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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze10.0ms (0.3%)

Memory

20.9MiB live, 20.9MiB 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)

sample592.0ms (18.5%)

Memory

-44.2MiB live, 979.3MiB allocated

Samples

356.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 172.0ms

ival-add: 102.0ms (59.4% of total)

ival-div: 61.0ms (35.6% of total)

ival-true: 6.0ms (3.5% of total)

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

Bogosity

explain64.0ms (2%)

Memory

28.0MiB live, 72.9MiB 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

38.0ms

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 (55.1% of total)

ival-div: 4.0ms (44.1% of total)

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

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

preprocess150.0ms (4.7%)

Memory

-33.1MiB live, 45.5MiB 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

2.0MiB live, 2.0MiB 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

11.3MiB live, 11.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y y)
accuracy	0	(+.f64 x y)
accuracy	0.015625	(/.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 (45.1% of total)

ival-add: 2.0ms (45.1% of total)

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

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

series6.0ms (0.2%)

Memory

5.5MiB live, 5.5MiB 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	@	-inf	((+ x y) (+ y y) (/ (+ x y) (+ y y)))
1.0ms	y	@	0	((+ x y) (+ y y) (/ (+ x y) (+ y y)))
1.0ms	x	@	inf	((+ x y) (+ y y) (/ (+ x y) (+ y y)))

simplify157.0ms (4.9%)

Memory

-12.8MiB live, 67.1MiB 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 (1.4%)

Memory

24.4MiB live, 24.4MiB 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
(.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (hypot.f64 x y) (.f64 y x))))
(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (-.f64 y x))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (hypot.f64 x y) (*.f64 y x))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 (+.f64 y x) (-.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (hypot.f64 x y) (*.f64 y x)) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 y y (-.f64 (.f64 x x) (.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (hypot.f64 x y) (*.f64 y x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(+.f64 y x)
(+.f64 x y)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 y #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y #s(literal 0 binary64)))
(neg.f64 (*.f64 #s(literal -2 binary64) y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -2 binary64) y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
(*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 (+.f64 y x) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
(.f64 (.f64 #s(literal -2 binary64) y) (+.f64 y x))
(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))) #s(literal -1 binary64))
(/.f64 (/.f64 (+.f64 y x) #s(literal 2 binary64)) y)
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (*.f64 #s(literal -2 binary64) y)) (-.f64 x y))
(/.f64 (.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -2 binary64) y)) (-.f64 (hypot.f64 x y) (*.f64 y x)))
(/.f64 (.f64 (+.f64 y x) #s(literal 1 binary64)) (.f64 #s(literal -2 binary64) y))
(/.f64 (neg.f64 (neg.f64 (+.f64 y x))) (*.f64 #s(literal -2 binary64) y))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (.f64 (-.f64 x y) (.f64 #s(literal -2 binary64) y)))
(/.f64 (.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (hypot.f64 x y) (.f64 y x)) (.f64 #s(literal -2 binary64) y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x)))))
(/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (*.f64 #s(literal -2 binary64) y) (-.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (.f64 #s(literal -2 binary64) y) (-.f64 (hypot.f64 x y) (*.f64 y x))))
(/.f64 (neg.f64 (+.f64 y x)) (*.f64 #s(literal -2 binary64) y))
(/.f64 (+.f64 y x) (*.f64 #s(literal -2 binary64) y))
(neg.f64 (*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))

eval35.0ms (1.1%)

Memory: -23.7MiB live, 14.9MiB allocated
Compiler: Compiled 1 126 to 173 computations (84.6% saved)

prune6.0ms (0.2%)

Memory

10.2MiB live, 10.2MiB 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
▶	1.2%	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
▶	4.2%	(.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)))
▶	47.3%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
▶	53.4%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 60 to 58 computations (3.3% saved)

simplify120.0ms (3.7%)

Memory

10.7MiB live, 49.9MiB 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`
824×	`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	3057	93
8	3623	93
9	3721	93
10	3782	93
11	3815	93
12	3815	93
13	3815	93
0	3815	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

localize76.0ms (2.4%)

