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

0.3MiB live, 0.3MiB 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)

sample734.0ms (51.9%)

Memory

-30.9MiB live, 703.3MiB allocated

Samples

398.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 179.0ms

ival-add: 112.0ms (62.7% of total)

ival-mult: 58.0ms (32.5% of total)

ival-true: 6.0ms (3.4% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

explain41.0ms (2.9%)

Memory

26.1MiB live, 64.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
1	-	-	`(*.f64 x (+.f64 y y))`
0	-	-	`(+.f64 y y)`
0	-	-	`y`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(*.f64 x (+.f64 y y))`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

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 (57.5% of total)

ival-add: 3.0ms (43.1% of total)

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

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

preprocess31.0ms (2.2%)

Memory

-19.4MiB live, 50.3MiB 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB 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 (0.2%)

Memory

8.1MiB live, 8.1MiB 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

localize17.0ms (1.2%)

Memory

-20.5MiB live, 28.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 y y)
accuracy	0.46859548070448764	(*.f64 x (+.f64 y y))

Samples

13.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-add: 2.0ms (54.4% of total)

ival-mult: 2.0ms (54.4% of total)

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

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

series5.0ms (0.3%)

Memory

10.0MiB live, 10.0MiB 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))

simplify3.0ms (0.2%)

Memory

6.6MiB live, 6.7MiB 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))

rewrite121.0ms (8.5%)

Memory

-7.0MiB live, 66.6MiB 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 (0.4%)

Memory: 11.3MiB live, 11.3MiB allocated
Compiler: Compiled 452 to 68 computations (85% saved)

prune1.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	0	0
Picked	1	0	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 y (+.f64 x x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.3%)

Memory

4.6MiB live, 4.5MiB 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))

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 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

localize35.0ms (2.5%)

Memory

-16.5MiB live, 21.3MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

9.0ms

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 (58.4% of total)

ival-add: 1.0ms (29.2% of total)

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

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

series3.0ms (0.2%)

Memory

7.5MiB live, 7.5MiB allocated

Counts

2 → 36

Calls

Call 1

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

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

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	@	0	((* y (+ x x)) (+ x x))
0.0ms	y	@	inf	((* y (+ x x)) (+ x x))

simplify4.0ms (0.3%)

Memory

6.7MiB live, 6.7MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`lower-*.f64`
24×	`lower-*.f32`
8×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	156
1	10	156
2	16	156
3	17	156
0	17	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)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

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

rewrite28.0ms (1.9%)

Memory

-12.4MiB live, 29.9MiB 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 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)

eval5.0ms (0.4%)

Memory: 13.1MiB live, 13.1MiB allocated
Compiler: Compiled 452 to 69 computations (84.7% saved)

prune2.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB 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 y (+.f64 x x))

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.7%)

Memory

-21.4MiB live, 15.6MiB 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:

4.0ms	y
2.0ms	(*.f64 x (+.f64 y y))
1.0ms	x
1.0ms	(+.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 (0.4%)

Memory

14.1MiB live, 14.1MiB 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)

simplify23.0ms (1.7%)

Memory

-13.4MiB live, 62.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`

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)

soundness27.0ms (1.9%)

Memory

4.4MiB live, 49.2MiB 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×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 20 to 12 computations (40% saved)

preprocess308.0ms (21.7%)

Memory: 25.7MiB live, 369.7MiB allocated
Compiler: Compiled 120 to 92 computations (23.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample734.0ms (51.9%)

explain41.0ms (2.9%)

preprocess31.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.2%)

localize17.0ms (1.2%)

series5.0ms (0.3%)

simplify3.0ms (0.2%)

rewrite121.0ms (8.5%)

eval5.0ms (0.4%)

prune1.0ms (0.1%)

simplify4.0ms (0.3%)

localize35.0ms (2.5%)

series3.0ms (0.2%)

simplify4.0ms (0.3%)

rewrite28.0ms (1.9%)

eval5.0ms (0.4%)

prune2.0ms (0.1%)

regimes9.0ms (0.7%)

regimes5.0ms (0.4%)

simplify23.0ms (1.7%)

soundness27.0ms (1.9%)

preprocess308.0ms (21.7%)

end0.0ms (0%)

Profiling