Metrics for Kahan p9 Example

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze5.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB 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)

sample937.0ms (15.1%)

Memory

32.5MiB live, 2 204.9MiB allocated

Samples

634.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 448.0ms

ival-mult: 156.0ms (34.8% of total)

ival-add: 79.0ms (17.6% of total)

ival-<: 70.0ms (15.6% of total)

ival-div: 61.0ms (13.6% of total)

ival-sub: 52.0ms (11.6% of total)

ival-and: 16.0ms (3.6% of total)

exact: 11.0ms (2.5% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain109.0ms (1.8%)

Memory

-28.2MiB live, 295.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
74	-	-	`(/.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)))`	o/o	39	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	overflow	39
↳	`(*.f64 y y)`	overflow	39
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	39
`/.f64`	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`	u/u	35	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	underflow	35
↳	`(*.f64 y y)`	underflow	91
↳	`(*.f64 x x)`	underflow	119
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	35

Confusion

	Predicted +	Predicted -
+	74	0
-	0	182

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	74	0	0
-	0	0	182

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	182
1	74

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 105 to 31 computations (70.5% saved)

Precisions

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

ival-mult: 10.0ms (48.3% of total)

ival-add: 4.0ms (19.3% of total)

ival-sub: 3.0ms (14.5% of total)

ival-div: 3.0ms (14.5% of total)

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

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

preprocess403.0ms (6.5%)

Memory

13.0MiB live, 328.9MiB 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 (fma.f64 (neg.f64 y) y (.f64 x x)) (fma.f64 y y (.f64 x x)))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 15 to 9 computations (40% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.1%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 15 to 9 computations (40% saved)

simplify320.0ms (5.2%)

Memory

-1.0MiB live, 236.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x y)
cost-diff	0	(-.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 (fma.f64 (neg.f64 y) y (.f64 x x)) (fma.f64 y y (.f64 x x)))
(*.f64 (-.f64 x y) (+.f64 x y))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(-.f64 x y)
x
y
(+.f64 x y)
(+.f64 y x)
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
(*.f64 y y)

localize24.0ms (0.4%)

Memory

12.6MiB live, 59.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	18.28638543818216	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Samples

18.0ms

256×

valid

Compiler

Compiled 45 to 11 computations (75.6% saved)

Precisions

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

ival-mult: 4.0ms (40.7% of total)

ival-div: 2.0ms (20.3% of total)

ival-add: 2.0ms (20.3% of total)

ival-sub: 1.0ms (10.2% of total)

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

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

series10.0ms (0.2%)

Memory

-16.7MiB live, 22.8MiB 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 x y) (patch (-.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 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 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 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 x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (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 (.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 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 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 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 (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 (.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 -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 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 y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (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 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 -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 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 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 (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 (.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 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 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 (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (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 (.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 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 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 -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (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>) () ())) ())

Calls

6 calls:

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

simplify132.0ms (2.1%)

Memory

11.3MiB live, 203.3MiB allocated

Algorithm

1×	egg-herbie

Rules

13 120×	`lower-fma.f64`
13 120×	`lower-fma.f32`
4 510×	`lower-*.f64`
4 510×	`lower-*.f32`
1 500×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	628
1	504	603
2	1609	563
3	6170	563
0	8190	525

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 111

Calls

Call 1

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

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

rewrite199.0ms (3.2%)

Memory

25.8MiB live, 223.7MiB 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	34
0	16	34
1	66	34
2	551	34
0	8160	32

