Metrics for Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, G

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 9 computations (0% saved)

sample665.0ms (16.4%)

Memory

43.4MiB live, 795.2MiB allocated

Samples

416.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 226.0ms

ival-div: 100.0ms (44.2% of total)

ival-add: 58.0ms (25.6% of total)

ival-mult: 52.0ms (23% of total)

exact: 7.0ms (3.1% of total)

ival-true: 6.0ms (2.7% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

preprocess29.0ms (0.7%)

Memory

-2.2MiB live, 35.8MiB allocated

Algorithm

1×	egg-herbie

Rules

56×	`sub-neg`
54×	`distribute-lft-neg-in`
50×	`associate--r+`
46×	`distribute-lft-in`
42×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	56	25
2	170	25
3	283	25
4	388	25
5	445	25
6	456	25
0	7	5
0	11	5
1	21	5
2	23	5
0	23	5

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

explain111.0ms (2.7%)

Memory

-23.7MiB live, 102.3MiB allocated

FPErrors

Click to see full error table

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

76.0ms

512×

valid

Compiler

Compiled 56 to 32 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-div: 3.0ms (27.8% of total)

ival-add: 3.0ms (27.8% of total)

ival-mult: 3.0ms (27.8% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify5.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))

Rules

12×	`lower-*.f32`
10×	`lower-*.f64`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
8×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
0	11	13
1	21	13
2	23	13
0	23	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize26.0ms (0.6%)

Memory

-7.5MiB live, 30.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

Samples

19.0ms

256×

valid

Compiler

Compiled 19 to 9 computations (52.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (38.6% of total)

ival-mult: 2.0ms (38.6% of total)

ival-add: 1.0ms (19.3% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

3 → 48

Calls

Call 1

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

Inputs

#s(alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())

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

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

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

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* (/ 1 2) (+ x y))
0.0ms	x	@	-inf	(* (/ 1 2) (+ x y))
0.0ms	y	@	inf	(* (/ 1 2) (+ x y))
0.0ms	y	@	0	(* (/ 1 2) (+ x y))
0.0ms	x	@	0	(* (/ 1 2) (+ x y))

simplify528.0ms (13%)

Memory

24.3MiB live, 338.7MiB allocated

Algorithm

1×	egg-herbie

Rules

17 664×	`lower-fma.f64`
17 664×	`lower-fma.f32`
2 856×	`lower-+.f64`
2 856×	`lower-+.f32`
2 768×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	168
1	115	168
2	264	168
3	783	168
4	1834	168
5	2668	168
6	3340	168
7	3639	168
8	3801	168
9	3837	168
10	6026	168
0	8686	168

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

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

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

rewrite749.0ms (18.4%)

Memory

-7.9MiB live, 468.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 694×	`lower-fma.f64`
8 694×	`lower-fma.f32`
4 456×	`lower-/.f64`
4 456×	`lower-/.f32`
3 962×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
0	11	9
1	34	9
2	182	9
3	1529	9
0	8403	9

Stop Event

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

Counts

3 → 254

Calls

Call 1

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

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

eval39.0ms (1%)

Memory: 13.6MiB live, 51.4MiB allocated
Compiler: Compiled 8 483 to 791 computations (90.7% saved)

prune117.0ms (2.9%)

Memory

-23.1MiB live, 99.6MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	293	3	296
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	294	3	297

Accuracy

100.0%

Counts

297 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
▶	52.9%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
▶	48.0%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 x y)
✓	cost-diff	(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Rules

12×	`lower-*.f32`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
8×	`lower-+.f32`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
0	18	39
1	25	39
2	26	39
0	26	39

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize70.0ms (1.7%)

Memory

7.9MiB live, 47.5MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) y)
✓	accuracy	52.9%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	48.0%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Samples

18.0ms

256×

valid

Compiler

Compiled 37 to 13 computations (64.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (59.8% of total)

ival-div: 2.0ms (19.9% of total)

ival-add: 1.0ms (10% of total)

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

exact: 0.0ms (0% of total)

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

series49.0ms (1.2%)

Memory

-22.1MiB live, 27.9MiB allocated

Counts

6 → 120

Calls

Call 1

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

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

Calls

30 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* 1/2 x)
0.0ms	x	@	inf	(* 1/2 x)
0.0ms	x	@	0	(* 1/2 x)
0.0ms	y	@	inf	(* 1/2 y)
0.0ms	y	@	-inf	(* 1/2 y)

simplify483.0ms (11.9%)

Memory

-9.8MiB live, 419.7MiB allocated

Algorithm

1×	egg-herbie

Rules

17 664×	`lower-fma.f64`
17 664×	`lower-fma.f32`
2 856×	`lower-+.f64`
2 856×	`lower-+.f32`
2 768×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	456
1	115	456
2	264	456
3	783	456
4	1834	456
5	2668	456
6	3340	456
7	3639	456
8	3801	456
9	3837	456
10	6026	456
0	8686	456