Memory

-24.4MiB live, 56.9MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.22265625	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	33.58502847124335	#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	0.01171875	(.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	0.01171875	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
accuracy	29.82244769419187	#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

64.0ms

256×

valid

Compiler

Compiled 85 to 19 computations (77.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-add: 25.0ms (53.3% of total)

ival-mult: 11.0ms (23.5% of total)

ival-div: 5.0ms (10.7% of total)

ival-neg: 5.0ms (10.7% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.6%)

Memory

18.2MiB live, 18.2MiB 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>) () ())) ())
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#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 (* 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 (+ (* -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 (+ (* -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 (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (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 (* 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 (* 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 (* 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 (* x (- (* -1 (/ y x)) 1)) (taylor inf x) (#s(alt (neg.f64 (+.f64 y x)) (patch (neg.f64 (+.f64 y x)) #<representation:binary64>) () ())) ())
#s(alt (* x (- (* -1 (/ y x)) 1)) (taylor inf x) (#s(alt (neg.f64 (+.f64 y x)) (patch (neg.f64 (+.f64 y x)) #<representation:binary64>) () ())) ())
#s(alt (* x (- (* -1 (/ y x)) 1)) (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>) () ())) ())
#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	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))
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))

simplify162.0ms (5.1%)

Memory

2.1MiB live, 115.0MiB 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)
(/.f64 x y)
(* 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))
(* -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)
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)
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 y x))
(* y (+ (* 2 x) (* 2 y)))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* y (+ (* 2 x) (* 2 y)))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* y (+ (* 2 x) (* 2 y)))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 x)
(neg.f64 x)
(- (* -1 y) x)
(-.f64 (neg.f64 y) x)
(- (* -1 y) x)
(-.f64 (neg.f64 y) x)
(- (* -1 y) x)
(-.f64 (neg.f64 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 #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 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 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 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x 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)
(/.f64 x y)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #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)
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)
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 y)
(neg.f64 y)
(* y (- (* -1 (/ x y)) 1))
(-.f64 (neg.f64 y) x)
(* y (- (* -1 (/ x y)) 1))
(-.f64 (neg.f64 y) x)
(* y (- (* -1 (/ x y)) 1))
(-.f64 (neg.f64 y) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x 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)
(/ 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 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x 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)
(/.f64 x y)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #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)
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)
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (/ x y))))
(-.f64 (neg.f64 y) x)
(* -1 (* y (+ 1 (/ x y))))
(-.f64 (neg.f64 y) x)
(* -1 (* y (+ 1 (/ x y))))
(-.f64 (neg.f64 y) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x 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)
(/ 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 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x 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)
(/.f64 x y)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #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)
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 y)
(neg.f64 y)
(- (* -1 x) y)
(-.f64 (neg.f64 y) x)
(- (* -1 x) y)
(-.f64 (neg.f64 y) x)
(- (* -1 x) y)
(-.f64 (neg.f64 y) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (/ x 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)
(* 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)
(* 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))
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x 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 #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))
(* -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)
x
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 y x))
(* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 x)
(neg.f64 x)
(* x (- (* -1 (/ y x)) 1))
(-.f64 (neg.f64 y) x)
(* x (- (* -1 (/ y x)) 1))
(-.f64 (neg.f64 y) x)
(* x (- (* -1 (/ y x)) 1))
(-.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)
(* 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)
(* x (+ (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(* x (+ (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(* x (+ (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))))
(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)
(/.f64 x 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 #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))
(* -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)
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)
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 y x))
(* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 y x)) y)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (/ y x))))
(-.f64 (neg.f64 y) x)
(* -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)

rewrite93.0ms (2.9%)