Stop Event

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

Counts

6 → 569

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 x y))) (fma.f64 (-.f64 x y) x (*.f64 y y)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 2 binary64)) (pow.f64 (.f64 (-.f64 x y) y) #s(literal 2 binary64)))) (.f64 (-.f64 x y) (-.f64 x y)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 x y) y) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 x y) x) #s(literal 3 binary64)))) (fma.f64 (.f64 (-.f64 x y) y) (-.f64 (.f64 (-.f64 x y) y) (.f64 (-.f64 x y) x)) (pow.f64 (*.f64 (-.f64 x y) x) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x))) (fma.f64 (+.f64 y x) y (*.f64 x x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (fma.f64 (-.f64 x y) x (.f64 y y))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (/.f64 (fma.f64 y y (.f64 x x)) (-.f64 x y)) (-.f64 x y))
(.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 y x) (-.f64 y x))))
(.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))
(.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (+.f64 y x))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (.f64 y y))))
(.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 y y (.f64 x x))))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (neg.f64 y) y (.f64 x x))) (fma.f64 (neg.f64 y) y (.f64 x x)))
(.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))
(.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 y y (.f64 x x)) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 y y (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (-.f64 x y))) (+.f64 y x))
(/.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x)))
(/.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (+.f64 y x)) (neg.f64 (-.f64 x y)))
(/.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (-.f64 x y)) (neg.f64 (+.f64 y x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x)))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x)))) (.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (fma.f64 (neg.f64 y) y (*.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x))) (.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 2 binary64)))
(/.f64 (.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (-.f64 x y))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) (.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1 binary64) (.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (+.f64 y x) (-.f64 y x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x (*.f64 y y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (+.f64 y x))
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(.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)))
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(*.f64 (+.f64 y x) (/.f64 (neg.f64 (-.f64 x y)) (neg.f64 (-.f64 x y))))
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(*.f64 (-.f64 x y) (/.f64 (neg.f64 (+.f64 y x)) (neg.f64 (-.f64 x y))))
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(*.f64 (-.f64 x y) (/.f64 (+.f64 y x) (-.f64 x y)))
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(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))
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(/.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal 2 binary64)) (.f64 (*.f64 (-.f64 x y) (-.f64 x y)) (+.f64 y x)))
(/.f64 (.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 x y)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
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(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x y) x (*.f64 y y)))
(neg.f64 (neg.f64 (+.f64 y x)))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 (neg.f64 x) x (.f64 y y))) (neg.f64 (+.f64 y x)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
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(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) y))
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(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) y)
(fma.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (/.f64 x (.f64 (/.f64 (-.f64 x y) (fma.f64 (-.f64 x y) x (.f64 y y))) #s(literal 1 binary64))) (/.f64 x (fma.f64 (-.f64 x y) x (.f64 y y))) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
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(fma.f64 (/.f64 x (fma.f64 (neg.f64 y) y (.f64 x x))) (.f64 (+.f64 y x) x) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (neg.f64 y) (-.f64 (neg.f64 y) x) (.f64 x x)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (+.f64 y x) y (.f64 x x)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 (neg.f64 y) y (.f64 x x))) (+.f64 y x) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 y x) y) (.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (*.f64 x x)))
(fma.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (fma.f64 y y (.f64 x x)) (.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (*.f64 y x)))
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(fma.f64 #s(literal 1 binary64) y (*.f64 #s(literal 1 binary64) x))
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(fma.f64 (.f64 (+.f64 y x) y) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (*.f64 x x))) #s(literal 1 binary64))))
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(fma.f64 (.f64 x x) (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 x #s(literal 1 binary64) (*.f64 y #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (-.f64 x y))) (neg.f64 (+.f64 y x)))
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(-.f64 x (neg.f64 y))
(+.f64 (-.f64 x #s(literal 0 binary64)) y)
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(+.f64 (.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 y x) y)) (.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (.f64 x x)))
(+.f64 (.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (.f64 x x)) (.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 y x) y)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) y))
(+.f64 (.f64 #s(literal 1 binary64) y) (.f64 #s(literal 1 binary64) x))
(+.f64 (.f64 x (/.f64 x (-.f64 x y))) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
(+.f64 y x)
(+.f64 x (*.f64 #s(literal 1 binary64) y))
(+.f64 x (neg.f64 (neg.f64 y)))
(+.f64 x y)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 (neg.f64 y) #s(literal -1 binary64)) y)
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) (neg.f64 y))
(.f64 #s(literal 1 binary64) (.f64 y y))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval195.0ms (3.1%)

