Metrics for Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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 8 computations (11.1% saved)

sample685.0ms (16.4%)

Memory

38.5MiB live, 1 144.5MiB allocated

Samples

383.0ms	7 686×	0	valid
21.0ms	270×	1	valid
20.0ms	134×	3	valid
18.0ms	166×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 227.0ms

ival-div: 96.0ms (42.3% of total)

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

ival-add: 44.0ms (19.4% of total)

adjust: 15.0ms (6.6% of total)

ival-true: 6.0ms (2.6% of total)

exact: 5.0ms (2.2% of total)

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

Bogosity

explain85.0ms (2%)

Memory

-8.7MiB live, 142.3MiB allocated

FPErrors

Click to see full error table

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

22.0ms	480×	0	valid
1.0ms	12×	2	valid
1.0ms	14×	1	valid
1.0ms	6×	3	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

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

ival-div: 4.0ms (35.5% of total)

ival-sub: 3.0ms (26.6% of total)

ival-add: 3.0ms (26.6% of total)

adjust: 1.0ms (8.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess56.0ms (1.3%)

Memory

12.0MiB live, 88.2MiB allocated

Algorithm

1×	egg-herbie

Rules

560×	`lower-fma.f64`
560×	`lower-fma.f32`
208×	`lower-*.f64`
208×	`lower-*.f32`
164×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
0	6	7
0	9	7
1	15	7
2	26	7
3	47	7
4	86	7
5	157	7
6	278	7
7	436	7
8	543	7
9	604	7
10	608	7
0	608	6

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify21.0ms (0.5%)

Memory

-15.1MiB live, 24.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x y)
cost-diff	128	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
cost-diff	384	(/.f64 (-.f64 x y) #s(literal 2 binary64))

Rules

560×	`lower-fma.f64`
560×	`lower-fma.f32`
208×	`lower-*.f64`
208×	`lower-*.f32`
128×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	15	18
2	26	18
3	47	18
4	86	18
5	157	18
6	278	18
7	436	18
8	543	18
9	604	18
10	608	18
0	608	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.4%)

Memory

1.5MiB live, 41.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 (-.f64 x y) #s(literal 2 binary64))
accuracy	0	(-.f64 x y)
accuracy	0.078125	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))

Samples

12.0ms	240×	0	valid
1.0ms	6×	2	valid
1.0ms	7×	1	valid
0.0ms	3×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 3.0ms (40.5% of total)

ival-sub: 2.0ms (27% of total)

ival-add: 2.0ms (27% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated

Counts

3 → 72

Calls

Call 1

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

Inputs

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

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

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	((/ (- x y) 2) (+ x (/ (- x y) 2)) (- x y))
1.0ms	x	@	inf	((/ (- x y) 2) (+ x (/ (- x y) 2)) (- x y))
0.0ms	x	@	-inf	((/ (- x y) 2) (+ x (/ (- x y) 2)) (- x y))
0.0ms	y	@	-inf	((/ (- x y) 2) (+ x (/ (- x y) 2)) (- x y))
0.0ms	y	@	0	((/ (- x y) 2) (+ x (/ (- x y) 2)) (- x y))

simplify130.0ms (3.1%)

Memory

-6.2MiB live, 111.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 504×	`lower-fma.f64`
7 504×	`lower-fma.f32`
2 794×	`lower-*.f64`
2 794×	`lower-*.f32`
1 232×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	387
1	176	351
2	487	351
3	1345	315
4	2959	315
5	4565	315
6	6536	315
7	7586	315
0	8072	297

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 69

Calls

Call 1

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

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

rewrite170.0ms (4.1%)

Memory

6.6MiB live, 236.2MiB allocated

Rules

4 050×	`lower-fma.f64`
4 050×	`lower-fma.f32`
3 870×	`lower-*.f64`
3 870×	`lower-*.f32`
2 640×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	48	15
2	400	15
3	5080	15
0	8183	14

Stop Event

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

Counts

3 → 353

Calls

Call 1

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

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

eval68.0ms (1.6%)

Memory: -17.7MiB live, 83.6MiB allocated
Compiler: Compiled 8 964 to 1 111 computations (87.6% saved)

prune91.0ms (2.2%)

Memory

-14.5MiB live, 140.4MiB allocated

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	410	12	422
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	411	12	423