Memory

14.5MiB live, 59.6MiB 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
#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal 1/2 binary64))
(.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (/.f64 x y) #s(literal 1/4 binary64)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 x y))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (/.f64 x y) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (/.f64 x y) #s(literal 1/4 binary64))) (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))))
(/.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) (.f64 (/.f64 x y) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (/.f64 x y) #s(literal 1/4 binary64))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal 2 binary64) y) #s(literal 1/2 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal -1/2 binary64))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y)))
(*.f64 (pow.f64 y #s(literal -1 binary64)) x)
(*.f64 #s(literal 1 binary64) (/.f64 x y))
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 x (pow.f64 y #s(literal -1 binary64)))
(pow.f64 (/.f64 y x) #s(literal -1 binary64))
(/.f64 (*.f64 x #s(literal 1 binary64)) y)
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 y x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 y x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y x))
(/.f64 (neg.f64 x) (neg.f64 y))
(/.f64 x y)
(neg.f64 (/.f64 (neg.f64 x) y))
(neg.f64 (/.f64 x (neg.f64 y)))
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 (+.f64 y x) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 (.f64 (neg.f64 (+.f64 y x)) y) #s(literal -2 binary64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) y) #s(literal -1 binary64)) (+.f64 y x))
(.f64 (.f64 (+.f64 y x) y) #s(literal -2 binary64))
(.f64 (.f64 (neg.f64 (+.f64 y x)) #s(literal -2 binary64)) y)
(.f64 (.f64 #s(literal -2 binary64) (+.f64 y x)) (neg.f64 y))
(.f64 (.f64 #s(literal -2 binary64) (+.f64 y x)) y)
(.f64 #s(literal -1 binary64) (.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) y) (neg.f64 (+.f64 y x)))
(.f64 (.f64 #s(literal 2 binary64) y) (+.f64 y x))
(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal 2 binary64) y))
(.f64 #s(literal -2 binary64) (.f64 y (neg.f64 (+.f64 y x))))
(.f64 #s(literal -2 binary64) (.f64 y (+.f64 y x)))
(.f64 (+.f64 y x) (.f64 #s(literal 2 binary64) y))
(.f64 y (.f64 (neg.f64 (+.f64 y x)) #s(literal -2 binary64)))
(.f64 y (.f64 #s(literal -2 binary64) (+.f64 y x)))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))) #s(literal -1 binary64))
(/.f64 (/.f64 (+.f64 y x) #s(literal 2 binary64)) y)
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) (*.f64 #s(literal 2 binary64) y)) (-.f64 y x))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (*.f64 #s(literal 2 binary64) y)) (-.f64 x y))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (.f64 #s(literal 2 binary64) y)) (-.f64 (hypot.f64 y x) (*.f64 y x)))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (.f64 #s(literal 2 binary64) y)) (-.f64 (hypot.f64 x y) (*.f64 y x)))
(/.f64 (.f64 (+.f64 y x) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) y))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (*.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (*.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (-.f64 (hypot.f64 y x) (*.f64 y x)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) y) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (-.f64 (hypot.f64 x y) (*.f64 y x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 y x))) (*.f64 #s(literal 2 binary64) y))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1 binary64)) (.f64 (-.f64 y x) (.f64 #s(literal 2 binary64) y)))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (.f64 (-.f64 x y) (.f64 #s(literal 2 binary64) y)))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (.f64 #s(literal 2 binary64) y)))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (hypot.f64 x y) (.f64 y x)) (.f64 #s(literal 2 binary64) y)))
(/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (.f64 (*.f64 #s(literal 2 binary64) y) (-.f64 y x)))
(/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (*.f64 #s(literal 2 binary64) y) (-.f64 x y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 y (+.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (.f64 (.f64 #s(literal 2 binary64) y) (-.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (.f64 (.f64 #s(literal 2 binary64) y) (-.f64 (hypot.f64 x y) (*.f64 y x))))
(/.f64 (neg.f64 (+.f64 y x)) (*.f64 #s(literal 2 binary64) y))
(/.f64 (+.f64 y x) (*.f64 #s(literal 2 binary64) y))
(neg.f64 (*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 y #s(literal -1 binary64)) (.f64 y (*.f64 #s(literal 2 binary64) y)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 y #s(literal -1 binary64)) (.f64 (*.f64 #s(literal 2 binary64) y) y))
(fma.f64 (.f64 #s(literal 2 binary64) y) (neg.f64 y) (.f64 (*.f64 #s(literal 2 binary64) y) (neg.f64 x)))
(fma.f64 (.f64 #s(literal 2 binary64) y) y (.f64 #s(literal 1/2 binary64) (/.f64 x y)))
(fma.f64 (.f64 #s(literal 2 binary64) y) x (.f64 y (*.f64 #s(literal 2 binary64) y)))
(fma.f64 (.f64 #s(literal 2 binary64) y) x (.f64 (*.f64 #s(literal 2 binary64) y) y))
(fma.f64 (neg.f64 y) (.f64 #s(literal 2 binary64) y) (.f64 (neg.f64 x) (*.f64 #s(literal 2 binary64) y)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) (.f64 y (.f64 #s(literal 2 binary64) y)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) (.f64 (.f64 #s(literal 2 binary64) y) y))
(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) (.f64 y (.f64 #s(literal 2 binary64) y)))
(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 2 binary64) y) y))
(fma.f64 y (.f64 #s(literal 2 binary64) y) (.f64 #s(literal 1/2 binary64) (/.f64 x y)))
(fma.f64 x (.f64 #s(literal 2 binary64) y) (.f64 y (*.f64 #s(literal 2 binary64) y)))
(fma.f64 x (.f64 #s(literal 2 binary64) y) (.f64 (*.f64 #s(literal 2 binary64) y) y))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 (neg.f64 y) (.f64 #s(literal 2 binary64) y)) (.f64 (neg.f64 x) (.f64 #s(literal 2 binary64) y)))
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(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)

