Metrics for Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze11.0ms (0.3%)

Memory

-19.4MiB live, 19.6MiB 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 9 to 7 computations (22.2% saved)

sample707.0ms (19%)

Memory

63.8MiB live, 911.3MiB allocated

Samples

437.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 229.0ms

ival-add: 162.0ms (70.6% of total)

ival-div: 57.0ms (24.8% of total)

ival-true: 7.0ms (3.1% of total)

ival-assert: 4.0ms (1.7% of total)

Bogosity

explain167.0ms (4.5%)

Memory

-30.5MiB live, 137.5MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

65.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

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

ival-add: 5.0ms (54.3% of total)

ival-div: 4.0ms (43.4% of total)

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

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

preprocess192.0ms (5.2%)

Memory

-0.5MiB live, 38.3MiB allocated

Algorithm

1×	egg-herbie

Rules

856×	`times-frac`
820×	`distribute-lft-in`
772×	`distribute-rgt-in`
636×	`div-sub`
544×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	42	35
2	106	35
3	310	35
4	1262	35
5	2388	35
6	3252	35
7	3801	35
8	4253	35
9	4303	35
10	4335	35
11	4411	35
12	4595	35
0	5	7
0	8	7
1	11	7
2	14	7
3	16	7
0	16	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-384	(/.f64 (+.f64 x y) (+.f64 y y))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(+.f64 x y)

Rules

10×	`lower-/.f32`
8×	`lower-/.f64`
6×	`lower-+.f32`
4×	`lift-+.f64`
4×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	11	15
2	14	15
3	16	15
0	16	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize14.0ms (0.4%)

Memory

17.3MiB live, 17.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y y)
accuracy	0	(+.f64 x y)
accuracy	0.00390625	(/.f64 (+.f64 x y) (+.f64 y y))

Samples

10.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-div: 2.0ms (45.3% of total)

ival-add: 2.0ms (45.3% of total)

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

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

series6.0ms (0.2%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

3 → 60

Calls

Call 1

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

Inputs

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

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

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

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

Calls

6 calls:

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

simplify125.0ms (3.4%)

Memory

-34.5MiB live, 61.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 672×	`lower-*.f64`
2 672×	`lower-*.f32`
1 728×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	95	240
2	195	240
3	532	240
4	2484	240
5	4892	240
6	6155	240
7	7112	240
8	7634	240
0	8014	222

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

Calls

Call 1

Inputs
x
(+ x y)
(+ x y)
(+ x y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 1/2 (/ x y))
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(/ (+ (* 1/2 x) (* 1/2 y)) y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
1/2
(+ 1/2 (* 1/2 (/ x y)))
(+ 1/2 (* 1/2 (/ x y)))
(+ 1/2 (* 1/2 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
1/2
(+ 1/2 (* 1/2 (/ x y)))
(+ 1/2 (* 1/2 (/ x y)))
(+ 1/2 (* 1/2 (/ x y)))
y
(+ x y)
(+ x y)
(+ x y)
1/2
(+ 1/2 (* 1/2 (/ x y)))
(+ 1/2 (* 1/2 (/ x y)))
(+ 1/2 (* 1/2 (/ x y)))
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* 1/2 (/ x y))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* 1/2 (/ x y))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))

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

rewrite45.0ms (1.2%)

Memory

9.1MiB live, 47.5MiB allocated

Rules

150×	`lower-/.f32`
148×	`lower-/.f64`
128×	`lower-*.f64`
128×	`lower-*.f32`
76×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	38	13
0	305	13

Stop Event

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

Counts

3 → 61

Calls

Call 1

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

Outputs
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eval23.0ms (0.6%)

Memory: -20.0MiB live, 17.4MiB allocated
Compiler: Compiled 1 133 to 170 computations (85% saved)

prune6.0ms (0.2%)

Memory

11.7MiB live, 11.7MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Accuracy

100.0%

Counts

116 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.1%	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
▶	4.5%	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
▶	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	44.7%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
▶	57.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 60 to 58 computations (3.3% saved)

simplify122.0ms (3.3%)

Memory

22.5MiB live, 59.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
cost-diff	0	(*.f64 #s(literal -2 binary64) y)
cost-diff	0	(+.f64 y x)
cost-diff	0	(neg.f64 (+.f64 y x))
cost-diff	128	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
cost-diff	0	(*.f64 #s(literal -2 binary64) y)
cost-diff	0	(+.f64 y x)
cost-diff	0	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 x y)
cost-diff	0	(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Rules

