Metrics for Linear.Projection:perspective from linear-1.19.1.3, B

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze36.0ms (1.5%)

Memory

-24.7MiB live, 14.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample805.0ms (34.9%)

Memory

35.7MiB live, 810.5MiB allocated

Samples

555.0ms

8 004×

valid

Precisions

Click to see histograms. Total time spent on operations: 364.0ms

ival-mult: 247.0ms (67.9% of total)

ival-div: 57.0ms (15.7% of total)

ival-sub: 46.0ms (12.6% of total)

ival-true: 6.0ms (1.6% of total)

exact: 5.0ms (1.4% of total)

ival-assert: 4.0ms (1.1% of total)

Bogosity

explain2.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
3	-	-	`(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))`
0	-	-	`(*.f64 x #s(literal 2 binary64))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`y`
0	-	-	`(-.f64 x y)`
0	-	-	`(.f64 (.f64 x #s(literal 2 binary64)) y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))`	o/n	2	0
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	2
`/.f64`	`(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))`	u/n	1	0
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	underflow	1

Confusion

	Predicted +	Predicted -
+	3	0
-	0	1

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	0	0	1

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	1
1	3

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

0.0ms

8×

valid

Compiler

Compiled 82 to 32 computations (61% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

preprocess182.0ms (7.9%)

Memory

-5.3MiB live, 69.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	53
1	62	45
2	212	45
3	775	45
4	2699	45
5	3378	45
6	3564	45
7	3578	45
8	3593	45
9	3598	45
10	3598	45
11	3802	45
12	3898	45
13	3898	45
14	4002	45
15	4621	45
0	7	9
0	11	9
1	19	9
2	40	9
3	64	9
4	84	9
5	148	9
6	310	9
7	682	9
8	1532	9
9	2375	9
10	2393	9
11	2407	9
12	2419	9
13	2419	9
0	2419	9

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	29.7%	(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify64.0ms (2.8%)

Memory

7.4MiB live, 51.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f64 x y)
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	19	23
2	40	23
3	64	23
4	84	23
5	148	23
6	310	23
7	682	23
8	1532	23
9	2375	23
10	2393	23
11	2407	23
12	2419	23
13	2419	23
0	2419	23

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
y
(-.f64 x y)

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

localize1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	45.01177697561203	(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

Samples

0.0ms

4×

valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.4%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())

Outputs
#s(alt (* 2 y) (taylor 0 y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* 2 (/ y x)))) (taylor 0 y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -2 (/ (pow x 2) y))) (taylor inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3)))))) (taylor inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -2 (/ (pow x 2) y))) (taylor -inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y))) (taylor -inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y))) (taylor -inf y) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -2 (/ x y)) 2)) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2)) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2)) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (* 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3)))))) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (* 2 (/ (pow y 2) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y)) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y)) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) (patch (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((/ (* (* x 2) y) (- x y)) (* (* x 2) y) (* x 2) (- x y))
1.0ms	x	@	inf	((/ (* (* x 2) y) (- x y)) (* (* x 2) y) (* x 2) (- x y))
1.0ms	y	@	inf	((/ (* (* x 2) y) (- x y)) (* (* x 2) y) (* x 2) (- x y))
1.0ms	y	@	0	((/ (* (* x 2) y) (- x y)) (* (* x 2) y) (* x 2) (- x y))
1.0ms	x	@	-inf	((/ (* (* x 2) y) (- x y)) (* (* x 2) y) (* x 2) (- x y))

simplify397.0ms (17.2%)

Memory

-19.9MiB live, 167.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	136	557
1	378	543
2	1014	523
3	3096	517
4	6425	517
0	8149	486

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

Calls

Call 1

Inputs
(* 2 y)
(* y (+ 2 (* 2 (/ y x))))
(* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))))
(* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -2 x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2)))))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3))))))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -2 x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y)))
(+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y)))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -2 x)
(* x (- (* -2 (/ x y)) 2))
(* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2))
(* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* -1 y)
(- x y)
(- x y)
(- x y)
(* 2 y)
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2)))))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3))))))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* 2 y)
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y))
(+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))