Accuracy

99.9%

Counts

423 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	14.1%	(fma.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (/.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 y x) y (.f64 x x))) x)
	50.1%	(fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) #s(literal 1/2 binary64)) x)
	99.9%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
▶	50.4%	(fma.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) x)
	48.5%	(fma.f64 x (/.f64 x (fma.f64 #s(literal -1/2 binary64) (-.f64 x y) x)) (neg.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (-.f64 x y) x)))))
▶	99.9%	(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))
▶	99.9%	(-.f64 (fma.f64 #s(literal 1/2 binary64) x x) (*.f64 #s(literal 1/2 binary64) y))
	99.8%	(+.f64 x (/.f64 (.f64 (+.f64 y x) (.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 y x)))) #s(literal 2 binary64)))
	99.7%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (-.f64 y x))))
▶	56.0%	(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
	46.8%	#s(approx (+ x (/ (- x y) 2)) (*.f64 y #s(literal -1/2 binary64)))
▶	54.7%	#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

Compiler

Compiled 328 to 176 computations (46.3% saved)

simplify190.0ms (4.5%)

Memory

8.5MiB live, 196.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x y)
cost-diff	0	(+.f64 y x)
cost-diff	0	(*.f64 (+.f64 y x) (-.f64 x y))
cost-diff	1408	(fma.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) x)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	64	(fma.f64 #s(literal 1/2 binary64) x x)
cost-diff	256	(-.f64 (fma.f64 #s(literal 1/2 binary64) x x) (*.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(*.f64 y #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64)))
cost-diff	0	(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
cost-diff	0	(*.f64 #s(literal 3/2 binary64) x)
cost-diff	0	#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))
cost-diff	0	(fma.f64 y #s(literal -1/2 binary64) x)
cost-diff	192	(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))

Rules

20 994×	`lower-fma.f32`
20 986×	`lower-fma.f64`
3 098×	`lower-*.f32`
3 090×	`lower-*.f64`
1 848×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	110
0	40	101
1	76	101
2	129	101
3	313	101
4	894	101
5	2585	101
6	6339	101
0	8237	98

Stop Event

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

Calls

Call 1

Inputs
(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))
x
#s(literal 1/2 binary64)
(fma.f64 y #s(literal -1/2 binary64) x)
y
#s(literal -1/2 binary64)
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))
(*.f64 #s(literal 3/2 binary64) x)
#s(literal 3/2 binary64)
x
(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
x
#s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
(-.f64 (fma.f64 #s(literal 1/2 binary64) x x) (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) x x)
#s(literal 1/2 binary64)
x
(*.f64 #s(literal 1/2 binary64) y)
y
(fma.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) x)
(*.f64 (+.f64 y x) (-.f64 x y))
(+.f64 y x)
y
x
(-.f64 x y)
(/.f64 #s(literal 1/2 binary64) (+.f64 y x))
#s(literal 1/2 binary64)

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

localize82.0ms (2%)

Memory

15.5MiB live, 100.4MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 (+.f64 y x) (-.f64 x y))
accuracy	0.01171875	(/.f64 #s(literal 1/2 binary64) (+.f64 y x))
accuracy	31.716518958737925	(fma.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) x)
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.078125	(-.f64 (fma.f64 #s(literal 1/2 binary64) x x) (*.f64 #s(literal 1/2 binary64) y))
accuracy	0	(*.f64 y #s(literal -1/2 binary64))
accuracy	0.078125	(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
accuracy	34.00093885288498	#s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64)))
accuracy	0	(*.f64 #s(literal 3/2 binary64) x)
accuracy	28.970969486722613	#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))
accuracy	0	(fma.f64 y #s(literal -1/2 binary64) x)
accuracy	0.07421875	(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))

Samples

54.0ms	222×	0	valid
5.0ms	13×	2	valid
5.0ms	17×	1	valid
4.0ms	4×	3	valid

Compiler

Compiled 106 to 25 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 33.0ms (63% of total)

ival-add: 8.0ms (15.3% of total)

ival-div: 4.0ms (7.6% of total)

adjust: 4.0ms (7.6% of total)

ival-sub: 3.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

series17.0ms (0.4%)