2 032×	`lower-fma.f32`
2 030×	`lower-fma.f64`
840×	`lower-*.f32`
832×	`lower-*.f64`
820×	`times-frac`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	19	97
0	29	97
1	57	97
2	116	96
3	319	96
4	539	96
5	725	96
6	1338	93
7	3053	93
8	3621	93
9	3719	93
10	3774	93
11	3807	93
12	3807	93
13	3807	93
0	3807	93

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x y)
x
y
#s(literal 1/2 binary64)
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(+.f64 y x)
y
x
(*.f64 #s(literal -2 binary64) y)
#s(literal -2 binary64)
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
(neg.f64 (+.f64 y x))
(+.f64 y x)
y
x
(*.f64 #s(literal -2 binary64) y)
#s(literal -2 binary64)
#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
x

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

localize106.0ms (2.9%)

Memory

-22.7MiB live, 90.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.21875	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	35.31864108916054	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	0	(neg.f64 (+.f64 y x))
accuracy	0.00390625	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	0.00390625	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
accuracy	27.13565491114414	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
accuracy	0	(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	0	(/.f64 x y)
accuracy	0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Samples

54.0ms

256×

valid

Compiler

Compiled 85 to 19 computations (77.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 25.0ms (60.3% of total)

ival-add: 9.0ms (21.7% of total)

ival-div: 5.0ms (12.1% of total)

ival-neg: 1.0ms (2.4% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.5%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

12 → 264

Calls

Call 1

Inputs
#s(alt #s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch #s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) (patch #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y)) (patch (.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y)) #<representation binary64>) () ())
#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -2 binary64) y) (patch (.f64 #s(literal -2 binary64) y) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y)) (patch (.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y)) #<representation binary64>) () ())
#s(alt (neg.f64 (+.f64 y x)) (patch (neg.f64 (+.f64 y x)) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (patch #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (patch (.f64 (/.f64 #s(literal 1/2 binary64) y) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	x	@	-inf	((/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	y	@	inf	((/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	x	@	inf	((/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	y	@	0	((/ (+ x y) (+ y y)) (+ (* (/ x y) 1/2) 1/2) (/ x y) (/ (+ x y) (+ y y)) (* (+ y x) (* -2 y)) (+ y x) (* -2 y) (* (neg (+ y x)) (* -2 y)) (neg (+ y x)) (/ (+ x y) (+ y y)) (* (/ 1/2 y) x) (/ 1/2 y))

simplify142.0ms (3.8%)

Memory

9.8MiB live, 127.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4 086×	`lower-fma.f64`
4 086×	`lower-fma.f32`
3 210×	`lower-*.f64`
3 210×	`lower-*.f32`
2 540×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	1296
1	226	1296
2	570	1296
3	1581	1296
4	4021	1296
5	6167	1296
0	8032	1224

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 258

Calls

Call 1

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

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

rewrite140.0ms (3.8%)

Memory

-16.7MiB live, 58.7MiB allocated

Rules

382×	`lower-*.f32`
378×	`lower-/.f32`
374×	`lower-*.f64`
374×	`lower-/.f64`
238×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	78
0	29	77
1	119	77
0	823	77

Stop Event

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

Counts

12 → 306

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x y)
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(+.f64 y x)
(*.f64 #s(literal -2 binary64) y)
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
(neg.f64 (+.f64 y x))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)

Outputs
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eval150.0ms (4%)

Memory: -4.9MiB live, 193.7MiB allocated
Compiler: Compiled 6 476 to 694 computations (89.3% saved)

prune21.0ms (0.6%)

Memory

31.2MiB live, 31.2MiB allocated

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	645	5	650
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	648	7	655

Accuracy

100.0%

Counts

655 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	34.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
▶	44.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
▶	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	57.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	1.7%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
▶	3.6%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))

Compiler

Compiled 71 to 70 computations (1.4% saved)

simplify143.0ms (3.8%)

Memory

9.3MiB live, 84.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) y)
cost-diff	0	(fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(.f64 (.f64 y y) #s(literal -2 binary64))
cost-diff	0	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(.f64 (.f64 y y) #s(literal 2 binary64))
cost-diff	0	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(*.f64 (+.f64 y y) x)
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Rules

