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

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB 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 9 to 8 computations (11.1% saved)

sample582.0ms (37.7%)

Memory

-0.8MiB live, 751.5MiB allocated; 214ms collecting garbage

Samples

330.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-mult!: 123.0ms (83.4% of total)

ival-add!: 23.0ms (15.6% of total)

adjust: 2.0ms (1.4% of total)

Bogosity

preprocess44.0ms (2.9%)

Memory

-6.9MiB live, 38.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	99	44

Stop Event

1×	iter-limit
1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.5%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Symmetry

(abs y)

(negabs x)

Compiler

Compiled 14 to 12 computations (14.3% saved)

series125.0ms (8.1%)

Memory

7.0MiB live, 96.4MiB allocated; 29ms collecting garbage

Counts

6 → 10

Calls

Call 1

Inputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
x
(+.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(*.f64 y y)
y

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

Calls

6 calls:

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

rewrite205.0ms (13.3%)

Memory

16.9MiB live, 215.2MiB allocated; 147ms collecting garbage

Counts

6 → 30

Calls

Call 1

Inputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
x
(+.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(*.f64 y y)
y

Outputs
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(.f64 (fma.f64 (.f64 y x) y x) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 y y) (*.f64 y y) #s(literal 1 binary64)) (/.f64 x (fma.f64 y y #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))
x
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) y) (-.f64 #s(literal 1 binary64) y))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))
(*.f64 (+.f64 (neg.f64 #s(literal 1 binary64)) y) (-.f64 (neg.f64 #s(literal 1 binary64)) y))
(*.f64 (+.f64 (neg.f64 #s(literal 1 binary64)) (fabs.f64 y)) (-.f64 (neg.f64 #s(literal 1 binary64)) (fabs.f64 y)))
#s(literal 1 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 y y)
(.f64 (.f64 y y) #s(literal 1 binary64))
(.f64 (.f64 y y) (neg.f64 #s(literal 1 binary64)))
(*.f64 (fabs.f64 y) (neg.f64 y))
(*.f64 (fabs.f64 y) y)
y
(*.f64 y #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) y)
(.f64 (neg.f64 #s(literal 1 binary64)) (.f64 (neg.f64 #s(literal 1 binary64)) y))
(/.f64 (*.f64 #s(literal 2 binary64) y) #s(literal 2 binary64))

eval4.0ms (0.2%)

Memory: 11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 402 to 121 computations (69.9% saved)

prune8.0ms (0.5%)

Memory

-45.6MiB live, 7.1MiB allocated; 9ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	3	37

Accuracy

100.0%

Counts

37 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (fma.f64 (.f64 y x) y x) #s(literal 1 binary64))
▶	91.5%	(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
▶	53.7%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 23 to 19 computations (17.4% saved)

series154.0ms (10%)

Memory

20.5MiB live, 113.5MiB allocated; 20ms collecting garbage

Counts

10 → 12

Calls

Call 1

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

Outputs
#s(approx (* x (+ 1 (* y y))) (*.f64 x (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 2 binary64)))))
#s(approx x x)
#s(approx (* y x) (*.f64 x y))
#s(approx (* (+ (* (* y x) y) x) 1) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 2 binary64))) #s(literal 1 binary64)))))
#s(approx (* x (+ 1 (* y y))) (+.f64 x (*.f64 x (pow.f64 y #s(literal 2 binary64)))))
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
#s(approx (+ 1 (* y y)) (+.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 2 binary64))))
#s(approx y y)
#s(approx (* x (+ 1 (* y y))) (*.f64 x (pow.f64 y #s(literal 2 binary64))))
#s(approx (* x (+ 1 (* y y))) (*.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 x (/.f64 x (pow.f64 y #s(literal 2 binary64))))))
#s(approx (+ 1 (* y y)) (pow.f64 y #s(literal 2 binary64)))
#s(approx (+ 1 (* y y)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 2 binary64))))))

Calls

6 calls:

Time	Variable	Point
2.0ms	x	inf
1.0ms	x	-inf
1.0ms	y	-inf
1.0ms	x	0
1.0ms	y	inf

rewrite280.0ms (18.2%)

Memory

-22.3MiB live, 169.3MiB allocated; 47ms collecting garbage

Counts

10 → 41

Calls

Call 1

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

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

eval8.0ms (0.5%)

Memory: 6.5MiB live, 6.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 711 to 170 computations (76.1% saved)

prune5.0ms (0.3%)

Memory

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

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	59	3	62

Accuracy

100.0%

Counts

62 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (fma.f64 (.f64 y x) y x) #s(literal 1 binary64))
✓	91.5%	(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
✓	53.7%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes76.0ms (4.9%)

Memory

-3.8MiB live, 42.7MiB allocated; 9ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

3 → 1

4 → 1

Calls

Call 1

Inputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Outputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Call 2

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

Outputs
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)

Call 3

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

Outputs
(.f64 (fma.f64 (.f64 y x) y x) #s(literal 1 binary64))

Calls

15 calls:

40.0ms	y
6.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
4.0ms	y
3.0ms	x
2.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Results

Accuracy	Segments	Branch
53.7%	1	`(*.f64 y y)`
53.7%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
53.7%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
53.7%	1	`y`
53.7%	1	`x`
91.5%	1	`(*.f64 y y)`
91.5%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
91.5%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
91.5%	1	`x`
91.5%	1	`y`
100.0%	1	`(*.f64 y y)`
100.0%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
100.0%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 81 to 70 computations (13.6% saved)

derivations1.0ms (0.1%)

Memory

0.8MiB live, 0.9MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 23 to 13 computations (43.5% saved)

preprocess51.0ms (3.3%)

Memory

18.6MiB live, 68.5MiB allocated; 8ms collecting garbage

Remove

(negabs x)

(abs y)

Compiler

Compiled 122 to 95 computations (22.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample582.0ms (37.7%)

preprocess44.0ms (2.9%)

series125.0ms (8.1%)

rewrite205.0ms (13.3%)

eval4.0ms (0.2%)

prune8.0ms (0.5%)

series154.0ms (10%)

rewrite280.0ms (18.2%)

eval8.0ms (0.5%)

prune5.0ms (0.3%)

regimes76.0ms (4.9%)

derivations1.0ms (0.1%)

preprocess51.0ms (3.3%)

end0.0ms (0%)

Profiling