Memory

13.9MiB live, 13.9MiB allocated

Counts

15 → 312

Calls

Call 1

Inputs
#s(alt (fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x)) (patch (fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (fma.f64 y #s(literal -1/2 binary64) x) (patch (fma.f64 y #s(literal -1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (+ x (/ (- x y) 2)) (.f64 #s(literal 3/2 binary64) x)) (patch #s(approx (+ x (/ (- x y) 2)) (.f64 #s(literal 3/2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 3/2 binary64) x) (patch (.f64 #s(literal 3/2 binary64) x) #<representation binary64>) () ())
#s(alt (+.f64 x #s(approx (/ (- x y) 2) (.f64 y #s(literal -1/2 binary64)))) (patch (+.f64 x #s(approx (/ (- x y) 2) (.f64 y #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- x y) 2) (.f64 y #s(literal -1/2 binary64))) (patch #s(approx (/ (- x y) 2) (.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 #s(literal 1/2 binary64) x x) (.f64 #s(literal 1/2 binary64) y)) (patch (-.f64 (fma.f64 #s(literal 1/2 binary64) x x) (.f64 #s(literal 1/2 binary64) y)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x x) (patch (fma.f64 #s(literal 1/2 binary64) x x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) y) (patch (.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) x) (patch (fma.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) x) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 y x) (-.f64 x y)) (patch (.f64 (+.f64 y x) (-.f64 x y)) #<representation binary64>) () ())
#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) (patch (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((+ (* x 1/2) (+ (* y -1/2) x)) (+ (* y -1/2) x) (+ x (/ (- x y) 2)) (* 3/2 x) (+ x (/ (- x y) 2)) (/ (- x y) 2) (* y -1/2) (- (+ (* 1/2 x) x) (* 1/2 y)) (+ (* 1/2 x) x) (* 1/2 y) (+ (* (* (+ y x) (- x y)) (/ 1/2 (+ y x))) x) (* (+ y x) (- x y)) (+ y x) (- x y) (/ 1/2 (+ y x)))
2.0ms	y	@	inf	((+ (* x 1/2) (+ (* y -1/2) x)) (+ (* y -1/2) x) (+ x (/ (- x y) 2)) (* 3/2 x) (+ x (/ (- x y) 2)) (/ (- x y) 2) (* y -1/2) (- (+ (* 1/2 x) x) (* 1/2 y)) (+ (* 1/2 x) x) (* 1/2 y) (+ (* (* (+ y x) (- x y)) (/ 1/2 (+ y x))) x) (* (+ y x) (- x y)) (+ y x) (- x y) (/ 1/2 (+ y x)))
2.0ms	x	@	inf	((+ (* x 1/2) (+ (* y -1/2) x)) (+ (* y -1/2) x) (+ x (/ (- x y) 2)) (* 3/2 x) (+ x (/ (- x y) 2)) (/ (- x y) 2) (* y -1/2) (- (+ (* 1/2 x) x) (* 1/2 y)) (+ (* 1/2 x) x) (* 1/2 y) (+ (* (* (+ y x) (- x y)) (/ 1/2 (+ y x))) x) (* (+ y x) (- x y)) (+ y x) (- x y) (/ 1/2 (+ y x)))
1.0ms	y	@	0	((+ (* x 1/2) (+ (* y -1/2) x)) (+ (* y -1/2) x) (+ x (/ (- x y) 2)) (* 3/2 x) (+ x (/ (- x y) 2)) (/ (- x y) 2) (* y -1/2) (- (+ (* 1/2 x) x) (* 1/2 y)) (+ (* 1/2 x) x) (* 1/2 y) (+ (* (* (+ y x) (- x y)) (/ 1/2 (+ y x))) x) (* (+ y x) (- x y)) (+ y x) (- x y) (/ 1/2 (+ y x)))
1.0ms	y	@	-inf	((+ (* x 1/2) (+ (* y -1/2) x)) (+ (* y -1/2) x) (+ x (/ (- x y) 2)) (* 3/2 x) (+ x (/ (- x y) 2)) (/ (- x y) 2) (* y -1/2) (- (+ (* 1/2 x) x) (* 1/2 y)) (+ (* 1/2 x) x) (* 1/2 y) (+ (* (* (+ y x) (- x y)) (/ 1/2 (+ y x))) x) (* (+ y x) (- x y)) (+ y x) (- x y) (/ 1/2 (+ y x)))

simplify211.0ms (5%)

Memory

-8.0MiB live, 220.5MiB allocated

Algorithm

1×	egg-herbie

Rules

10 540×	`lower-fma.f64`
10 540×	`lower-fma.f32`
4 234×	`lower-*.f64`
4 234×	`lower-*.f32`
2 796×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	252	2195
1	776	2041
2	2134	1983
3	7555	1975
0	8816	1827

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 300

Calls

Call 1

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

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

rewrite271.0ms (6.5%)

Memory

18.4MiB live, 397.9MiB allocated

Rules

6 194×	`lower-fma.f32`
6 186×	`lower-fma.f64`
4 592×	`lower-*.f32`
4 584×	`lower-*.f64`
4 546×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	95
0	40	86
1	190	86
2	1698	86
0	8747	82

Stop Event

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

Counts

15 → 951

Calls

Call 1

Inputs
(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))
(fma.f64 y #s(literal -1/2 binary64) x)
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))
(*.f64 #s(literal 3/2 binary64) x)
(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
#s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 y #s(literal -1/2 binary64))
(-.f64 (fma.f64 #s(literal 1/2 binary64) x x) (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) x x)
(*.f64 #s(literal 1/2 binary64) y)
(fma.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)) x)
(*.f64 (+.f64 y x) (-.f64 x y))
(+.f64 y x)
(-.f64 x y)
(/.f64 #s(literal 1/2 binary64) (+.f64 y x))