2 208×	`lower-fma.f32`
2 206×	`lower-fma.f64`
872×	`lower-*.f32`
860×	`lower-*.f64`
838×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	121
0	37	121
1	69	121
2	140	120
3	329	120
4	522	120
5	738	120
6	1408	120
7	3028	120
8	3465	120
9	3611	120
10	3665	120
11	3677	120
12	3679	120
13	3679	120
14	3719	120
15	3747	120
16	3747	120
0	3747	117

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
(*.f64 (+.f64 y y) x)
(+.f64 y y)
y
x
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
(.f64 (.f64 y y) #s(literal 2 binary64))
(*.f64 y y)
y
#s(literal 2 binary64)
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
(.f64 (.f64 y y) #s(literal -2 binary64))
(*.f64 y y)
y
#s(literal -2 binary64)
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) y)
#s(literal 2 binary64)
y
x
#s(literal 1/2 binary64)

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

localize194.0ms (5.2%)

Memory

-16.0MiB live, 222.3MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) y)
accuracy	42.209720921566515	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0.00390625	(.f64 (.f64 y y) #s(literal -2 binary64))
accuracy	23.677494455872026	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0.00390625	(.f64 (.f64 y y) #s(literal 2 binary64))
accuracy	23.677494455872026	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 (+.f64 y y) x)
accuracy	61.53101607508737	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
accuracy	0	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	35.31864108916054	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Samples

160.0ms

256×

valid

Compiler

Compiled 93 to 24 computations (74.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-div: 116.0ms (79% of total)

ival-mult: 23.0ms (15.7% of total)

ival-add: 5.0ms (3.4% of total)

ival-neg: 2.0ms (1.4% of total)

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

exact: 0.0ms (0% of total)

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

series20.0ms (0.5%)

Memory

12.6MiB live, 49.3MiB allocated

Counts

14 → 264

Calls

Call 1

Inputs
#s(alt #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (patch #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 1/2 binary64) x) y) (patch (/.f64 (.f64 #s(literal 1/2 binary64) x) y) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ x y) (+ y y)) (.f64 (+.f64 y y) x)) (patch #s(approx (/ (+ x y) (+ y y)) (.f64 (+.f64 y y) x)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 y y) x) (patch (.f64 (+.f64 y y) x) #<representation binary64>) () ())
#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64))) (patch #s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 y y) #s(literal 2 binary64)) (patch (.f64 (.f64 y y) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64))) (patch #s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 y y) #s(literal -2 binary64)) (patch (.f64 (.f64 y y) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ x y) (+ y y)) (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))) (patch #s(approx (/ (+ x y) (+ y y)) (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (* (neg (+ y x)) (* -2 y)) (* (* y y) 2) (* y y) (* (+ y x) (* -2 y)) (* (* y y) -2) (/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
2.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (* (neg (+ y x)) (* -2 y)) (* (* y y) 2) (* y y) (* (+ y x) (* -2 y)) (* (* y y) -2) (/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
2.0ms	y	@	inf	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (* (neg (+ y x)) (* -2 y)) (* (* y y) 2) (* y y) (* (+ y x) (* -2 y)) (* (* y y) -2) (/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
2.0ms	y	@	0	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (* (neg (+ y x)) (* -2 y)) (* (* y y) 2) (* y y) (* (+ y x) (* -2 y)) (* (* y y) -2) (/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
2.0ms	x	@	inf	((/ (+ x y) (+ y y)) (/ (* 1/2 x) y) (* 1/2 x) (/ (+ x y) (+ y y)) (* (+ y y) x) (+ y y) (* (neg (+ y x)) (* -2 y)) (* (* y y) 2) (* y y) (* (+ y x) (* -2 y)) (* (* y y) -2) (/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))

simplify111.0ms (3%)

Memory

-0.8MiB live, 118.0MiB allocated

Algorithm

1×	egg-herbie

Rules

4 388×	`lower-fma.f64`
4 388×	`lower-fma.f32`
2 744×	`lower-*.f64`
2 744×	`lower-*.f32`
1 842×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	1396
1	197	1396
2	497	1396
3	1110	1396
4	2633	1396
5	5008	1396
6	6828	1396
0	8113	1324

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

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

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

rewrite51.0ms (1.4%)

Memory

-20.6MiB live, 57.0MiB allocated

Rules

428×	`lower-*.f32`
416×	`lower-*.f64`
362×	`lower-/.f32`
360×	`lower-/.f64`
350×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	105
0	37	102
1	126	96
0	809	96

