Metrics for Kahan p9 Example

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze5.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	18.7%	81.3%	0%	0%	0%	0
0%	0%	18.7%	81.3%	0%	0%	0%	1
0%	0%	18.7%	81.3%	0%	0%	0%	2
50%	9.4%	9.4%	81.3%	0%	0%	0%	3
50%	9.4%	9.4%	81.3%	0%	0%	0%	4
87.5%	16.4%	2.3%	81.3%	0%	0%	0%	5
87.5%	16.4%	2.3%	81.3%	0%	0%	0%	6
96.9%	18.1%	0.6%	81.3%	0%	0%	0%	7
96.9%	18.1%	0.6%	81.3%	0%	0%	0%	8
99.2%	18.6%	0.1%	81.3%	0%	0%	0%	9
99.2%	18.6%	0.1%	81.3%	0%	0%	0%	10
99.8%	18.7%	0%	81.3%	0%	0%	0%	11
99.8%	18.7%	0%	81.3%	0%	0%	0%	12

Compiler

Compiled 27 to 17 computations (37% saved)

sample1.6s (19.1%)

Memory

-67.3MiB live, 1 549.0MiB allocated

Samples

895.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 589.0ms

ival-mult: 227.0ms (38.5% of total)

ival-add: 106.0ms (18% of total)

ival-sub: 85.0ms (14.4% of total)

ival-<: 78.0ms (13.2% of total)

ival-div: 65.0ms (11% of total)

ival-and: 16.0ms (2.7% of total)

exact: 11.0ms (1.9% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain127.0ms (1.5%)

Memory

-26.1MiB live, 289.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
71	-	-	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`
0	-	-	`(*.f64 (-.f64 x y) (+.f64 x y))`
0	-	-	`(*.f64 x x)`
0	-	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	-	`y`
0	-	-	`(+.f64 x y)`
0	-	-	`(-.f64 x y)`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`	u/u	36	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	underflow	36
↳	`(*.f64 y y)`	underflow	75
↳	`(*.f64 x x)`	underflow	125
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	36
`/.f64`	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`	o/o	35	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	overflow	35
↳	`(*.f64 y y)`	overflow	35
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	35

Confusion

	Predicted +	Predicted -
+	71	0
-	0	185

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	71	0	0
-	0	0	185

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	185
1	71

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 107 to 31 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 10.0ms (47.5% of total)

ival-add: 4.0ms (19% of total)

ival-sub: 3.0ms (14.2% of total)

ival-div: 3.0ms (14.2% of total)

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

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

preprocess467.0ms (5.7%)

Memory

52.4MiB live, 429.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 712×	`lower-fma.f64`
16 712×	`lower-fma.f32`
2 536×	`lower-*.f32`
2 530×	`lower-*.f64`
2 028×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	83
1	94	83
2	301	75
3	799	75
4	2239	75
5	4876	75
6	5512	75
7	5947	75
8	6282	75
9	6355	75
10	6883	75
0	9	15
0	16	15
1	29	15
2	55	15
3	120	15
4	245	15
5	532	15
6	1278	15
7	2989	15
8	5193	15
9	6736	15
10	7289	15
11	7520	15
12	7616	15
13	7625	15
14	7625	15
15	7683	15
16	7687	15
17	7687	15
18	7687	15
19	7946	15
0	8006	14

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 17 to 9 computations (47.1% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.3%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 17 to 9 computations (47.1% saved)

simplify391.0ms (4.8%)

Memory

-41.9MiB live, 330.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

16 712×	`lower-fma.f64`
16 712×	`lower-fma.f32`
2 536×	`lower-*.f32`
2 530×	`lower-*.f64`
2 028×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	16	43
1	29	43
2	55	43
3	120	43
4	245	43
5	532	43
6	1278	43
7	2989	43
8	5193	43
9	6736	43
10	7289	43
11	7520	43
12	7616	43
13	7625	43
14	7625	43
15	7683	43
16	7687	43
17	7687	43
18	7687	43
19	7946	43
0	8006	41

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
(*.f64 (-.f64 x y) (+.f64 x y))
(-.f64 x y)
x
y
(+.f64 x y)
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(*.f64 x x)
(*.f64 y y)

localize28.0ms (0.3%)

Memory

2.2MiB live, 46.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(+.f64 (.f64 x x) (.f64 y y))
accuracy	17.53343324727173	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Samples

19.0ms

256×

valid

Compiler

Compiled 45 to 11 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 4.0ms (32.4% of total)

ival-mult: 4.0ms (32.4% of total)

ival-div: 2.0ms (16.2% of total)

ival-add: 2.0ms (16.2% of total)

