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

0.1MiB live, 0.1MiB 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)

sample407.0ms (61.3%)

Memory

154.2MiB live, 154.2MiB allocated

Samples

233.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-mult: 53.0ms (53.1% of total)

ival-add: 38.0ms (38% of total)

ival-true: 6.0ms (6% of total)

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

Bogosity

explain50.0ms (7.5%)

Memory

25.9MiB live, 25.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(2.9325524114916505e-27 1.2947044637906273e+308)	`(*.f64 x (+.f64 y y))`
0	-	0	-	`(+.f64 y y)`
0	-	0	-	`y`
0	-	0	-	`x`

Confusion

	Predicted +	Predicted -
+	0	1
-	0	255

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	1
-	0	0	255

Precision?

0/0

Recall?

0.0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	1
-	0	0	0

Precision?

0/0

Recall?

0.0

Samples

17.0ms

512×

valid

Compiler

Compiled 49 to 24 computations (51% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 3.0ms (46.2% of total)

ival-mult: 3.0ms (46.2% of total)

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

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

preprocess21.0ms (3.2%)

Memory

6.8MiB live, 6.8MiB 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: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0.1%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 x (+.f64 y y))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.4%)

Memory

0.4MiB live, 0.4MiB 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 (1.7%)

Memory

5.2MiB live, 5.2MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 y y)
accuracy	0.4657977853136115	(*.f64 x (+.f64 y y))

Samples

8.0ms

256×

valid

Compiler

Compiled 22 to 10 computations (54.5% saved)

Precisions

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

ival-mult: 2.0ms (66.5% of total)

ival-add: 1.0ms (33.3% of total)

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

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

series4.0ms (0.6%)

Memory

1.9MiB live, 1.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

Outputs
(* 2 (* x y))
(* 2 y)

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))
1.0ms	x	@	inf	((* x (+ y y)) (+ y y))

simplify2.0ms (0.3%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	11	8
2	16	8
0	16	8

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 2

Calls

Call 1

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

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

rewrite24.0ms (3.6%)

Memory

5.6MiB live, 5.6MiB 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
(.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)

eval2.0ms (0.3%)

Memory: 1.9MiB live, 1.9MiB allocated
Compiler: Compiled 256 to 70 computations (72.7% saved)

prune1.0ms (0.1%)

Memory

1.3MiB live, 1.3MiB allocated

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Accuracy

100.0%

Counts

28 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.4%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

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 y (+.f64 x x))
y
(+.f64 x x)
x

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

localize12.0ms (1.7%)

Memory

5.1MiB live, 5.1MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

8.0ms

256×

valid

Compiler

Compiled 22 to 10 computations (54.5% saved)

Precisions

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

ival-mult: 2.0ms (66.3% of total)

ival-add: 1.0ms (33.2% of total)

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

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

series2.0ms (0.3%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

2 → 2

Calls

Call 1

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

Outputs
(* 2 (* x y))
(* 2 x)

Calls

6 calls:

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

simplify2.0ms (0.3%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	16	8
3	17	8
0	17	8

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 2

Calls

Call 1

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

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

rewrite17.0ms (2.6%)

Memory

1.1MiB live, 1.1MiB 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 y (+.f64 x x))
(+.f64 x x)

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

eval2.0ms (0.3%)

Memory: 1.9MiB live, 1.9MiB allocated
Compiler: Compiled 256 to 70 computations (72.7% saved)

prune1.0ms (0.2%)

Memory

1.6MiB live, 1.6MiB allocated

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Accuracy

100.0%

Counts

28 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0.8%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(*.f64 x (+.f64 y y))`
100.0%	1	`(+.f64 y y)`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes5.0ms (0.7%)

Memory

5.7MiB live, 5.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

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
99.3%	1	`x`
99.3%	1	`y`
99.3%	1	`(*.f64 x (+.f64 y y))`
99.3%	1	`(+.f64 y y)`

Compiler

Compiled 10 to 11 computations (-10% saved)

simplify19.0ms (2.8%)

Memory

18.3MiB live, 18.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	8	10

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness17.0ms (2.6%)

Memory

0.8MiB live, 0.8MiB 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×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 20 to 12 computations (40% saved)

preprocess54.0ms (8.1%)

Memory

30.2MiB live, 30.2MiB allocated

Remove

(negabs x)

(negabs y)

Compiler

Compiled 150 to 116 computations (22.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample407.0ms (61.3%)

explain50.0ms (7.5%)

preprocess21.0ms (3.2%)

eval0.0ms (0%)

prune0.0ms (0.1%)

simplify3.0ms (0.4%)

localize12.0ms (1.7%)

series4.0ms (0.6%)

simplify2.0ms (0.3%)

rewrite24.0ms (3.6%)

eval2.0ms (0.3%)

prune1.0ms (0.1%)

simplify3.0ms (0.4%)

localize12.0ms (1.7%)

series2.0ms (0.3%)

simplify2.0ms (0.3%)

rewrite17.0ms (2.6%)

eval2.0ms (0.3%)

prune1.0ms (0.2%)

regimes6.0ms (0.8%)

regimes5.0ms (0.7%)

simplify19.0ms (2.8%)

soundness17.0ms (2.6%)

preprocess54.0ms (8.1%)

end0.0ms (0%)

Profiling