Outputs
(.f64 (-.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64)))))
(.f64 (-.f64 (.f64 x x) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 (-.f64 x y) #s(literal 1/2 binary64)))))
(.f64 (fma.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64) (*.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) (neg.f64 x))))
(.f64 (.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x) (-.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal -1/2 binary64) y x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal -1/2 binary64) y x))))
(.f64 (fma.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 y y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 y #s(literal 1/2 binary64)) (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64)))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (-.f64 x y)) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) (neg.f64 x)) (*.f64 x x))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (-.f64 x y)) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64) (.f64 x (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) y x) (fma.f64 #s(literal -1/2 binary64) y x)) (fma.f64 #s(literal -1/2 binary64) y x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -1/2 binary64) y x) (-.f64 (fma.f64 #s(literal -1/2 binary64) y x) (.f64 #s(literal 1/2 binary64) x))))))
(pow.f64 (/.f64 (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (-.f64 x y)) (.f64 (.f64 x x) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64))) (-.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (*.f64 y y)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 y #s(literal 1/2 binary64)) (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64))))) (fma.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x) (.f64 #s(literal 1/8 binary64) (.f64 (*.f64 y y) y)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal -1/2 binary64) y x)) (.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal -1/2 binary64) y x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -1/2 binary64) y x) (-.f64 (fma.f64 #s(literal -1/2 binary64) y x) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x) (.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) y x) (fma.f64 #s(literal -1/2 binary64) y x)) (fma.f64 #s(literal -1/2 binary64) y x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) (neg.f64 x)) (fma.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64) (.f64 (neg.f64 x) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64) (.f64 x (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (-.f64 x y)) (.f64 (*.f64 x x) x))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64)) (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) (/.f64 (.f64 x x) (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64)) (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64)) (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) (.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) (/.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64)) (-.f64 x (*.f64 (-.f64 x y) #s(literal 1/2 binary64))))))))
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(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x))
(.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))) (fma.f64 y y (*.f64 x (-.f64 x y))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 y x)))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
(pow.f64 (/.f64 (*.f64 (+.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (+.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (+.f64 y x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (+.f64 y x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 y x) #s(literal 2 binary64)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (neg.f64 (neg.f64 (+.f64 y x)))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (+.f64 y x)))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 (+.f64 y x))))
(/.f64 #s(literal 1/2 binary64) (+.f64 y x))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 y x)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)))

eval236.0ms (5.6%)

Memory: 24.9MiB live, 381.7MiB allocated
Compiler: Compiled 34 571 to 1 813 computations (94.8% saved)

prune140.0ms (3.4%)

Memory

-19.8MiB live, 220.8MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 299	2	1 301
Fresh	6	1	7
Picked	3	2	5
Done	0	0	0
Total	1 308	5	1 313

Accuracy

100.0%

Counts

1 313 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
▶	100.0%	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
✓	56.0%	(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
▶	46.8%	#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))
✓	54.7%	#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify18.0ms (0.4%)

Memory

12.7MiB live, 12.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 y x)
cost-diff	0	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
cost-diff	0	(*.f64 #s(literal -1/2 binary64) y)
cost-diff	128	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
cost-diff	0	(*.f64 y #s(literal -1/2 binary64))
cost-diff	0	#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))

Rules

560×	`lower-fma.f32`
556×	`lower-fma.f64`
208×	`lower-*.f32`
204×	`lower-*.f64`
128×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
0	22	40
1	41	40
2	69	40
3	118	40
4	198	40
5	314	40
6	478	40
7	531	40
8	539	40
0	539	40

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
x
#s(literal 3/2 binary64)
(*.f64 #s(literal -1/2 binary64) y)
#s(literal -1/2 binary64)
y
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(-.f64 y x)
y
x
#s(literal -1/2 binary64)

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

localize53.0ms (1.3%)

Memory

2.8MiB live, 47.1MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 y x)
accuracy	0.078125	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
accuracy	0	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
accuracy	0	(*.f64 #s(literal -1/2 binary64) y)
accuracy	0	(*.f64 y #s(literal -1/2 binary64))
accuracy	34.03450781810437	#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))

Samples

41.0ms	240×	0	valid
1.0ms	6×	2	valid
1.0ms	7×	1	valid
1.0ms	3×	3	valid

Compiler

Compiled 43 to 18 computations (58.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 27.0ms (77.1% of total)

ival-add: 4.0ms (11.4% of total)

ival-sub: 3.0ms (8.6% of total)

adjust: 1.0ms (2.9% of total)

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.7%)