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 114

Calls

Call 1

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

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

rewrite388.0ms (9.6%)

Memory

2.3MiB live, 570.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 694×	`lower-fma.f64`
8 694×	`lower-fma.f32`
4 456×	`lower-/.f64`
4 456×	`lower-/.f32`
3 962×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
0	18	32
1	38	32
2	167	32
3	1512	32
0	8354	32

Stop Event

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

Counts

6 → 259

Calls

Call 1

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

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

eval43.0ms (1.1%)

Memory: 0.6MiB live, 116.9MiB allocated
Compiler: Compiled 8 512 to 788 computations (90.7% saved)

prune44.0ms (1.1%)

Memory

-5.0MiB live, 111.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	373	0	373
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	373	3	376

Accuracy

100.0%

Counts

376 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
✓	52.9%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
✓	48.0%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 41 to 24 computations (41.5% saved)

regimes9.0ms (0.2%)

Memory

25.6MiB live, 25.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
2.0ms	(+.f64 x y)
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
100.0%	1	`(+.f64 x y)`

Compiler

Compiled 20 to 14 computations (30% saved)

regimes13.0ms (0.3%)

Memory

-21.4MiB live, 25.1MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

4 calls:

7.0ms	y
2.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
2.0ms	x
2.0ms	(+.f64 x y)

Results

Accuracy	Segments	Branch
82.7%	2	`x`
83.9%	2	`y`
97.6%	2	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
97.6%	2	`(+.f64 x y)`

Compiler

Compiled 20 to 14 computations (30% saved)

regimes5.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

1.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
1.0ms	(+.f64 x y)
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
48.0%	1	`x`
48.0%	1	`y`
48.0%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
48.0%	1	`(+.f64 x y)`

Compiler

Compiled 20 to 14 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5508040057160282e-268	4.672008559970556e-303

Compiler

Compiled 12 to 12 computations (0% saved)

simplify9.0ms (0.2%)

Memory

-20.3MiB live, 16.9MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	24	38

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (+.f64 x y) #s(literal -7435084542388915/74350845423889153139903124907495028006563010082969722952788592965797032858020218677258415724807817529489936189509648652522729262277245285389541529055119731289148542022372993697134320491714886843511959789117571860303387435343894004407854947017432904150602255272707195641188267440734208 binary64)) #s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y)))

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

Outputs
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(if (<=.f64 (+.f64 x y) #s(literal -7435084542388915/74350845423889153139903124907495028006563010082969722952788592965797032858020218677258415724807817529489936189509648652522729262277245285389541529055119731289148542022372993697134320491714886843511959789117571860303387435343894004407854947017432904150602255272707195641188267440734208 binary64)) #s(approx (* (/ 1 2) (+ x y)) (.f64 #s(literal 1/2 binary64) x)) #s(approx ( (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y)))
(if (<=.f64 (+.f64 x y) #s(literal -7435084542388915/74350845423889153139903124907495028006563010082969722952788592965797032858020218677258415724807817529489936189509648652522729262277245285389541529055119731289148542022372993697134320491714886843511959789117571860303387435343894004407854947017432904150602255272707195641188267440734208 binary64)) #s(approx (* (/ 1 2) (+ x y)) (.f64 x #s(literal 1/2 binary64))) #s(approx ( (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64))))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))

soundness637.0ms (15.7%)

Memory

8.9MiB live, 285.7MiB allocated

Rules

17 664×	`lower-fma.f64`
17 664×	`lower-fma.f32`
8 694×	`lower-fma.f64`
8 694×	`lower-fma.f32`
4 456×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
0	11	9
1	34	9
2	182	9
3	1529	9
0	8403	9
0	38	168
1	115	168
2	264	168
3	783	168
4	1834	168
5	2668	168
6	3340	168
7	3639	168
8	3801	168
9	3837	168
10	6026	168
0	8686	168

Stop Event

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

Compiler

Compiled 61 to 32 computations (47.5% saved)

preprocess35.0ms (0.9%)

Memory: 12.9MiB live, 90.9MiB allocated
Remove: (sort x y)
Compiler: Compiled 110 to 64 computations (41.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample665.0ms (16.4%)

preprocess29.0ms (0.7%)

explain111.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize26.0ms (0.6%)

series3.0ms (0.1%)

simplify528.0ms (13%)

rewrite749.0ms (18.4%)

eval39.0ms (1%)

prune117.0ms (2.9%)

simplify6.0ms (0.1%)

localize70.0ms (1.7%)

series49.0ms (1.2%)

simplify483.0ms (11.9%)

rewrite388.0ms (9.6%)

eval43.0ms (1.1%)

prune44.0ms (1.1%)

regimes9.0ms (0.2%)

regimes13.0ms (0.3%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

soundness637.0ms (15.7%)

preprocess35.0ms (0.9%)

end0.0ms (0%)

Profiling