Memory: -6.0MiB live, 234.4MiB allocated
Compiler: Compiled 18 891 to 1 857 computations (90.2% saved)

prune17.0ms (0.3%)

Memory

-25.3MiB live, 49.4MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	675	5	680
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	676	5	681

Accuracy

100.0%

Counts

681 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.1%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
▶	40.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
▶	63.6%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))
▶	38.5%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
▶	62.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 82 to 66 computations (19.5% saved)

simplify149.0ms (2.4%)

Memory

30.4MiB live, 188.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

14 398×	`lower-fma.f32`
14 394×	`lower-fma.f64`
3 172×	`lower-*.f32`
3 166×	`lower-*.f64`
2 020×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	168
0	38	168
1	63	168
2	113	168
3	220	168
4	390	168
5	797	168
6	1860	168
7	4473	168
8	7658	168
0	8217	168

Stop Event

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

Calls

Call 1

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

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

localize117.0ms (1.9%)

Memory

-14.2MiB live, 150.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 2 binary64) y)
accuracy	0.09212875976844201	(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
accuracy	0.1015625	(*.f64 (/.f64 x y) x)
accuracy	23.292020032418357	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))
accuracy	0	(*.f64 (-.f64 x y) (+.f64 x y))
accuracy	0	(*.f64 y y)
accuracy	18.28638543818216	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
accuracy	19.07671479989851	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	39.38856855343794	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
accuracy	24.262043104118458	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))
accuracy	0	(*.f64 (-.f64 x y) (+.f64 x y))
accuracy	0	(*.f64 y y)
accuracy	0.0078125	(fma.f64 x x (*.f64 y y))
accuracy	18.28638543818216	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Samples

102.0ms

256×

valid

Compiler

Compiled 155 to 19 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-mult: 77.0ms (88.5% of total)

ival-div: 5.0ms (5.7% of total)

ival-add: 3.0ms (3.4% of total)

ival-sub: 1.0ms (1.1% of total)

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

exact: 0.0ms (0% of total)

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

series25.0ms (0.4%)

Memory

-33.1MiB live, 36.9MiB allocated

Counts

14 → 312

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (* y y) (* (- x y) (+ x y)))
1.0ms	y	@	0	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (* y y) (* (- x y) (+ x y)))
1.0ms	y	@	-inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (* y y) (* (- x y) (+ x y)))
1.0ms	x	@	-inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (* y y) (* (- x y) (+ x y)))
1.0ms	y	@	inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (* y y) (* (- x y) (+ x y)))

simplify163.0ms (2.6%)

Memory

-3.9MiB live, 187.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 974×	`lower-fma.f64`
12 974×	`lower-fma.f32`
3 796×	`lower-*.f64`
3 796×	`lower-*.f32`
2 836×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	195	2930
1	611	2679
2	1999	2395
0	8133	2234

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 303

Calls

Call 1

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

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

rewrite216.0ms (3.5%)

Memory

8.6MiB live, 328.1MiB allocated

Rules

8 068×	`lower-fma.f32`
8 064×	`lower-fma.f64`
6 628×	`lower-*.f32`
6 622×	`lower-*.f64`
4 604×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	139
0	38	139
1	128	139
2	938	139
0	9271	139