eval158.0ms (4.9%)

Memory: -15.3MiB live, 175.5MiB allocated
Compiler: Compiled 6 438 to 698 computations (89.2% saved)

prune50.0ms (1.6%)

Memory

-5.7MiB live, 72.4MiB allocated

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	644	6	650
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	647	8	655

Accuracy

100.0%

Counts

655 → 8

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)))
	26.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
▶	47.5%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
▶	3.6%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	53.4%	#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)))
▶	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
▶	3.6%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 #s(literal 2 binary64) (.f64 y x)))

Compiler

Compiled 83 to 82 computations (1.2% saved)

simplify115.0ms (3.6%)

Memory

-1.4MiB live, 84.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	-5952	(.f64 (.f64 y y) #s(literal -2 binary64))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
cost-diff	-5824	(.f64 (.f64 y y) #s(literal 2 binary64))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
cost-diff	0	(*.f64 y x)
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 y x))
cost-diff	0	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 #s(literal 2 binary64) (.f64 y x)))
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

2 032×	`lower-fma.f64`
2 032×	`lower-fma.f32`
840×	`lower-*.f32`
826×	`lower-*.f64`
826×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	119
0	36	119
1	66	119
2	133	117
3	318	117
4	507	117
5	720	117
6	1382	117
7	2987	117
8	3411	117
9	3513	117
10	3586	117
11	3619	117
12	3619	117
13	3619	117
0	3619	109

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

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 #s(literal 2 binary64) (.f64 y x)))
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y x) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 y x))
(.f64 (.f64 y x) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 y x)
y
x
#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(approx (* (neg (+ y x)) (* -2 y)) (hypot.f64 y y))
(.f64 (.f64 y y) #s(literal 2 binary64))
(hypot.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)))
#s(approx (* (+ y x) (* -2 y)) (neg.f64 (hypot.f64 y y)))
(.f64 (.f64 y y) #s(literal -2 binary64))
(neg.f64 (hypot.f64 y y))
(*.f64 y y)
y
#s(literal -2 binary64)

localize72.0ms (2.3%)

Memory

18.1MiB live, 96.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.0078125	(.f64 (.f64 y y) #s(literal -2 binary64))
accuracy	24.494612181720402	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0.0078125	(.f64 (.f64 y y) #s(literal 2 binary64))
accuracy	24.494612181720402	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
accuracy	0	(*.f64 y x)
accuracy	0.0078125	(.f64 #s(literal 2 binary64) (.f64 y x))
accuracy	30.679355675443354	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 #s(literal 2 binary64) (.f64 y x)))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 (+.f64 y y) x)
accuracy	61.71754627315845	#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	33.58502847124335	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Samples