Stop Event

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

Counts

14 → 257

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
(*.f64 (+.f64 y y) x)
(+.f64 y y)
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
(.f64 (.f64 y y) #s(literal 2 binary64))
(*.f64 y y)
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
(.f64 (.f64 y y) #s(literal -2 binary64))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) y)

Outputs
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eval78.0ms (2.1%)

Memory: -11.1MiB live, 133.0MiB allocated
Compiler: Compiled 4 220 to 522 computations (87.6% saved)

prune18.0ms (0.5%)

Memory

14.3MiB live, 52.3MiB allocated

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	533	4	537
Fresh	0	0	0
Picked	1	4	5
Done	0	2	2
Total	534	10	544

Accuracy

100.0%

Counts

544 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	34.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	44.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	57.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	3.6%	#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
▶	3.1%	#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
✓	1.7%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
▶	3.0%	#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
✓	3.6%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))

Compiler

Compiled 52 to 53 computations (-1.9% saved)

simplify6.0ms (0.2%)

Memory

10.4MiB live, 10.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score
cost-diff	-128	(+.f64 y y)
cost-diff	0	(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
cost-diff	-128	(+.f64 y y)
cost-diff	0	#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
cost-diff	0	(*.f64 y #s(literal -2 binary64))
cost-diff	0	#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))

Rules

74×	`lower-*.f32`
72×	`lower-*.f64`
58×	`lower-fma.f32`
56×	`lower-fma.f64`
34×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	73
0	23	73
1	32	73
2	57	73
3	99	73
4	107	73
0	107	73

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
(*.f64 y #s(literal -2 binary64))
y
#s(literal -2 binary64)
#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
(+.f64 y y)
y
#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
(+.f64 y y)
y
x
#s(literal 1/2 binary64)

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

localize80.0ms (2.1%)

Memory

-31.3MiB live, 52.1MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
accuracy	0	(+.f64 y y)
accuracy	42.209720921566515	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	62.45202840506666	#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(+.f64 y y)
accuracy	61.24734053948953	#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
accuracy	0	(*.f64 y #s(literal -2 binary64))
accuracy	61.448762731610856	#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))

Samples

71.0ms

256×

valid

Compiler

Compiled 57 to 16 computations (71.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 6.0ms (40.6% of total)

ival-add: 5.0ms (33.8% of total)

ival-div: 3.0ms (20.3% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

20.0MiB live, 20.0MiB allocated

Counts

8 → 156

Calls

Call 1

Inputs
#s(alt #s(approx (* (+ y x) (* -2 y)) (.f64 y #s(literal -2 binary64))) (patch #s(approx ( (+ y x) (* -2 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>) () ())
#s(alt #s(approx (* (+ y x) (* -2 y)) (+.f64 y y)) (patch #s(approx (* (+ y x) (* -2 y)) (+.f64 y y)) #<representation binary64>) () ())
#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y)) (patch #s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))) (patch #s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)) (patch (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	((* (+ y x) (* -2 y)) (* y -2) (* (+ y x) (* -2 y)) (+ y y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2))
1.0ms	y	@	-inf	((* (+ y x) (* -2 y)) (* y -2) (* (+ y x) (* -2 y)) (+ y y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2))
1.0ms	y	@	0	((* (+ y x) (* -2 y)) (* y -2) (* (+ y x) (* -2 y)) (+ y y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2))
1.0ms	x	@	-inf	((* (+ y x) (* -2 y)) (* y -2) (* (+ y x) (* -2 y)) (+ y y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2))
1.0ms	x	@	inf	((* (+ y x) (* -2 y)) (* y -2) (* (+ y x) (* -2 y)) (+ y y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2))

simplify123.0ms (3.3%)

Memory

-15.3MiB live, 142.6MiB allocated

Algorithm

1×	egg-herbie

Rules

5 678×	`lower-fma.f64`
5 678×	`lower-fma.f32`
3 568×	`lower-*.f64`
3 568×	`lower-*.f32`
1 554×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	868
1	167	868
2	392	868
3	862	868
4	1625	868
5	3521	868
6	6460	868
0	8557	832

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

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

rewrite65.0ms (1.7%)

Memory

-4.8MiB live, 72.9MiB allocated

Rules

304×	`lower-/.f32`
302×	`lower-/.f64`
300×	`lower-*.f32`
298×	`lower-*.f64`
210×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	62
0	23	62
1	90	62
0	663	62