Memory

-26.0MiB live, 13.3MiB allocated

Counts

6 → 120

Calls

Call 1

Inputs
#s(alt #s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (.f64 y #s(literal -1/2 binary64))) (patch #s(approx (- (+ ( 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 3/2 binary64) (.f64 #s(literal -1/2 binary64) y)) (patch (fma.f64 x #s(literal 3/2 binary64) (.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 (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x) (patch (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x) #<representation binary64>) () ())
#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
23.0ms	x	@	inf	((- (+ (* 1/2 x) x) (* 1/2 y)) (* y -1/2) (+ (* x 3/2) (* -1/2 y)) (* -1/2 y) (+ (* (- y x) -1/2) x) (- y x))
1.0ms	y	@	inf	((- (+ (* 1/2 x) x) (* 1/2 y)) (* y -1/2) (+ (* x 3/2) (* -1/2 y)) (* -1/2 y) (+ (* (- y x) -1/2) x) (- y x))
1.0ms	y	@	0	((- (+ (* 1/2 x) x) (* 1/2 y)) (* y -1/2) (+ (* x 3/2) (* -1/2 y)) (* -1/2 y) (+ (* (- y x) -1/2) x) (- y x))
1.0ms	y	@	-inf	((- (+ (* 1/2 x) x) (* 1/2 y)) (* y -1/2) (+ (* x 3/2) (* -1/2 y)) (* -1/2 y) (+ (* (- y x) -1/2) x) (- y x))
1.0ms	x	@	-inf	((- (+ (* 1/2 x) x) (* 1/2 y)) (* y -1/2) (+ (* x 3/2) (* -1/2 y)) (* -1/2 y) (+ (* (- y x) -1/2) x) (- y x))

simplify163.0ms (3.9%)

Memory

-9.8MiB live, 150.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 376×	`lower-fma.f64`
7 376×	`lower-fma.f32`
2 758×	`lower-*.f64`
2 758×	`lower-*.f32`
1 382×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	675
1	169	567
2	451	567
3	1300	567
4	3209	567
5	4725	567
6	6774	567
0	8210	513

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 117

Calls

Call 1

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

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

rewrite491.0ms (11.7%)

Memory

-3.3MiB live, 227.0MiB allocated

Rules

6 906×	`lower-fma.f32`
6 902×	`lower-fma.f64`
4 850×	`lower-*.f32`
4 846×	`lower-*.f64`
3 554×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
0	22	31
1	103	31
2	814	31
0	8600	31

Stop Event

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

Counts

6 → 214

Calls

Call 1

Inputs
#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))
(*.f64 y #s(literal -1/2 binary64))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(*.f64 #s(literal -1/2 binary64) y)
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(-.f64 y x)