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

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

series9.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

6 → 120

Calls

Call 1

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

Outputs
#s(alt (pow y 2) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor 0 x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (/ x y)) 1) (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (* -1 x)) y)) 1) (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor 0 x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow y 2)) (* x (+ y (* -1 y)))) (taylor 0 x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y))))) (taylor 0 x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y))))) (taylor 0 x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x)))) (taylor inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (taylor inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (taylor inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ x (* -1 x))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1)) (taylor inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1)) (taylor inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1)) (taylor inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor -inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1)) (taylor -inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1)) (taylor -inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1)) (taylor -inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<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 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 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>) () ())) ())
#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 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 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 (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())

Calls

30 calls:

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

simplify250.0ms (3.1%)

Memory

-21.9MiB live, 341.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 670×	`lower-fma.f64`
11 670×	`lower-fma.f32`
3 562×	`lower-*.f64`
3 562×	`lower-*.f32`
2 656×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	178	967
1	568	844
2	1897	797
3	7844	797
0	8853	755

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 117

Calls

Call 1

Inputs
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(* -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)))))
(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)))))
(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))))
(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))
(* -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))
(* -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))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)

Outputs
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x x)) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x x)) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x x)) #s(literal 1 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x x)) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x x)) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x x)) #s(literal 1 binary64))))
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal 1 binary64))))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal 1 binary64))))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 #s(literal -2 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x (+.f64 x x)) (fma.f64 x (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y (+.f64 y y)) (fma.f64 y (/.f64 y (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 y (.f64 y (fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x)))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
#s(literal -1 binary64)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64))
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64))
(* -1 (pow y 2))
(*.f64 y (neg.f64 y))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(*.f64 y (neg.f64 y))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(*.f64 (+.f64 y x) (-.f64 x y))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(*.f64 (+.f64 y x) (-.f64 x y))
(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 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(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 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(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))
(* -1 (pow y 2))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* -1 (pow y 2))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
x
(* x (+ 1 (* -1 (/ y x))))
(fma.f64 y (/.f64 (neg.f64 x) x) x)
(* x (+ 1 (* -1 (/ y x))))
(fma.f64 y (/.f64 (neg.f64 x) x) x)
(* x (+ 1 (* -1 (/ y x))))
(fma.f64 y (/.f64 (neg.f64 x) x) x)
x
(* -1 (* x (- (/ y x) 1)))
(fma.f64 y (/.f64 (neg.f64 x) x) x)
(* -1 (* x (- (/ y x) 1)))
(fma.f64 y (/.f64 (neg.f64 x) x) x)
(* -1 (* x (- (/ y x) 1)))
(fma.f64 y (/.f64 (neg.f64 x) x) x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 (/.f64 (*.f64 y x) y) y)
(* y (- (/ x y) 1))
(-.f64 (/.f64 (*.f64 y x) y) y)
(* y (- (/ x y) 1))
(-.f64 (/.f64 (*.f64 y x) y) y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 (/.f64 (*.f64 y x) y) y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 (/.f64 (*.f64 y x) y) y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 (/.f64 (*.f64 y x) y) y)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)

rewrite301.0ms (3.7%)

Memory

-3.8MiB live, 272.8MiB allocated

Rules

5 274×	`lower-*.f32`
5 268×	`lower-*.f64`
5 048×	`lower-fma.f64`
5 048×	`lower-fma.f32`
4 376×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
0	16	38
1	66	38
2	551	38
0	8160	36

Stop Event

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

Counts

6 → 708

Calls

Call 1

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

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

eval361.0ms (4.4%)

Memory: 10.0MiB live, 159.1MiB allocated
Compiler: Compiled 27 765 to 2 126 computations (92.3% saved)

prune1.7s (21.3%)

Memory

10.5MiB live, 216.9MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	821	4	825
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	822	4	826

Accuracy

99.0%

Counts

826 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.3%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
▶	63.4%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64)))
▶	30.0%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
▶	70.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 37 to 22 computations (40.5% saved)

simplify238.0ms (2.9%)

Memory

8.2MiB live, 244.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

13 222×	`lower-fma.f32`
13 218×	`lower-fma.f64`
2 592×	`lower-*.f32`
2 586×	`lower-*.f64`
1 964×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	125
0	32	122
1	56	122
2	98	122
3	186	122
4	329	122
5	658	122
6	1447	122
7	3528	122
8	7030	122
0	8122	122

Stop Event

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

Calls

Call 1

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

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

localize121.0ms (1.5%)