Outputs
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(* y (+ 2 (* 2 (/ y x))))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))))
(*.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) #s(literal 2 binary64))
(* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) y #s(literal 2 binary64)) y)
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2)))))
(*.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) x x) x) #s(literal -2 binary64))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3))))))
(*.f64 (fma.f64 x (fma.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 x y) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 3 binary64)))) #s(literal -2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y)))
(*.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) x x) x) #s(literal -2 binary64))
(+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y)))
(fma.f64 #s(literal -2 binary64) x (/.f64 (*.f64 #s(literal -2 binary64) (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y))) y))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* x (- (* -2 (/ x y)) 2))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2))
(*.f64 (fma.f64 (/.f64 x y) (fma.f64 (/.f64 x y) x x) x) #s(literal -2 binary64))
(* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2))
(.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 y y)) (fma.f64 (/.f64 x y) x x) (/.f64 #s(literal -2 binary64) y)) x #s(literal -2 binary64)) x)
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #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))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2)))))
(*.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) #s(literal 2 binary64))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3))))))
(*.f64 (fma.f64 y (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #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))
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y))
(*.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 y x) y y) y) #s(literal 2 binary64))
(+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y))
(fma.f64 y #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (fma.f64 y y (/.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (pow.f64 y #s(literal 3 binary64))) x))) x))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #s(literal 2 binary64))
(* 2 (* x y))
(.f64 (.f64 x y) #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))
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)

rewrite180.0ms (7.8%)

Memory

32.3MiB live, 187.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	40	20
2	250	20
3	2754	20
0	9208	20

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 405

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 x y))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
(-.f64 x y)

Outputs
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eval170.0ms (7.4%)

Memory: -28.0MiB live, 10.7MiB allocated
Compiler: Compiled 11 154 to 1 335 computations (88% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	484	2	486
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	485	2	487

Accuracy

100.0%

Counts

487 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.5%	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64)))
▶	52.8%	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x))

Compiler

Compiled 8 to 10 computations (-25% saved)

simplify87.0ms (3.8%)

Memory

6.3MiB live, 42.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64)))
cost-diff	0	(*.f64 #s(literal -2 binary64) x)
cost-diff	0	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
0	14	36
1	24	36
2	44	36
3	67	36
4	87	36
5	155	36
6	324	36
7	702	36
8	1564	36
9	2413	36
10	2431	36
11	2445	36
12	2457	36
13	2457	36
0	2457	36

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) x)
#s(literal -2 binary64)
x
#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64)))
(*.f64 y #s(literal 2 binary64))
y
#s(literal 2 binary64)

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

localize1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	31.019605843037425	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64)))
accuracy	0	(*.f64 #s(literal -2 binary64) x)
accuracy	30.19924565869625	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x))

Samples

0.0ms

4×

valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.2%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 2 y) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* 2 (/ y x)))) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* 2 (/ y x)))) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -2 (/ (pow x 2) y))) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3)))))) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -2 (/ (pow x 2) y))) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3)))))) (taylor inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -2 (/ (pow x 2) y))) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y))) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y))) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -2 (/ (pow x 2) y))) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y))) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y))) (taylor -inf y) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -2 (/ x y)) 2)) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2)) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2)) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -2 (/ x y)) 2)) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2)) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2)) (taylor 0 x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (* 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3)))))) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (* 2 (/ (pow y 2) x))) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3)))))) (taylor inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (* 2 (/ (pow y 2) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y)) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y)) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 #s(literal -2 binary64) x)) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (* 2 (/ (pow y 2) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y)) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y)) (taylor -inf x) (#s(alt #s(approx (/ (* (* x 2) y) (- x y)) (.f64 y #s(literal 2 binary64))) (patch #s(approx (/ ( (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	y	@	inf	((/ (* (* x 2) y) (- x y)) (* -2 x) (/ (* (* x 2) y) (- x y)) (* y 2))
0.0ms	x	@	0	((/ (* (* x 2) y) (- x y)) (* -2 x) (/ (* (* x 2) y) (- x y)) (* y 2))
0.0ms	y	@	0	((/ (* (* x 2) y) (- x y)) (* -2 x) (/ (* (* x 2) y) (- x y)) (* y 2))
0.0ms	y	@	-inf	((/ (* (* x 2) y) (- x y)) (* -2 x) (/ (* (* x 2) y) (- x y)) (* y 2))
0.0ms	x	@	inf	((/ (* (* x 2) y) (- x y)) (* -2 x) (/ (* (* x 2) y) (- x y)) (* y 2))

