

rewrite24.0ms (2.9%)

eval8.0ms (0.9%)

prune1.0ms (0.1%)

series1.0ms (0.1%)

rewrite26.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes8.0ms (0.9%)

regimes7.0ms (0.9%)

regimes4.0ms (0.5%)

derivations3.0ms (0.4%)

preprocess85.0ms (10.5%)

end0.0ms (0%)

Profiling