Outputs
#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 #s(literal -1/2 binary64) y))
(*.f64 (neg.f64 y) #s(literal 1/2 binary64))
(.f64 #s(literal -1 binary64) (.f64 y #s(literal 1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) y)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (neg.f64 y))
(/.f64 (.f64 #s(literal -1/4 binary64) (.f64 y y)) (+.f64 #s(literal 0 binary64) (*.f64 y #s(literal 1/2 binary64))))
(/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) y)) (+.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (.f64 #s(literal 0 binary64) (.f64 y #s(literal 1/2 binary64))))))
(neg.f64 (*.f64 y #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 y #s(literal 1/2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) y))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal 3/2 binary64) x)) (-.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) y))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 (-.f64 x (.f64 y #s(literal 1/2 binary64))) (-.f64 x (.f64 y #s(literal 1/2 binary64)))) (-.f64 x (.f64 y #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (-.f64 x (.f64 y #s(literal 1/2 binary64))) (-.f64 (-.f64 x (.f64 y #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/2 binary64)))))))
(.f64 (fma.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (.f64 (.f64 #s(literal 3/2 binary64) x) (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64)))))))
(.f64 (fma.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y))))))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (.f64 #s(literal -9/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y))))
(.f64 (neg.f64 (fma.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) y)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y)))))))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal 3/2 binary64) x)))
(.f64 (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 #s(literal -1/4 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 3/2 binary64) x (*.f64 y #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64))))) (.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 y y)) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 y y)) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y))))) (+.f64 (/.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (fma.f64 #s(literal 3/2 binary64) x (.f64 y #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 y y)) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x)) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y))))) (/.f64 (.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x)) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y)))))) (.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) y)) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y))))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) y)) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y))))))) (+.f64 (/.f64 (.f64 #s(literal 27/8 binary64) (.f64 (.f64 x x) x)) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y))))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) y)) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 #s(literal -3/2 binary64) x (.f64 #s(literal -1/2 binary64) y)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 y) x)) (.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 y) x))) (.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 y) x)) x))
(/.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) y x) (fma.f64 #s(literal -1/2 binary64) y x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 (fma.f64 #s(literal -1/2 binary64) y x) (.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 (-.f64 x (.f64 y #s(literal 1/2 binary64))) (-.f64 x (.f64 y #s(literal 1/2 binary64)))) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 (-.f64 x (.f64 y #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/2 binary64))))
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(+.f64 (*.f64 (-.f64 y x) #s(literal -1/2 binary64)) x)
(+.f64 (*.f64 #s(literal -1/2 binary64) y) (fma.f64 (neg.f64 x) #s(literal -1/2 binary64) x))
(+.f64 x (*.f64 (-.f64 y x) #s(literal -1/2 binary64)))
(.f64 (.f64 (neg.f64 (+.f64 y x)) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))))
(.f64 (.f64 (neg.f64 (fma.f64 y y (.f64 x (+.f64 y x)))) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y y (.f64 x (+.f64 y x))))))
(*.f64 #s(literal 1 binary64) (-.f64 y x))
(.f64 (.f64 (+.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
(.f64 (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 (neg.f64 x) (-.f64 (neg.f64 x) y)))))
(.f64 (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x (+.f64 y x)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)) #s(literal -1 binary64))
(/.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))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x))))) (.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x)))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x)))))) (+.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x))))))
(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (-.f64 (neg.f64 x) y))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y y) (+.f64 y x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (+.f64 y x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 y y) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)) (fma.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))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (fma.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x)))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x)))) (.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (*.f64 x (+.f64 y x))))))))
(/.f64 (fma.f64 (.f64 (neg.f64 x) x) x (.f64 (.f64 y y) y)) (fma.f64 x x (-.f64 (.f64 y y) (*.f64 (neg.f64 x) y))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 y x))) (neg.f64 (neg.f64 (+.f64 y x))))
(/.f64 (neg.f64 (.f64 (neg.f64 (fma.f64 y y (.f64 x (+.f64 y x)))) (-.f64 y x))) (neg.f64 (neg.f64 (fma.f64 y y (*.f64 x (+.f64 y x))))))
(/.f64 (.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (+.f64 y x) (-.f64 y x))) #s(literal 1 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (-.f64 y x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y y) (.f64 y y) (.f64 (.f64 x x) (fma.f64 x x (*.f64 y y)))) (+.f64 y x)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (-.f64 y x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 y y (.f64 x (+.f64 y x)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y) (.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)))) (fma.f64 y y (*.f64 x (+.f64 y x)))))
(/.f64 (-.f64 (.f64 (.f64 y y) (+.f64 y x)) (.f64 (+.f64 y x) (.f64 x x))) (*.f64 (+.f64 y x) (+.f64 y x)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (.f64 (.f64 x x) x))) (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (fma.f64 y y (*.f64 x (+.f64 y x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))
(/.f64 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 y x)) (neg.f64 (+.f64 y x)))
(/.f64 (.f64 (neg.f64 (fma.f64 y y (.f64 x (+.f64 y x)))) (-.f64 y x)) (neg.f64 (fma.f64 y y (*.f64 (neg.f64 x) (-.f64 (neg.f64 x) y)))))
(/.f64 (.f64 (neg.f64 (fma.f64 y y (.f64 x (+.f64 y x)))) (-.f64 y x)) (neg.f64 (fma.f64 y y (*.f64 x (+.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y (.f64 (neg.f64 x) (-.f64 (neg.f64 x) y))) (.f64 (fma.f64 y y (*.f64 x (+.f64 y x))) (-.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 y x)))
(/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (+.f64 y x))
(/.f64 (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (-.f64 y x)) (fma.f64 y y (*.f64 (neg.f64 x) (-.f64 (neg.f64 x) y))))
(/.f64 (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (-.f64 y x)) (fma.f64 y y (*.f64 x (+.f64 y x))))
(neg.f64 (/.f64 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 y x)) (+.f64 y x)))
(neg.f64 (/.f64 (.f64 (neg.f64 (fma.f64 y y (.f64 x (+.f64 y x)))) (-.f64 y x)) (fma.f64 y y (*.f64 x (+.f64 y x)))))
(neg.f64 (/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (neg.f64 (+.f64 y x))))
(neg.f64 (/.f64 (.f64 (fma.f64 y y (.f64 x (+.f64 y x))) (-.f64 y x)) (neg.f64 (fma.f64 y y (*.f64 x (+.f64 y x))))))
(fma.f64 #s(literal -1 binary64) x y)
(fma.f64 (.f64 y y) (/.f64 #s(literal 1 binary64) (+.f64 y x)) (neg.f64 (/.f64 (.f64 x x) (+.f64 y x))))
(fma.f64 (.f64 (.f64 y y) y) (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x (+.f64 y x)))) (neg.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x))))))
(-.f64 (+.f64 y #s(literal 0 binary64)) x)
(-.f64 (/.f64 (.f64 y y) (+.f64 y x)) (/.f64 (.f64 x x) (+.f64 y x)))
(-.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x)))))
(-.f64 #s(literal 0 binary64) (-.f64 x y))
(-.f64 y x)
(+.f64 (/.f64 (.f64 y y) (+.f64 y x)) (neg.f64 (/.f64 (.f64 x x) (+.f64 y x))))
(+.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 y y (.f64 x (+.f64 y x)))) (neg.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 y y (.f64 x (+.f64 y x))))))
(+.f64 (neg.f64 x) y)
(+.f64 y (neg.f64 x))

eval39.0ms (0.9%)