Stop Event

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

Counts

14 → 887

Calls

Call 1

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

Outputs
(.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 x x (*.f64 y y))) #s(literal 1 binary64)) (-.f64 x y))
(.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 (-.f64 y x) y (*.f64 x x)))
(.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64)) (+.f64 y x)) (-.f64 x y))
(.f64 (.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64)) (-.f64 x y)) (+.f64 y x))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (.f64 (-.f64 x y) (/.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (*.f64 (+.f64 y x) (-.f64 x y)))
(.f64 (.f64 (-.f64 x y) (/.f64 (+.f64 y x) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (/.f64 (/.f64 (fma.f64 x x (.f64 y y)) (-.f64 x y)) (+.f64 y x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (-.f64 x y)) (+.f64 y x)) #s(literal -1/2 binary64)))
(.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (+.f64 y x) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (.f64 y y)))))
(.f64 (/.f64 (-.f64 x y) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (+.f64 y x) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 y x) #s(literal -1 binary64)) (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))))
(.f64 (/.f64 (neg.f64 (+.f64 y x)) #s(literal -1 binary64)) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))
(.f64 (/.f64 (+.f64 y x) #s(literal -1 binary64)) (/.f64 (-.f64 y x) (fma.f64 x x (.f64 y y))))
(.f64 (/.f64 (-.f64 x y) #s(literal -1 binary64)) (/.f64 (neg.f64 (+.f64 y x)) (fma.f64 x x (.f64 y y))))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (/.f64 (/.f64 (+.f64 y x) (fma.f64 x x (*.f64 y y))) (+.f64 y x)))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (/.f64 (-.f64 x y) (fma.f64 x x (*.f64 y y)))))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (/.f64 (+.f64 y x) (fma.f64 x x (*.f64 y y)))))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (-.f64 x y) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (.f64 y y)))))
(.f64 (/.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (.f64 (*.f64 (-.f64 x y) (-.f64 x y)) (+.f64 y x)))
(.f64 (/.f64 (+.f64 y x) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 x y)))
(.f64 (/.f64 (+.f64 y x) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (-.f64 x y) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 2 binary64)))
(.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (+.f64 y x) (-.f64 x y))))
(.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (.f64 (+.f64 y x) (-.f64 x y))) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x)) (fma.f64 x x (.f64 y y))) (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (*.f64 y y))) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (*.f64 (+.f64 y x) (-.f64 x y)))
(.f64 (-.f64 y x) (.f64 (+.f64 y x) (/.f64 #s(literal -1 binary64) (fma.f64 x x (*.f64 y y)))))
(.f64 (neg.f64 (+.f64 y x)) (.f64 (-.f64 x y) (/.f64 #s(literal -1 binary64) (fma.f64 x x (*.f64 y y)))))
(.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 y x)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 y x) (fma.f64 x x (*.f64 y y)))))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (fma.f64 x x (*.f64 y y)))))
(.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (-.f64 x y))
(.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y)))))
(.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y)))))
(.f64 (.f64 (+.f64 y x) (-.f64 x y)) (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)) (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y)))))
(.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y)))))
(.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) (/.f64 #s(literal -1 binary64) (fma.f64 x x (*.f64 y y))))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 y x) (fma.f64 x x (*.f64 y y))) (-.f64 x y)))
(.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) (fma.f64 x x (*.f64 y y))))
(.f64 (+.f64 y x) (.f64 (-.f64 y x) (/.f64 #s(literal -1 binary64) (fma.f64 x x (*.f64 y y)))))
(.f64 (+.f64 y x) (.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1 binary64)) (-.f64 x y)))
(.f64 (+.f64 y x) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))
(.f64 (-.f64 x y) (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))))
(pow.f64 (/.f64 (/.f64 (fma.f64 x x (*.f64 y y)) (-.f64 x y)) (+.f64 y x)) #s(literal -1 binary64))
(/.f64 (.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64)))))
(/.f64 (.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)))) (+.f64 (pow.f64 x #s(literal 8 binary64)) (.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))