59.0ms

256×

valid

Compiler

Compiled 91 to 23 computations (74.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 14.0ms (49.5% of total)

ival-add: 9.0ms (31.8% of total)

ival-div: 3.0ms (10.6% of total)

ival-neg: 1.0ms (3.5% of total)

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

exact: 0.0ms (0% of total)

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

series34.0ms (1.1%)

Memory

8.6MiB live, 50.2MiB allocated

Counts

14 → 276

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	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)) (* 2 (* y x)) (* y x) (* (neg (+ y x)) (* -2 y)) (* y y) (* (* y y) 2) (* (+ y x) (* -2 y)) (* (* y y) -2))
9.0ms	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)) (* 2 (* y x)) (* y x) (* (neg (+ y x)) (* -2 y)) (* y y) (* (* y y) 2) (* (+ y x) (* -2 y)) (* (* y y) -2))
4.0ms	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)) (* 2 (* y x)) (* y x) (* (neg (+ y x)) (* -2 y)) (* y y) (* (* y y) 2) (* (+ y x) (* -2 y)) (* (* y y) -2))
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)) (* 2 (* y x)) (* y x) (* (neg (+ y x)) (* -2 y)) (* y y) (* (* y y) 2) (* (+ y x) (* -2 y)) (* (* y y) -2))
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)) (* 2 (* y x)) (* y x) (* (neg (+ y x)) (* -2 y)) (* y y) (* (* y y) 2) (* (+ y x) (* -2 y)) (* (* y y) -2))

simplify174.0ms (5.4%)

Memory

-5.7MiB live, 194.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4 094×	`lower-fma.f64`
4 094×	`lower-fma.f32`
2 510×	`lower-*.f64`
2 510×	`lower-*.f32`
1 900×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	1416
1	155	1416
2	372	1416
3	804	1416
4	2273	1416
5	3794	1416
6	5579	1416
7	6674	1416
8	7844	1416
0	8179	1380

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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

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

rewrite99.0ms (3.1%)

Memory

-17.9MiB live, 104.0MiB allocated

Rules

340×	`lower-*.f32`
326×	`lower-*.f64`
304×	`lower-/.f32`
302×	`lower-/.f64`
182×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	104
0	36	104
1	109	102
0	647	102

Stop Event

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

Counts

14 → 146

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

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

eval67.0ms (2.1%)

Memory: -2.9MiB live, 112.5MiB allocated
Compiler: Compiled 3 168 to 299 computations (90.6% saved)

prune31.0ms (1%)

Memory

14.0MiB live, 57.2MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	438	0	438
Fresh	0	1	1
Picked	0	5	5
Done	0	2	2
Total	438	8	446

Accuracy

100.0%

Counts

446 → 8

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)))
▶	26.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
✓	47.5%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	3.6%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	53.4%	#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)))
✓	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
✓	3.6%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 #s(literal 2 binary64) (.f64 y x)))

Compiler

Compiled 46 to 46 computations (0% saved)

simplify6.0ms (0.2%)

Memory

-24.7MiB live, 14.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

cost-diff

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

cost-diff

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

cost-diff

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

Rules

24×	`lower-fma.f32`
24×	`lower-*.f32`
22×	`lower-*.f64`
22×	`lower-fma.f64`
22×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
0	13	27
1	20	27
2	33	27
3	41	27
4	43	27
0	43	27

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#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)) (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)

localize35.0ms (1.1%)

Memory

9.9MiB live, 49.1MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

accuracy

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

accuracy

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

accuracy

46.818554215395174

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

Samples

15.0ms

256×

valid

Compiler

Compiled 23 to 12 computations (47.8% saved)

Precisions

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

ival-add: 3.0ms (34.8% of total)

ival-mult: 3.0ms (34.8% of total)

ival-div: 2.0ms (23.2% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.2%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs

#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)) (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 (/ (+ (* 1/2 x) (* 1/2 y)) y) (taylor 0 y) (#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 (/ (+ (* 1/2 x) (* 1/2 y)) y) (taylor 0 y) (#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 (/ (+ (* 1/2 x) (* 1/2 y)) y) (taylor 0 y) (#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 1/2 (taylor 0 y) (#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 (* 2 (* x y))) (taylor 0 y) (#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 (* 2 (* x y))) (taylor 0 y) (#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 (* 2 (* x y))) (taylor 0 y) (#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 (* 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 1/2 (taylor inf y) (#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 (+ 1/2 (* 1/2 (/ x y))) (taylor inf y) (#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 (+ 1/2 (* 1/2 (/ x y))) (taylor inf y) (#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 (+ 1/2 (* 1/2 (/ x y))) (taylor inf y) (#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 y) (#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 (* y (+ (* 2 x) (* 1/2 (/ 1 y)))) (taylor inf y) (#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 (* y (+ (* 2 x) (* 1/2 (/ 1 y)))) (taylor inf y) (#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 (* y (+ (* 2 x) (* 1/2 (/ 1 y)))) (taylor inf y) (#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 (* 2 y) (taylor inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt 1/2 (taylor -inf y) (#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 (+ 1/2 (* 1/2 (/ x y))) (taylor -inf y) (#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 (+ 1/2 (* 1/2 (/ x y))) (taylor -inf y) (#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 (+ 1/2 (* 1/2 (/ x y))) (taylor -inf y) (#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 y) (#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 (* y (- (* -2 x) (* 1/2 (/ 1 y))))) (taylor -inf y) (#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 (* y (- (* -2 x) (* 1/2 (/ 1 y))))) (taylor -inf y) (#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 (* y (- (* -2 x) (* 1/2 (/ 1 y))))) (taylor -inf y) (#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 (* 2 y) (taylor -inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt 1/2 (taylor 0 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 (+ 1/2 (* 1/2 (/ x y))) (taylor 0 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 (+ 1/2 (* 1/2 (/ x y))) (taylor 0 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 (+ 1/2 (* 1/2 (/ x y))) (taylor 0 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 1/2 (taylor 0 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 (* 2 (* x y))) (taylor 0 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 (* 2 (* x y))) (taylor 0 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 (* 2 (* x y))) (taylor 0 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)) (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)) (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
1.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
1.0ms	y	@	inf	((/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
1.0ms	y	@	0	((/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
0.0ms	x	@	inf	((/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))
0.0ms	x	@	-inf	((/ (+ x y) (+ y y)) (+ (* (* 2 y) x) 1/2) (* 2 y))

simplify82.0ms (2.5%)

Memory

1.0MiB live, 82.2MiB allocated

Algorithm

1×	egg-herbie

Rules

1 248×	`lower-fma.f64`
1 248×	`lower-fma.f32`
768×	`lower-*.f64`
768×	`lower-*.f32`
484×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	328
1	104	328
2	219	328
3	519	328
4	713	328
5	1257	328
6	2292	328
7	2860	328
8	2894	328
9	2898	328
10	2898	328
0	2898	292

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

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

rewrite70.0ms (2.2%)

Memory

-2.9MiB live, 76.3MiB allocated

Rules

244×	`lower-*.f32`
242×	`lower-*.f64`
216×	`lower-/.f64`
216×	`lower-/.f32`
192×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
0	13	23
1	62	23
0	485	23

Stop Event

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

Counts

3 → 49

Calls

Call 1

Inputs

#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
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal -2 binary64) y) x #s(literal 1/2 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) #s(literal 2 binary64) #s(literal -1/2 binary64))))
(.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal -2 binary64) y) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (fma.f64 (*.f64 y x) #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (*.f64 y x) #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 y x) #s(literal 2 binary64) #s(literal -1/2 binary64)) (-.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 1/2 binary64))) (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 1/2 binary64))))
(fma.f64 (*.f64 x #s(literal 2 binary64)) y #s(literal 1/2 binary64))
(fma.f64 (*.f64 y x) #s(literal 2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal -2 binary64) y) x #s(literal 1/2 binary64))
(fma.f64 y (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal -2 binary64) y) #s(literal 1/2 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 2 binary64)) (fma.f64 (.f64 y x) #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 y x) #s(literal 2 binary64) #s(literal -1/2 binary64))))
(+.f64 (.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal -2 binary64) y) x))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(*.f64 (neg.f64 y) #s(literal 2 binary64))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) y))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal -2 binary64))
(*.f64 y #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 1/2 binary64) y)
(neg.f64 (*.f64 #s(literal -2 binary64) y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -2 binary64) y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)

eval28.0ms (0.9%)