Memory

-11.8MiB live, 71.7MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x y)
accuracy	0	(*.f64 (-.f64 x y) (+.f64 x y))
accuracy	0	(*.f64 x x)
accuracy	17.53343324727173	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
accuracy	0	(*.f64 x x)
accuracy	0.43309001187281704	(/.f64 #s(literal 2 binary64) (*.f64 y y))
accuracy	13.03401284994929	(fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64))
accuracy	18.166681899072884	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64)))
accuracy	44.77134954607635	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
accuracy	19.162995785749267	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Samples

67.0ms

256×

valid

Compiler

Compiled 115 to 19 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 45.0ms (80.9% of total)

ival-div: 5.0ms (9% of total)

ival-add: 4.0ms (7.2% of total)

ival-sub: 2.0ms (3.6% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

10 → 216

Calls

Call 1

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

Outputs
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (/ x y)) 1) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (* -1 x)) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (/ x y)) 1) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (* -1 x)) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt x (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
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#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())

Calls

54 calls:

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

simplify458.0ms (5.6%)

Memory

-10.1MiB live, 307.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12 116×	`lower-fma.f64`
12 116×	`lower-fma.f32`
3 608×	`lower-*.f64`
3 608×	`lower-*.f32`
2 716×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	190	2056
1	591	1795
2	1949	1643
3	7802	1643
0	8846	1538

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 207

Calls

Call 1

Inputs
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(* 2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
(/ 2 (pow y 2))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(* -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)))))
(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)))))
(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))))
(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))
(* -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))
(* -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))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))

Outputs
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 #s(literal -2 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x (+.f64 x x)) (fma.f64 x (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y (+.f64 y y)) (fma.f64 y (/.f64 y (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
#s(literal -1 binary64)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 #s(literal -2 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x (+.f64 x x)) (fma.f64 x (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y (+.f64 y y)) (fma.f64 y (/.f64 y (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
#s(literal -1 binary64)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(* 2 (/ (pow x 2) (pow y 2)))
(/.f64 (.f64 x (+.f64 x x)) (.f64 y y))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(* 2 (/ (pow x 2) (pow y 2)))
(/.f64 (.f64 x (+.f64 x x)) (.f64 y y))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(* 2 (/ (pow x 2) (pow y 2)))
(/.f64 (.f64 x (+.f64 x x)) (.f64 y y))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/.f64 (fma.f64 x (+.f64 x x) (.f64 y (neg.f64 y))) (.f64 y y))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/.f64 (fma.f64 x (+.f64 x x) (.f64 y (neg.f64 y))) (.f64 y y))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/.f64 (fma.f64 x (+.f64 x x) (.f64 y (neg.f64 y))) (.f64 y y))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 #s(literal -2 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x (+.f64 x x)) (fma.f64 x (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y (+.f64 y y)) (fma.f64 y (/.f64 y (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
#s(literal -1 binary64)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
(/ 2 (pow y 2))
(/.f64 #s(literal 2 binary64) (*.f64 y y))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 #s(literal -2 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x (+.f64 x x)) (fma.f64 x (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y (+.f64 y y)) (fma.f64 y (/.f64 y (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
#s(literal -1 binary64)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 #s(literal 2 binary64) (.f64 x (/.f64 x (.f64 y y))) #s(literal -1 binary64))
(* -1 (pow y 2))
(*.f64 y (neg.f64 y))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(*.f64 y (neg.f64 y))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(*.f64 (+.f64 x y) (-.f64 x y))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(*.f64 (+.f64 x y) (-.f64 x y))
(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 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(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 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 x (.f64 x (fma.f64 y (/.f64 y (*.f64 x (neg.f64 x))) #s(literal 1 binary64))))
(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 x y) (-.f64 x y))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(*.f64 (+.f64 x y) (-.f64 x y))
(* -1 (pow y 2))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* -1 (pow y 2))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(*.f64 y (neg.f64 y))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(.f64 y (.f64 y (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal -1 binary64))))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x (/.f64 (*.f64 x y) x))
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x (/.f64 (*.f64 x y) x))
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x (/.f64 (*.f64 x y) x))
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x (/.f64 (*.f64 x y) x))
(* -1 (* x (- (/ y x) 1)))
(-.f64 x (/.f64 (*.f64 x y) x))
(* -1 (* x (- (/ y x) 1)))
(-.f64 x (/.f64 (*.f64 x y) x))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(fma.f64 x (/.f64 y y) (neg.f64 y))
(* y (- (/ x y) 1))
(fma.f64 x (/.f64 y y) (neg.f64 y))
(* y (- (/ x y) 1))
(fma.f64 x (/.f64 y y) (neg.f64 y))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(fma.f64 x (/.f64 y y) (neg.f64 y))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(fma.f64 x (/.f64 y y) (neg.f64 y))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(fma.f64 x (/.f64 y y) (neg.f64 y))
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(fma.f64 x (/.f64 y x) x)
(* x (+ 1 (/ y x)))
(fma.f64 x (/.f64 y x) x)
(* x (+ 1 (/ y x)))
(fma.f64 x (/.f64 y x) x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 x (/.f64 y x) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 x (/.f64 y x) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 x (/.f64 y x) x)
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(fma.f64 x (/.f64 y y) y)
(* y (+ 1 (/ x y)))
(fma.f64 x (/.f64 y y) y)
(* y (+ 1 (/ x y)))
(fma.f64 x (/.f64 y y) y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 x (/.f64 y y) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 x (/.f64 y y) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 x (/.f64 y y) y)