(/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 x x (.f64 y y))) (fma.f64 (neg.f64 x) x (*.f64 y y))) (neg.f64 (+.f64 y x)))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal -1 binary64)) (neg.f64 (fma.f64 x x (*.f64 y y))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 x y))) (fma.f64 (-.f64 y x) y (.f64 x x)))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (fma.f64 y (+.f64 y x) (.f64 x x)))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (+.f64 y x))) (-.f64 x y))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (-.f64 x y) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 (-.f64 y x) y (.f64 x x)))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 2 binary64)) (pow.f64 (.f64 (-.f64 x y) y) #s(literal 2 binary64)))) (*.f64 (-.f64 x y) (-.f64 x y)))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (+.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 x y) y) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 x y) y) (-.f64 (.f64 (-.f64 x y) y) (*.f64 (-.f64 x y) x)))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (.f64 (-.f64 x y) (fma.f64 y (+.f64 y x) (.f64 x x))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (+.f64 y x) (-.f64 x y)))) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (pow.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 2 binary64))) (.f64 (+.f64 y x) (-.f64 x y)))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (.f64 (+.f64 y x) (fma.f64 (-.f64 y x) y (.f64 x x))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x)) (-.f64 x y))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (fma.f64 (-.f64 y x) y (.f64 x x))))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 y x))) (+.f64 y x))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x))) (fma.f64 y (+.f64 y x) (.f64 x x)))
(/.f64 (.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 x x (*.f64 y y)))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 x y) y) (-.f64 (.f64 (-.f64 x y) y) (.f64 (-.f64 x y) x)))) (+.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 x y) y) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 x y) (fma.f64 y (+.f64 y x) (.f64 x x))) (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (+.f64 y x) (-.f64 x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (fma.f64 y (+.f64 y x) (*.f64 x x))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (pow.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 y x) (fma.f64 (-.f64 y x) y (.f64 x x))) (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x)) (-.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (fma.f64 (-.f64 y x) y (.f64 x x))) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y x) (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (*.f64 y y)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (+.f64 y x) (pow.f64 (-.f64 x y) #s(literal -1 binary64)))
(/.f64 (-.f64 x y) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))
(fma.f64 (.f64 x (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (fma.f64 y (+.f64 y x) (.f64 x x)) (.f64 (neg.f64 y) (+.f64 y x)))
(fma.f64 (.f64 (+.f64 y x) #s(literal -1 binary64)) y (.f64 (+.f64 y x) x))
(fma.f64 (.f64 y (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 (-.f64 y x) y (.f64 x x)) (.f64 (-.f64 x y) x))
(fma.f64 (.f64 (neg.f64 y) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (fma.f64 y (+.f64 y x) (.f64 x x)) (.f64 x (+.f64 y x)))
(fma.f64 (.f64 x (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 (-.f64 y x) y (.f64 x x)) (.f64 (-.f64 x y) y))
(fma.f64 (.f64 (neg.f64 y) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) (*.f64 x (+.f64 y x)))
(fma.f64 (.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) (*.f64 (neg.f64 y) (+.f64 y x)))
(fma.f64 (.f64 (neg.f64 y) (.f64 (+.f64 y x) (-.f64 x y))) (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (*.f64 x (+.f64 y x)))
(fma.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (+.f64 y x) (.f64 x (+.f64 y x)))
(fma.f64 (/.f64 y (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (fma.f64 y (+.f64 y x) (.f64 x x))) (.f64 (-.f64 x y) x))
(fma.f64 (/.f64 y (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64))) (*.f64 (-.f64 x y) x))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 y (fma.f64 y (+.f64 y x) (.f64 x x))) (.f64 (-.f64 x y) x))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 x (fma.f64 y (+.f64 y x) (.f64 x x))) (.f64 (-.f64 x y) y))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (/.f64 y (+.f64 y x)) (.f64 (-.f64 x y) x))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (/.f64 x (+.f64 y x)) (.f64 (-.f64 x y) y))
(fma.f64 (/.f64 x (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (fma.f64 y (+.f64 y x) (.f64 x x))) (.f64 (-.f64 x y) y))
(fma.f64 (/.f64 x #s(literal 1 binary64)) (-.f64 x y) (*.f64 (-.f64 x y) y))
(fma.f64 (/.f64 x (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64))) (*.f64 (-.f64 x y) y))
(fma.f64 (/.f64 y (.f64 (+.f64 y x) (-.f64 x y))) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (+.f64 y x)) (.f64 (-.f64 x y) x))