simplify210.0ms (9.1%)

Memory

8.4MiB live, 178.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	118	748
1	318	720
2	852	680
3	2193	668
4	5962	668
0	8136	606

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* 2 y)
(* y (+ 2 (* 2 (/ y x))))
(* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))))
(* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))))
(* 2 y)
(* y (+ 2 (* 2 (/ y x))))
(* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))))
(* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* -2 x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2)))))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3))))))
(* -2 x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2)))))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3))))))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* -2 x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y)))
(+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y)))
(* -2 x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y)))
(+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y)))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* -2 x)
(* x (- (* -2 (/ x y)) 2))
(* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2))
(* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2))
(* -2 x)
(* -2 x)
(* -2 x)
(* -2 x)
(* -2 x)
(* x (- (* -2 (/ x y)) 2))
(* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2))
(* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2))
(* 2 y)
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2)))))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3))))))
(* -2 x)
(* -2 x)
(* -2 x)
(* -2 x)
(* 2 y)
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2)))))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3))))))
(* 2 y)
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y))
(+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y))
(* -2 x)
(* -2 x)
(* -2 x)
(* -2 x)
(* 2 y)
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y))
(+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y))

Outputs
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(* y (+ 2 (* 2 (/ y x))))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))))
(*.f64 (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y) #s(literal 2 binary64))
(* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) y #s(literal 2 binary64)) y)
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(* y (+ 2 (* 2 (/ y x))))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(* y (+ 2 (* y (+ (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))))
(*.f64 (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y) #s(literal 2 binary64))
(* y (+ 2 (* y (+ (* y (+ (* 2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) y #s(literal 2 binary64)) y)
(* 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)
(*.f64 #s(literal -2 binary64) x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2)))))
(*.f64 (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x y) x) #s(literal -2 binary64))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3))))))
(*.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x y) x)) #s(literal -2 binary64))
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (* -2 (/ (pow x 3) (pow y 2)))))
(*.f64 (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x y) x) #s(literal -2 binary64))
(+ (* -2 x) (+ (* -2 (/ (pow x 2) y)) (+ (* -2 (/ (pow x 3) (pow y 2))) (* -2 (/ (pow x 4) (pow y 3))))))
(*.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x 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)
(*.f64 #s(literal -2 binary64) x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y)))
(*.f64 (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x y) x) #s(literal -2 binary64))
(+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y)))
(fma.f64 #s(literal -2 binary64) x (/.f64 (*.f64 #s(literal -2 binary64) (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y))) y))
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(+ (* -2 x) (* -2 (/ (pow x 2) y)))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(+ (* -2 x) (* -1 (/ (+ (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y)))
(*.f64 (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x y) x) #s(literal -2 binary64))
(+ (* -2 x) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (pow x 4) y)) (* -2 (pow x 3))) y)) (* 2 (pow x 2))) y)))