rewrite382.0ms (4.7%)

Memory

35.5MiB live, 506.5MiB allocated

Rules

9 218×	`lower-fma.f32`
9 214×	`lower-fma.f64`
6 756×	`lower-*.f32`
6 750×	`lower-*.f64`
4 608×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	105
0	32	102
1	125	102
2	921	102
0	9151	102

Stop Event

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

Counts

10 → 712

Calls

Call 1

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

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

eval196.0ms (2.4%)

Memory: -2.3MiB live, 313.5MiB allocated
Compiler: Compiled 26 582 to 2 178 computations (91.8% saved)

prune146.0ms (1.8%)

Memory

-8.6MiB live, 313.1MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	939	1	940
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	939	5	944

Accuracy

99.3%

Counts

944 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	72.3%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
▶	71.6%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)))
✓	63.4%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64)))
✓	30.0%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
✓	70.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 50 to 30 computations (40% saved)

simplify210.0ms (2.6%)

Memory

-23.3MiB live, 354.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 x y)
cost-diff	0	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)))
cost-diff	128	(/.f64 x (*.f64 y #s(literal 1/2 binary64)))
cost-diff	384	(fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))

Rules

10 936×	`lower-fma.f32`
10 934×	`lower-fma.f64`
2 386×	`lower-*.f32`
2 384×	`lower-*.f64`
1 784×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	51
0	21	51
1	42	51
2	86	51
3	173	51
4	302	51
5	617	51
6	1379	51
7	3431	51
8	6148	51
9	7507	51
0	8010	50

Stop Event

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

Calls

Call 1

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

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

localize41.0ms (0.5%)

Memory

-4.7MiB live, 118.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 y #s(literal 1/2 binary64))
accuracy	0.11947250976844202	(fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))
accuracy	18.166681899072884	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)))

Samples

29.0ms

256×

valid

Compiler

Compiled 43 to 18 computations (58.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 10.0ms (50.8% of total)

ival-div: 5.0ms (25.4% of total)

ival-add: 3.0ms (15.2% of total)

ival-sub: 2.0ms (10.2% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Memory

-12.3MiB live, 26.2MiB allocated

Counts

5 → 108

Calls

Call 1

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

Outputs
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow x 2) (pow y 2))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow x 2) (pow y 2))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor -inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor -inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor -inf y) (#s(alt (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf x) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor 0 y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ x y)) (taylor -inf y) (#s(alt (/.f64 x (.f64 y #s(literal 1/2 binary64))) (patch (/.f64 x (.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow x 2) (pow y 2))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1) (taylor 0 x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2))) (taylor inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (/ x y)) 1) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (* -1 x)) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<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 (* 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 (.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>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/ x (* y 1/2))
1.0ms	x	@	inf	(/ x (* y 1/2))
0.0ms	y	@	inf	(/ x (* y 1/2))
0.0ms	y	@	0	(/ x (* y 1/2))
0.0ms	x	@	-inf	(/ x (* y 1/2))

simplify213.0ms (2.6%)

Memory

1.4MiB live, 440.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 398×	`lower-fma.f64`
9 398×	`lower-fma.f32`
4 198×	`lower-*.f64`
4 198×	`lower-*.f32`
1 896×	`lower-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	140	760
1	428	715
2	1389	680
3	4967	680
0	8248	642

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(* 2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* 2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
(* 2 (/ x y))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)