(fma.f64 (/.f64 x (.f64 (+.f64 y x) (-.f64 x y))) (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (+.f64 y x)) (.f64 (-.f64 x y) y))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (fma.f64 (neg.f64 y) x (*.f64 (-.f64 x y) y)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 (neg.f64 y) y))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (neg.f64 y)) (.f64 (+.f64 y x) x))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) x) (.f64 (+.f64 y x) (neg.f64 y)))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) y) (.f64 (-.f64 x y) x))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) x) (.f64 (-.f64 x y) y))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 y (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64))) (*.f64 (-.f64 x y) x))
(fma.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 x (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64))) (*.f64 (-.f64 x y) y))
(fma.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) y) (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (*.f64 (-.f64 x y) x))
(fma.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) y) (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)) (*.f64 (-.f64 x y) x))
(fma.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) x) (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (*.f64 (-.f64 x y) y))
(fma.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) x) (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)) (*.f64 (-.f64 x y) y))
(fma.f64 (fma.f64 (.f64 x x) y (pow.f64 (neg.f64 y) #s(literal 3 binary64))) (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (.f64 (-.f64 x y) x))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) y (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)) (.f64 (-.f64 x y) x))
(fma.f64 (.f64 (.f64 x (+.f64 y x)) (-.f64 x y)) (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (*.f64 (neg.f64 y) (+.f64 y x)))
(fma.f64 (.f64 (.f64 x (+.f64 y x)) (-.f64 x y)) (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (*.f64 (-.f64 x y) y))
(fma.f64 (.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)) (*.f64 (-.f64 x y) y))
(fma.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (neg.f64 y)) (*.f64 (+.f64 y x) x))
(fma.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) y) (*.f64 (-.f64 x y) x))
(fma.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) x) (*.f64 (+.f64 y x) (neg.f64 y)))
(fma.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) x) (*.f64 (-.f64 x y) y))
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)) y) (*.f64 (-.f64 x y) x))
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) #s(literal -1 binary64)) x) (*.f64 (-.f64 x y) y))
(fma.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) (neg.f64 y)) (*.f64 (+.f64 y x) x))
(fma.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) x) (*.f64 (+.f64 y x) (neg.f64 y)))
(fma.f64 (neg.f64 y) (+.f64 y x) (*.f64 x (+.f64 y x)))
(fma.f64 #s(literal 1 binary64) (.f64 (+.f64 y x) (neg.f64 y)) (.f64 (+.f64 y x) x))
(fma.f64 #s(literal 1 binary64) (.f64 (+.f64 y x) x) (.f64 (+.f64 y x) (neg.f64 y)))
(fma.f64 #s(literal 1 binary64) (.f64 (-.f64 x y) y) (.f64 (-.f64 x y) x))
(fma.f64 #s(literal 1 binary64) (.f64 (-.f64 x y) x) (.f64 (-.f64 x y) y))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (fma.f64 (neg.f64 y) x (.f64 (-.f64 x y) y)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (neg.f64 y) y))
(fma.f64 #s(literal -1 binary64) (.f64 y (+.f64 y x)) (.f64 x (+.f64 y x)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (fma.f64 (neg.f64 y) x (.f64 (-.f64 x y) y)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (neg.f64 y) y))
(fma.f64 (+.f64 y x) (neg.f64 y) (*.f64 (+.f64 y x) x))
(fma.f64 (+.f64 y x) x (*.f64 (+.f64 y x) (neg.f64 y)))
(fma.f64 (-.f64 x y) y (*.f64 (-.f64 x y) x))
(fma.f64 (-.f64 x y) x (*.f64 (-.f64 x y) y))
(fma.f64 y (-.f64 x y) (*.f64 (-.f64 x y) x))
(fma.f64 y x (fma.f64 (neg.f64 y) y (*.f64 (-.f64 x y) x)))
(fma.f64 x (+.f64 y x) (*.f64 (neg.f64 y) (+.f64 y x)))
(fma.f64 x (-.f64 x y) (*.f64 (-.f64 x y) y))
(fma.f64 x y (fma.f64 (neg.f64 y) y (*.f64 (-.f64 x y) x)))
(fma.f64 x x (fma.f64 (neg.f64 y) x (*.f64 (-.f64 x y) y)))
(fma.f64 x x (*.f64 (neg.f64 y) y))
(-.f64 (/.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 2 binary64)) (.f64 (-.f64 x y) (-.f64 x y))) (/.f64 (pow.f64 (.f64 (-.f64 x y) y) #s(literal 2 binary64)) (.f64 (-.f64 x y) (-.f64 x y))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (.f64 y y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 x x (.f64 y y))))
(-.f64 #s(literal 0 binary64) (fma.f64 (neg.f64 x) x (*.f64 y y)))
(-.f64 (.f64 x x) (.f64 y y))
(+.f64 (fma.f64 (-.f64 x y) y (.f64 x x)) (.f64 (neg.f64 y) x))
(+.f64 (fma.f64 (-.f64 x y) x (.f64 y x)) (.f64 (neg.f64 y) y))
(+.f64 (neg.f64 (.f64 (-.f64 y x) x)) (neg.f64 (.f64 (-.f64 y x) y)))
(+.f64 (.f64 (neg.f64 y) (+.f64 y x)) (.f64 x (+.f64 y x)))
(+.f64 (.f64 x (+.f64 y x)) (.f64 (neg.f64 y) (+.f64 y x)))
(+.f64 (.f64 (+.f64 y x) (neg.f64 y)) (.f64 (+.f64 y x) x))
(+.f64 (.f64 (+.f64 y x) x) (.f64 (+.f64 y x) (neg.f64 y)))
(+.f64 (.f64 (-.f64 x y) y) (.f64 (-.f64 x y) x))
(+.f64 (.f64 (-.f64 x y) x) (.f64 (-.f64 x y) y))
(+.f64 (.f64 y x) (fma.f64 (neg.f64 y) y (.f64 (-.f64 x y) x)))
(+.f64 (.f64 x x) (fma.f64 (neg.f64 y) x (.f64 (-.f64 x y) y)))
(+.f64 (.f64 x x) (.f64 (neg.f64 y) y))

