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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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)

sample808.0ms (77.6%)

Memory

2.7MiB live, 712.4MiB allocated

Samples

579.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 417.0ms

ival-add: 254.0ms (60.9% of total)

ival-mult: 153.0ms (36.7% of total)

ival-true: 7.0ms (1.7% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

explain63.0ms (6%)

Memory

-22.8MiB live, 99.0MiB 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

18.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

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

ival-mult: 4.0ms (57% of total)

ival-add: 3.0ms (42.7% of total)

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

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

preprocess24.0ms (2.3%)

Memory

3.0MiB live, 41.1MiB allocated

Algorithm

1×	egg-herbie

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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

simplify3.0ms (0.3%)

Memory

1.4MiB live, 1.4MiB 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))

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

localize12.0ms (1.2%)

Memory

9.7MiB live, 9.7MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

8.0ms

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 (63.2% of total)

ival-add: 1.0ms (31.6% of total)

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

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

series5.0ms (0.5%)

Memory

4.2MiB live, 4.2MiB 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
2.0ms	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))
1.0ms	x	@	inf	((* x (+ y y)) (+ y y))

simplify3.0ms (0.3%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×	egg-herbie

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))

rewrite42.0ms (4%)

Memory

-16.7MiB live, 20.7MiB allocated

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
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval5.0ms (0.5%)

Memory: 13.0MiB live, 13.0MiB allocated
Compiler: Compiled 452 to 68 computations (85% saved)

prune2.0ms (0.2%)

Memory

5.4MiB live, 5.4MiB 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)

simplify29.0ms (2.7%)

Memory

6.9MiB live, 49.5MiB allocated

Algorithm

1×	egg-herbie

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)

preprocess46.0ms (4.4%)

Memory

-8.4MiB live, 102.8MiB 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%)

sample808.0ms (77.6%)

explain63.0ms (6%)

preprocess24.0ms (2.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.3%)

localize12.0ms (1.2%)

series5.0ms (0.5%)

simplify3.0ms (0.3%)

rewrite42.0ms (4%)

eval5.0ms (0.5%)

prune2.0ms (0.2%)

simplify29.0ms (2.7%)

soundness0.0ms (0%)

preprocess46.0ms (4.4%)

end0.0ms (0%)

Profiling