Outputs
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* 2 (/ (pow x 2) (pow y 2)))
(/.f64 (.f64 x (+.f64 x x)) (.f64 y y))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* 2 (/ (pow x 2) (pow y 2)))
(/.f64 (.f64 x (+.f64 x x)) (.f64 y y))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* 2 (/ (pow x 2) (pow y 2)))
(/.f64 (.f64 x (+.f64 x x)) (.f64 y y))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
(* 2 (/ x y))
(*.f64 #s(literal 2 binary64) (/.f64 x y))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (.f64 x x) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 x x) (.f64 (.f64 y y) (.f64 y y))) (/.f64 #s(literal 2 binary64) (.f64 y y))) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 x (.f64 x (fma.f64 (.f64 x (+.f64 x x)) (fma.f64 x (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 y y) (.f64 y y)))) (/.f64 #s(literal 2 binary64) (.f64 y y)))) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y (+.f64 y y)) (fma.f64 y (/.f64 y (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y (fma.f64 y (.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal -2 binary64)) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
#s(literal -1 binary64)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.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))
(* 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))
(* 1/2 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))

rewrite253.0ms (3.1%)

Memory

30.7MiB live, 513.7MiB allocated

Rules

8 112×	`lower-fma.f32`
8 110×	`lower-fma.f64`
6 068×	`lower-*.f32`
6 066×	`lower-*.f64`
3 558×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	47
0	21	47
1	105	47
2	933	45
0	8827	42

Stop Event

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

Counts

5 → 175

Calls

Call 1

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

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

eval36.0ms (0.4%)

Memory: -32.8MiB live, 88.1MiB allocated
Compiler: Compiled 4 738 to 473 computations (90% saved)

prune35.0ms (0.4%)

Memory

18.9MiB live, 97.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	283	5	288

Accuracy

99.3%

Counts

288 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	72.3%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
✓	71.6%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (/.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)))
✓	63.4%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal -1 binary64)))
✓	30.0%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
✓	70.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 107 to 51 computations (52.3% saved)

regimes9.0ms (0.1%)

Memory

-16.5MiB live, 22.9MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (*.f64 x x)))

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

Calls

3 calls:

3.0ms	x
3.0ms	y
2.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Results

Accuracy	Segments	Branch
87.1%	2	`x`
92.3%	3	`y`
93.3%	2	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes2.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Counts

4 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
93.3%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 17 to 9 computations (47.1% saved)

regimes2.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

Calls

1 calls:

1.0ms

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

Results

Accuracy	Segments	Branch
92.4%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 17 to 9 computations (47.1% saved)

regimes4.0ms (0%)

Memory

12.1MiB live, 12.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

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

Calls

3 calls:

1.0ms	x
1.0ms	y
1.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Results

Accuracy	Segments	Branch
70.1%	1	`x`
70.1%	1	`y`
70.1%	1	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN

Compiler

Compiled 20 to 14 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.9999999733021422	1.0

Compiler

Compiled 20 to 14 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.9999999733021422	1.0

Compiler

Compiled 20 to 14 computations (30% saved)

simplify9.0ms (0.1%)

Memory

-20.4MiB live, 21.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	267
1	46	267
2	49	267
3	51	267
4	52	267

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness525.0ms (6.4%)

Memory

7.4MiB live, 486.6MiB allocated

Rules

11 670×	`lower-fma.f64`
11 670×	`lower-fma.f32`
9 218×	`lower-fma.f32`
9 214×	`lower-fma.f64`
6 756×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	105
0	32	102
1	125	102
2	921	102
0	9151	102
0	9	38
0	16	38
1	66	38
2	551	38
0	8160	36
0	178	967
1	568	844
2	1897	797
3	7844	797
0	8853	755

Stop Event

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

Compiler

Compiled 242 to 82 computations (66.1% saved)

preprocess45.0ms (0.5%)

Memory

21.9MiB live, 136.5MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 600 to 196 computations (67.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze5.0ms (0.1%)

sample1.6s (19.1%)

explain127.0ms (1.5%)

preprocess467.0ms (5.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify391.0ms (4.8%)

localize28.0ms (0.3%)

series9.0ms (0.1%)

simplify250.0ms (3.1%)

rewrite301.0ms (3.7%)

eval361.0ms (4.4%)

prune1.7s (21.3%)

simplify238.0ms (2.9%)

localize121.0ms (1.5%)

series9.0ms (0.1%)

simplify458.0ms (5.6%)

rewrite382.0ms (4.7%)

eval196.0ms (2.4%)

prune146.0ms (1.8%)

simplify210.0ms (2.6%)

localize41.0ms (0.5%)

series10.0ms (0.1%)

simplify213.0ms (2.6%)

rewrite253.0ms (3.1%)

eval36.0ms (0.4%)

prune35.0ms (0.4%)

regimes9.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes4.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

soundness525.0ms (6.4%)

preprocess45.0ms (0.5%)

end0.0ms (0%)

Profiling