Memory: -7.3MiB live, 31.6MiB allocated
Compiler: Compiled 1 043 to 192 computations (81.6% saved)

prune24.0ms (0.7%)

Memory

-3.3MiB live, 47.2MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	0	0
Picked	1	0	1
Done	0	7	7
Total	109	8	117

Accuracy

100.0%

Counts

117 → 8

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)))
	26.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	47.5%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	3.6%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	53.4%	#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)))
✓	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
✓	3.6%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 #s(literal 2 binary64) (.f64 y x)))

Compiler

Compiled 127 to 83 computations (34.6% saved)

regimes22.0ms (0.7%)

Memory

-2.6MiB live, 37.0MiB allocated

Counts

13 → 1

Calls

Call 1

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

12.0ms	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)

regimes13.0ms (0.4%)

Memory

3.4MiB live, 42.7MiB allocated

Counts

11 → 3

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
75.9%	3	`x`
78.1%	3	`y`
97.6%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes4.0ms (0.1%)

Memory

14.6MiB live, 14.5MiB allocated

Counts

10 → 3

Calls

Call 1

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

3.0ms

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

Results

Accuracy	Segments	Branch
97.4%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes13.0ms (0.4%)

Memory

-33.7MiB live, 45.7MiB allocated

Accuracy

Total -33.5b remaining (-112.3%)

Threshold costs -33.5b (-112.3%)

Counts

9 → 1

Calls

Call 1

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

4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
53.4%	1	`x`
53.4%	1	`y`
53.4%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5008083080336599	32466.618888340636
0.0ms	-520.8345753526751	0.49997798218789097

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5008083080336599	32466.618888340636
0.0ms	-520.8345753526751	0.49997798218789097

Compiler

Compiled 10 to 10 computations (0% saved)

simplify28.0ms (0.9%)

Memory

4.8MiB live, 82.8MiB 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 -500 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 -500 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 -500 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 -500 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 -500 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 -500 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))

soundness482.0ms (15.1%)

Memory

-1.2MiB live, 272.5MiB 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×	fuel
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)

preprocess37.0ms (1.2%)

Memory: 16.9MiB live, 92.7MiB allocated
Compiler: Compiled 182 to 70 computations (61.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze10.0ms (0.3%)

sample592.0ms (18.5%)

explain64.0ms (2%)

preprocess150.0ms (4.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize14.0ms (0.4%)

series6.0ms (0.2%)

simplify157.0ms (4.9%)

rewrite45.0ms (1.4%)

eval35.0ms (1.1%)

prune6.0ms (0.2%)

simplify120.0ms (3.7%)

localize76.0ms (2.4%)

series18.0ms (0.6%)

simplify162.0ms (5.1%)

rewrite93.0ms (2.9%)

eval158.0ms (4.9%)

prune50.0ms (1.6%)

simplify115.0ms (3.6%)

localize72.0ms (2.3%)

series34.0ms (1.1%)

simplify174.0ms (5.4%)

rewrite99.0ms (3.1%)

eval67.0ms (2.1%)

prune31.0ms (1%)

simplify6.0ms (0.2%)

localize35.0ms (1.1%)

series5.0ms (0.2%)

simplify82.0ms (2.5%)

rewrite70.0ms (2.2%)

eval28.0ms (0.9%)

prune24.0ms (0.7%)

regimes22.0ms (0.7%)

regimes13.0ms (0.4%)

regimes4.0ms (0.1%)

regimes13.0ms (0.4%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify28.0ms (0.9%)

soundness482.0ms (15.1%)

preprocess37.0ms (1.2%)

end0.0ms (0%)

Profiling