Stop Event

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

Counts

8 → 129

Calls

Call 1

Inputs
#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
(*.f64 y #s(literal -2 binary64))
#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
(+.f64 y y)
#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
(/.f64 #s(literal 1/2 binary64) y)
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))

Outputs
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval45.0ms (1.2%)

Memory: 22.1MiB live, 59.8MiB allocated
Compiler: Compiled 2 573 to 263 computations (89.8% saved)

prune17.0ms (0.5%)

Memory

-2.4MiB live, 38.0MiB allocated

Pruning

10 alts after pruning (0 fresh and 10 done)

	Pruned	Kept	Total
New	333	0	333
Fresh	0	0	0
Picked	0	4	4
Done	0	6	6
Total	333	10	343

Accuracy

100.0%

Counts

343 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	34.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	44.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	57.6%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
✓	3.6%	#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
✓	3.1%	#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
✓	1.7%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
✓	3.0%	#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
✓	3.6%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))

Compiler

Compiled 139 to 92 computations (33.8% saved)

regimes18.0ms (0.5%)

Memory

0.7MiB live, 38.9MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Calls

3 calls:

7.0ms	y
5.0ms	x
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

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

Compiler

Compiled 9 to 9 computations (0% saved)

regimes16.0ms (0.4%)

Memory

-8.3MiB live, 29.5MiB allocated

Counts

13 → 3

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Outputs

#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Calls

3 calls:

6.0ms	y
4.0ms	x
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
79.8%	3	`x`
76.6%	3	`y`
99.1%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes5.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

12 → 3

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))

Outputs

#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))

#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
98.9%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes36.0ms (1%)

Memory

-11.9MiB live, 25.7MiB allocated

Accuracy

Total -36.3b remaining (-133.8%)

Threshold costs -36.3b (-133.8%)

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
#s(approx (* (+ y x) (* -2 y)) (*.f64 y #s(literal -2 binary64)))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))

Outputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Calls

3 calls:

27.0ms	y
4.0ms	x
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
57.6%	1	`y`
57.6%	1	`x`
57.6%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5000032514086733	205219913697139620.0
0.0ms	-11.398779364670814	0.5

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5000032514086733	205219913697139620.0
0.0ms	-11.398779364670814	0.5

Compiler

Compiled 10 to 10 computations (0% saved)

simplify53.0ms (1.4%)

Memory

-7.5MiB live, 45.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	133
1	33	133

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -10 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -10 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Outputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -10 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal -10 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -10 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
(if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal -10 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

soundness520.0ms (14%)

Memory

37.1MiB live, 225.3MiB allocated

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 672×	`lower-*.f64`
2 672×	`lower-*.f32`
1 728×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	95	240
2	195	240
3	532	240
4	2484	240
5	4892	240
6	6155	240
7	7112	240
8	7634	240
0	8014	222
0	19	78
0	29	77
1	119	77
0	823	77

Stop Event

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

Compiler

Compiled 102 to 54 computations (47.1% saved)

preprocess106.0ms (2.8%)

Memory: -8.9MiB live, 116.9MiB allocated
Compiler: Compiled 182 to 70 computations (61.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze11.0ms (0.3%)

sample707.0ms (19%)

explain167.0ms (4.5%)

preprocess192.0ms (5.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize14.0ms (0.4%)

series6.0ms (0.2%)

simplify125.0ms (3.4%)

rewrite45.0ms (1.2%)

eval23.0ms (0.6%)

prune6.0ms (0.2%)

simplify122.0ms (3.3%)

localize106.0ms (2.9%)

series18.0ms (0.5%)

simplify142.0ms (3.8%)

rewrite140.0ms (3.8%)

eval150.0ms (4%)

prune21.0ms (0.6%)

simplify143.0ms (3.8%)

localize194.0ms (5.2%)

series20.0ms (0.5%)

simplify111.0ms (3%)

rewrite51.0ms (1.4%)

eval78.0ms (2.1%)

prune18.0ms (0.5%)

simplify6.0ms (0.2%)

localize80.0ms (2.1%)

series9.0ms (0.2%)

simplify123.0ms (3.3%)

rewrite65.0ms (1.7%)

eval45.0ms (1.2%)

prune17.0ms (0.5%)

regimes18.0ms (0.5%)

regimes16.0ms (0.4%)

regimes5.0ms (0.1%)

regimes36.0ms (1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify53.0ms (1.4%)

soundness520.0ms (14%)

preprocess106.0ms (2.8%)

end0.0ms (0%)

Profiling