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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

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)

sample487.0ms (48.3%)

Memory

10.9MiB live, 634.5MiB allocated

Samples

315.0ms

8 256×

valid

Precisions

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

ival-add: 84.0ms (57.7% of total)

ival-mult: 54.0ms (37.1% of total)

ival-true: 5.0ms (3.4% of total)

ival-assert: 3.0ms (2.1% of total)

Bogosity

explain130.0ms (12.9%)

Memory

12.0MiB live, 49.5MiB allocated

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

109.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-add: 95.0ms (95.7% of total)

ival-mult: 3.0ms (3% of total)

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

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

preprocess104.0ms (10.3%)

Memory

-19.5MiB live, 24.6MiB allocated

Algorithm

1×	egg-herbie

Rules

76×	`distribute-lft-neg-in`
70×	`associate-r`
54×	`cancel-sign-sub-inv`
48×	`distribute-lft-in`
44×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	51	25
2	133	25
3	340	25
4	444	25
5	452	25
0	4	5
0	6	5
1	13	5
2	20	5
3	24	5
0	24	5

Stop Event

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

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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0.1%)

Memory

1.0MiB live, 1.0MiB allocated

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)

simplify4.0ms (0.4%)

Memory

5.6MiB live, 5.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	-128	(+.f64 y y)
cost-diff	0	(*.f64 x (+.f64 y y))

Rules

24×	`lower-*.f32`
22×	`lower-*.f64`
10×	`*-commutative`
8×	`count-2`
6×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	13	10
2	20	10
3	24	10
0	24	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize40.0ms (4%)

Memory

-9.9MiB live, 26.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 x (+.f64 y y))

Samples

36.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (65.2% of total)

ival-add: 1.0ms (32.6% of total)

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

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

series5.0ms (0.5%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs
#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())
#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())

Outputs
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 x (+.f64 y y)) (patch (.f64 x (+.f64 y y)) #<representation:binary64>) () ())) ())

Calls

6 calls:

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

simplify4.0ms (0.4%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`lower-*.f64`
24×	`lower-*.f32`
10×	`*-commutative`
4×	`associate-r`
4×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	156
1	11	156
2	16	156
0	16	156

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))

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

rewrite32.0ms (3.2%)

Memory

-9.6MiB live, 61.9MiB allocated

Rules

56×	`lower-*.f32`
54×	`lower-*.f64`
38×	`lower-/.f64`
38×	`lower-/.f32`
32×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	22	8
0	134	8

Stop Event

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

Counts

2 → 25

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))
(+.f64 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 y x))
(*.f64 #s(literal 2 binary64) y)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 y #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) y))
(/.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 y y)

eval5.0ms (0.5%)

Memory: 16.1MiB live, 16.1MiB allocated
Compiler: Compiled 452 to 68 computations (85% saved)

prune9.0ms (0.8%)

Memory

-56.0MiB live, 5.5MiB allocated

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	1	62

Accuracy

100.0%

Counts

62 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 10 to 8 computations (20% saved)

simplify27.0ms (2.7%)

Memory

17.7MiB live, 54.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	5	5

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Stop Event

1×

done

Compiler

Compiled 5 to 4 computations (20% saved)

preprocess161.0ms (15.9%)

Memory

23.7MiB live, 97.4MiB allocated

Remove

(sort x y)

(negabs x)

(negabs y)

Compiler

Compiled 80 to 64 computations (20% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample487.0ms (48.3%)

explain130.0ms (12.9%)

preprocess104.0ms (10.3%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify4.0ms (0.4%)

localize40.0ms (4%)

series5.0ms (0.5%)

simplify4.0ms (0.4%)

rewrite32.0ms (3.2%)

eval5.0ms (0.5%)

prune9.0ms (0.8%)

simplify27.0ms (2.7%)

soundness0.0ms (0%)

preprocess161.0ms (15.9%)

end0.0ms (0%)

Profiling