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

analyze0.0ms (0%)

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 8 to 5 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample617.0ms (77.5%)

Results

413.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-mult: 73.0ms (54% of total)

ival-add: 53.0ms (39.2% of total)

const: 7.0ms (5.2% of total)

backward-pass: 2.0ms (1.5% of total)

Bogosity

preprocess19.0ms (2.4%)

Algorithm

2×	egg-herbie

Rules

80×	`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	13	32
1	52	30
2	135	30
3	341	30
4	442	30
5	450	30
0	4	5
1	11	5
2	18	5
3	21	5
0	21	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* x (+ y y))

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

Call 2

Inputs
(* x (+ y y))
(* (neg x) (+ y y))
(* x (+ (neg y) (neg y)))
(neg (* (neg x) (+ y y)))
(neg (* x (+ (neg y) (neg y))))
(* y (+ x x))

Outputs
(* x (+ y y))
(* (neg x) (+ y y))
(* y (* x -2))
(* x (+ (neg y) (neg y)))
(* y (* x -2))
(neg (* (neg x) (+ y y)))
(* x (+ y y))
(neg (* x (+ (neg y) (neg y))))
(* x (+ y y))
(* y (+ x x))
(* x (+ y y))

Symmetry

(negabs x)

(negabs y)

(sort x y)

explain43.0ms (5.4%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`y`
-	-	`(+.f64 y y)`
-	-	`(*.f64 x (+.f64 y y))`

Results

27.0ms

512×

valid

Compiler

Compiled 33 to 14 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 5.0ms (55.2% of total)

ival-add: 3.0ms (33.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 4 computations (42.9% saved)

localize28.0ms (3.5%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(*.f64 x (+.f64 y y))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 x (+.f64 y y))

Rules

24×	`-lowering-.f32`
24×	`-lowering-.f64`
8×	`*-commutative`
8×	`count-2`
6×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	11	10
2	18	10
3	21	10
0	21	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x (+ y y))
x
(+ y y)
y

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

Results

11.0ms

256×

valid

Compiler

Compiled 13 to 5 computations (61.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (50% of total)

ival-add: 1.0ms (25% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series7.0ms (0.9%)

Counts

2 → 36

Calls

Call 1

Inputs
#<alt (* x (+ y y))>
#<alt (+ y y)>

Outputs
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>

Calls

9 calls:

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

rewrite37.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

56×	`-lowering-.f32`
56×	`-lowering-.f64`
38×	`/-lowering-/.f32`
38×	`/-lowering-/.f64`
32×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	20	8
0	132	8

Stop Event

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

Counts

2 → 25

Calls

Call 1

Inputs
(* x (+ y y))
(+ y y)

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

simplify10.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

24×	`-lowering-.f32`
24×	`-lowering-.f64`
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 (* 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))
(* 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 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)

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

eval6.0ms (0.8%)

Compiler: Compiled 449 to 245 computations (45.4% saved)

prune6.0ms (0.7%)

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 14 to 8 computations (42.9% saved)

soundness0.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 7 to 4 computations (42.9% saved)

preprocess22.0ms (2.8%)

Remove

(sort x y)

(negabs y)

(negabs x)

Compiler

Compiled 112 to 64 computations (42.9% saved)

Numeric.Integration.TanhSinh:simpson from integration-0.2.1

analyze0.0ms (0%)

sample617.0ms (77.5%)

preprocess19.0ms (2.4%)

explain43.0ms (5.4%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize28.0ms (3.5%)

series7.0ms (0.9%)

rewrite37.0ms (4.7%)

simplify10.0ms (1.2%)

eval6.0ms (0.8%)

prune6.0ms (0.7%)

soundness0.0ms (0%)

preprocess22.0ms (2.8%)

end0.0ms (0%)

Profiling