Memory: -10.9MiB live, 75.7MiB allocated
Compiler: Compiled 6 597 to 669 computations (89.9% saved)

prune58.0ms (1.4%)

Memory

-9.7MiB live, 67.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	331	0	331
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	331	5	336

Accuracy

100.0%

Counts

336 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
✓	100.0%	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
✓	56.0%	(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
✓	46.8%	#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))
✓	54.7%	#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

Compiler

Compiled 195 to 77 computations (60.5% saved)

regimes15.0ms (0.4%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
5.0ms	x
5.0ms	y

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.2%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))
#s(approx (+ x (/ (- x y) 2)) (*.f64 y #s(literal -1/2 binary64)))
#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))
(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.2%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

4 → 3

Calls

Call 1

Inputs
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))
#s(approx (+ x (/ (- x y) 2)) (*.f64 y #s(literal -1/2 binary64)))
#s(approx (- (+ (* 1/2 x) x) (* 1/2 y)) (*.f64 y #s(literal -1/2 binary64)))
(+.f64 x #s(approx (/ (- x y) 2) (*.f64 y #s(literal -1/2 binary64))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
82.5%	3	`x`
79.9%	3	`y`
63.0%	3	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes2.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
80.4%	3	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes19.0ms (0.5%)

Memory

-28.5MiB live, 10.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

Outputs
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

Calls

3 calls:

16.0ms	x
1.0ms	y
1.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
54.7%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`
54.7%	1	`y`
54.7%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch28.0ms (0.7%)

Memory

6.8MiB live, 45.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.4662981093544885e+113	3.851274442322867e+114
13.0ms	-7587583.651110935	-2.695292322027469e-5

Samples

13.0ms	243×	0	valid
2.0ms	14×	2	valid
1.0ms	11×	1	valid
1.0ms	4×	3	valid

Compiler

Compiled 284 to 198 computations (30.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 2.0ms (29.1% of total)

ival-sub: 2.0ms (29.1% of total)

ival-add: 2.0ms (29.1% of total)

adjust: 1.0ms (14.6% of total)

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

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

exact: 0.0ms (0% of total)

bsearch12.0ms (0.3%)

Memory

21.3MiB live, 21.3MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	1.2262682722444775e+98	1.1600827194977121e+101
1.0ms	-7587583.651110935	-2.695292322027469e-5

Samples

4.0ms	117×	0	valid
0.0ms	3×	3	valid
0.0ms	4×	2	valid
0.0ms	4×	1	valid

Compiler

Compiled 264 to 191 computations (27.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 1.0ms (32.9% of total)

ival-sub: 1.0ms (32.9% of total)

ival-add: 1.0ms (32.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

simplify10.0ms (0.2%)

Memory

-22.3MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	105
1	33	105
2	38	105
3	40	105
4	41	105

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 x #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (+ x (/ (- x y) 2)) (.f64 #s(literal 3/2 binary64) x)) (if (<=.f64 x #s(literal 229999999999999996743507194830461631917616861549277362946392761957802905837360666719843517182411152892048766402560 binary64)) (+.f64 x #s(approx (/ (- x y) 2) (.f64 y #s(literal -1/2 binary64)))) #s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))))
(if (<=.f64 x #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (+ x (/ (- x y) 2)) (.f64 #s(literal 3/2 binary64) x)) (if (<=.f64 x #s(literal 124999999999999995917021100514586409231191648225819434114745222433911980740215982826092483556933632 binary64)) #s(approx (+ x (/ (- x y) 2)) (.f64 y #s(literal -1/2 binary64))) #s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))))
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

