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

1.6MiB live, 1.6MiB 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)

sample6.0s (93.3%)

Memory

-215.8MiB live, 2 288.6MiB allocated; 5.7s collecting garbage

Samples

419.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 145.0ms

ival-add!: 93.0ms (64.1% of total)

ival-mult!: 51.0ms (35.2% of total)

adjust: 1.0ms (0.7% of total)

Bogosity

preprocess109.0ms (1.7%)

Memory

-30.4MiB live, 58.9MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	41	30
2	101	30
3	182	30
4	343	30
5	529	30
6	2796	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 (0.1%)

Memory

13.8MiB live, 13.8MiB 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)

rewrite46.0ms (0.7%)

Memory

-18.2MiB live, 78.1MiB allocated; 13ms 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%)

Memory: 5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 106 to 58 computations (45.3% saved)

prune1.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Accuracy

100.0%

Counts

28 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.9%	(+.f64 x x)
▶	100.0%	(*.f64 (+.f64 x x) y)

Compiler

Compiled 6 to 7 computations (-16.7% saved)

series3.0ms (0%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Counts

4 → 4

Calls

Call 1

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

Outputs
#s(approx (* (+ x x) y) #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	((* (+ x x) y) (+ x x) x y)
1.0ms	x	@	inf	((* (+ x x) y) (+ x x) x y)
0.0ms	x	@	0	((* (+ x x) y) (+ x x) x y)
0.0ms	y	@	inf	((* (+ x x) y) (+ x x) x y)
0.0ms	y	@	-inf	((* (+ x x) y) (+ x x) x y)

rewrite34.0ms (0.5%)

Memory

22.3MiB live, 67.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

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

eval4.0ms (0.1%)

Memory: -39.5MiB live, 7.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 112 to 59 computations (47.3% saved)

prune4.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	28	4	32

Accuracy

100.0%

Counts

32 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.9%	(+.f64 x x)
✓	100.0%	(*.f64 (+.f64 x x) y)
▶	5.9%	(*.f64 #s(approx (+ x x) #s(literal 2 binary64)) y)
▶	5.1%	#s(approx (+ x x) #s(literal 2 binary64))

Compiler

Compiled 16 to 18 computations (-12.5% saved)

series3.0ms (0%)

Memory

8.2MiB live, 8.2MiB allocated; 0ms collecting garbage

Counts

4 → 3

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ x x) 2 (* (+ x x) y) y)
1.0ms	x	@	-inf	((+ x x) 2 (* (+ x x) y) y)
0.0ms	x	@	0	((+ x x) 2 (* (+ x x) y) y)
0.0ms	y	@	-inf	((+ x x) 2 (* (+ x x) y) y)
0.0ms	y	@	inf	((+ x x) 2 (* (+ x x) y) y)

rewrite35.0ms (0.5%)

Memory

-4.2MiB live, 49.8MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	35
0	14	33
1	33	23
0	163	23

Stop Event

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

Counts

7 → 8

Calls

Call 1

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

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

eval0.0ms (0%)

Memory: 1.0MiB live, 1.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 14 to 11 computations (21.4% saved)

prune2.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	3	0	3
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	3	4	7

Accuracy

100.0%

Counts

7 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.9%	(+.f64 x x)
✓	100.0%	(*.f64 (+.f64 x x) y)
✓	5.9%	(*.f64 #s(approx (+ x x) #s(literal 2 binary64)) y)
✓	5.1%	#s(approx (+ x x) #s(literal 2 binary64))

Compiler

Compiled 29 to 28 computations (3.4% saved)

regimes10.0ms (0.2%)

Memory

-22.9MiB live, 24.5MiB allocated; 1ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	(+.f64 y y)
2.0ms	x
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 8 to 11 computations (-37.5% saved)

regimes8.0ms (0.1%)

Memory

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

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

regimes6.0ms (0.1%)

Memory

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

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.9%	1	`(+.f64 y y)`
5.9%	1	`(*.f64 x (+.f64 y y))`
5.9%	1	`x`
5.9%	1	`y`

Compiler

Compiled 8 to 11 computations (-37.5% saved)

regimes6.0ms (0.1%)

Memory

-31.9MiB live, 15.1MiB allocated; 2ms 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:

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

Results

Accuracy	Segments	Branch
5.9%	1	`x`
5.9%	1	`(+.f64 y y)`
5.9%	1	`(*.f64 x (+.f64 y y))`
5.9%	1	`y`

Compiler

Compiled 8 to 11 computations (-37.5% saved)

regimes4.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB 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	(+.f64 y y)
1.0ms	x
1.0ms	y
1.0ms	(*.f64 x (+.f64 y y))

Results

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

Compiler

Compiled 8 to 11 computations (-37.5% saved)

derivations6.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 10 computations (23.1% saved)

preprocess141.0ms (2.2%)

Memory: -27.5MiB live, 305.6MiB allocated; 35ms collecting garbage
Remove: (sort x y)
Compiler: Compiled 165 to 184 computations (-11.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample6.0s (93.3%)

preprocess109.0ms (1.7%)

series6.0ms (0.1%)

rewrite46.0ms (0.7%)

eval2.0ms (0%)

prune1.0ms (0%)

series3.0ms (0%)

rewrite34.0ms (0.5%)

eval4.0ms (0.1%)

prune4.0ms (0.1%)

series3.0ms (0%)

rewrite35.0ms (0.5%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes10.0ms (0.2%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

derivations6.0ms (0.1%)

preprocess141.0ms (2.2%)

end0.0ms (0%)

Profiling