(fma.f64 #s(literal -2 binary64) x (/.f64 (*.f64 #s(literal -2 binary64) (fma.f64 x x (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (pow.f64 x #s(literal 3 binary64))) y))) y))
(* 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)
(*.f64 #s(literal -2 binary64) x)
(* x (- (* -2 (/ x y)) 2))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2))
(*.f64 (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x y) x) #s(literal -2 binary64))
(* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2))
(.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 y y)) (fma.f64 (/.f64 x y) x x) (/.f64 #s(literal -2 binary64) y)) x #s(literal -2 binary64)) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* x (- (* -2 (/ x y)) 2))
(*.f64 (fma.f64 (/.f64 x y) x x) #s(literal -2 binary64))
(* x (- (* x (- (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 2))
(*.f64 (fma.f64 (fma.f64 (/.f64 x y) x x) (/.f64 x y) x) #s(literal -2 binary64))
(* x (- (* x (- (* x (- (* -2 (/ x (pow y 3))) (* 2 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))) 2))
(.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 y y)) (fma.f64 (/.f64 x y) x x) (/.f64 #s(literal -2 binary64) y)) x #s(literal -2 binary64)) x)
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y) #s(literal 2 binary64))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3))))))
(*.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y)) #s(literal 2 binary64))
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (* 2 (/ (pow y 3) (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y) #s(literal 2 binary64))
(+ (* 2 y) (+ (* 2 (/ (pow y 2) x)) (+ (* 2 (/ (pow y 3) (pow x 2))) (* 2 (/ (pow y 4) (pow x 3))))))
(*.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y)) #s(literal 2 binary64))
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y))
(*.f64 (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y) #s(literal 2 binary64))
(+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y))
(fma.f64 y #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (fma.f64 y y (/.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (pow.f64 y #s(literal 3 binary64))) x))) x))
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* 2 y)
(*.f64 y #s(literal 2 binary64))
(+ (* 2 y) (* 2 (/ (pow y 2) x)))
(*.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 2 binary64)) y)
(+ (* -1 (/ (+ (* -2 (/ (pow y 3) x)) (* -2 (pow y 2))) x)) (* 2 y))
(*.f64 (fma.f64 (fma.f64 (/.f64 y x) y y) (/.f64 y x) y) #s(literal 2 binary64))
(+ (* -1 (/ (+ (* -2 (pow y 2)) (* -1 (/ (+ (* 2 (/ (pow y 4) x)) (* 2 (pow y 3))) x))) x)) (* 2 y))
(fma.f64 y #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (fma.f64 y y (/.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (pow.f64 y #s(literal 3 binary64))) x))) x))

rewrite159.0ms (6.9%)

Memory

-19.8MiB live, 144.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
0	14	32
1	45	32
2	253	32
3	2750	32
0	9195	32

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 11

Calls

Call 1

Inputs
#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) x)
#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64)))
(*.f64 y #s(literal 2 binary64))

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

eval1.0ms (0%)

Memory: 0.8MiB live, 0.8MiB allocated
Compiler: Compiled 753 to 90 computations (88% saved)

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	83	2	85

Accuracy

100.0%

Counts

85 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.5%	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 y #s(literal 2 binary64)))
✓	52.8%	#s(approx (/ (* (* x 2) y) (- x y)) (*.f64 #s(literal -2 binary64) x))

Compiler

Compiled 25 to 22 computations (12% saved)

regimes0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 9 to 7 computations (22.2% saved)

end0.0ms (0%)

Memory

0.0MiB live, 0.0MiB allocated

Calls

1 calls:

0.0ms

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

start0.0ms (0%)

analyze36.0ms (1.5%)

sample805.0ms (34.9%)

explain2.0ms (0.1%)

preprocess182.0ms (7.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify64.0ms (2.8%)

localize1.0ms (0%)

series9.0ms (0.4%)

simplify397.0ms (17.2%)

rewrite180.0ms (7.8%)

eval170.0ms (7.4%)

prune1.0ms (0%)

simplify87.0ms (3.8%)

localize1.0ms (0%)

series4.0ms (0.2%)

simplify210.0ms (9.1%)

rewrite159.0ms (6.9%)

eval1.0ms (0%)

prune1.0ms (0%)

regimes0.0ms (0%)

end0.0ms (0%)

Profiling