Outputs
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 y #s(literal -1/2 binary64)))
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 x #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (+ x (/ (- x y) 2)) (.f64 #s(literal 3/2 binary64) x)) (if (<=.f64 x #s(literal 229999999999999996743507194830461631917616861549277362946392761957802905837360666719843517182411152892048766402560 binary64)) (+.f64 x #s(approx (/ (- x y) 2) (.f64 y #s(literal -1/2 binary64)))) #s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))))
(if (<=.f64 x #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (+ x (/ (- x y) 2)) (.f64 #s(literal 3/2 binary64) x)) (if (<=.f64 x #s(literal 229999999999999996743507194830461631917616861549277362946392761957802905837360666719843517182411152892048766402560 binary64)) (+.f64 #s(approx (/ (- x y) 2) (.f64 y #s(literal -1/2 binary64))) x) #s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))))
(if (<=.f64 x #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (+ x (/ (- x y) 2)) (.f64 #s(literal 3/2 binary64) x)) (if (<=.f64 x #s(literal 124999999999999995917021100514586409231191648225819434114745222433911980740215982826092483556933632 binary64)) #s(approx (+ x (/ (- x y) 2)) (.f64 y #s(literal -1/2 binary64))) #s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))))
#s(approx (+ x (/ (- x y) 2)) (*.f64 #s(literal 3/2 binary64) x))

soundness691.0ms (16.5%)

Memory

4.6MiB live, 363.3MiB allocated

Rules

7 504×	`lower-fma.f64`
7 504×	`lower-fma.f32`
6 194×	`lower-fma.f32`
6 186×	`lower-fma.f64`
4 592×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	48	15
2	400	15
3	5080	15
0	8183	14
0	58	387
1	176	351
2	487	351
3	1345	315
4	2959	315
5	4565	315
6	6536	315
7	7586	315
0	8072	297
0	24	95
0	40	86
1	190	86
2	1698	86
0	8747	82

Stop Event

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

Compiler

Compiled 139 to 71 computations (48.9% saved)

preprocess68.0ms (1.6%)

Memory: 24.5MiB live, 177.6MiB allocated
Compiler: Compiled 156 to 66 computations (57.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
0	6	7
0	9	7
1	15	7
2	26	7
3	47	7
4	86	7
5	157	7
6	278	7
7	436	7
8	543	7
9	604	7
10	608	7
0	608	6

Iter	Nodes	Cost
0	6	18
0	9	18
1	15	18
2	26	18
3	47	18
4	86	18
5	157	18
6	278	18
7	436	18
8	543	18
9	604	18
10	608	18
0	608	17

Iter	Nodes	Cost
0	15	43
0	22	40
1	41	40
2	69	40
3	118	40
4	198	40
5	314	40
6	478	40
7	531	40
8	539	40
0	539	40

Iter	Nodes	Cost
0	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
0	6	7
0	9	7
1	15	7
2	26	7
3	47	7
4	86	7
5	157	7
6	278	7
7	436	7
8	543	7
9	604	7
10	608	7
0	608	6

Iter	Nodes	Cost
0	6	18
0	9	18
1	15	18
2	26	18
3	47	18
4	86	18
5	157	18
6	278	18
7	436	18
8	543	18
9	604	18
10	608	18
0	608	17

Iter	Nodes	Cost
0	15	43
0	22	40
1	41	40
2	69	40
3	118	40
4	198	40
5	314	40
6	478	40
7	531	40
8	539	40
0	539	40

start0.0ms (0%)

analyze0.0ms (0%)

sample685.0ms (16.4%)

explain85.0ms (2%)

preprocess56.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.5%)

localize18.0ms (0.4%)

series4.0ms (0.1%)

simplify130.0ms (3.1%)

rewrite170.0ms (4.1%)

eval68.0ms (1.6%)

prune91.0ms (2.2%)

simplify190.0ms (4.5%)

localize82.0ms (2%)

series17.0ms (0.4%)

simplify211.0ms (5%)

rewrite271.0ms (6.5%)

eval236.0ms (5.6%)

prune140.0ms (3.4%)

simplify18.0ms (0.4%)

localize53.0ms (1.3%)

series29.0ms (0.7%)

simplify163.0ms (3.9%)

rewrite491.0ms (11.7%)

eval39.0ms (0.9%)

prune58.0ms (1.4%)

regimes15.0ms (0.4%)

regimes8.0ms (0.2%)

regimes7.0ms (0.2%)

regimes2.0ms (0%)

regimes19.0ms (0.5%)

bsearch28.0ms (0.7%)

bsearch12.0ms (0.3%)

simplify10.0ms (0.2%)

soundness691.0ms (16.5%)

preprocess68.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	41
1	45	35
2	139	35
3	373	35
4	647	35
5	807	35
6	846	35
0	6	7
0	9	7
1	15	7
2	26	7
3	47	7
4	86	7
5	157	7
6	278	7
7	436	7
8	543	7
9	604	7
10	608	7
0	608	6

Iter	Nodes	Cost
0	6	18
0	9	18
1	15	18
2	26	18
3	47	18
4	86	18
5	157	18
6	278	18
7	436	18
8	543	18
9	604	18
10	608	18
0	608	17

Iter	Nodes	Cost
0	15	43
0	22	40
1	41	40
2	69	40
3	118	40
4	198	40
5	314	40
6	478	40
7	531	40
8	539	40
0	539	40