eval255.0ms (4.1%)

Memory: 46.8MiB live, 383.3MiB allocated
Compiler: Compiled 40 646 to 3 124 computations (92.3% saved)

prune46.0ms (0.7%)

Memory

-22.1MiB live, 99.2MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1 671	3	1 674
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	1 672	7	1 679

Accuracy

100.0%

Counts

1 679 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.1%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
✓	40.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
▶	41.2%	(.f64 (+.f64 y x) (/.f64 (-.f64 x y) #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
▶	40.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 y #s(literal -2 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))
▶	55.3%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64)))
✓	38.5%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
✓	62.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 66 to 52 computations (21.2% saved)

simplify145.0ms (2.3%)

Memory

18.6MiB live, 133.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

11 828×	`lower-fma.f32`
11 824×	`lower-fma.f64`
2 596×	`lower-*.f32`
2 586×	`lower-*.f64`
1 712×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	168
0	43	168
1	85	166
2	173	166
3	385	166
4	792	166
5	1513	166
6	2989	166
7	5643	166
0	8140	159

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

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

localize60.0ms (1%)

Memory

-5.8MiB live, 105.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.139003759768442	(.f64 (+.f64 y x) (/.f64 (-.f64 x y) #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
accuracy	17.675838457216557	(/.f64 (-.f64 x y) #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	19.07671479989851	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	0	(/.f64 y x)
accuracy	0	(*.f64 y #s(literal -2 binary64))
accuracy	0.13900375976844204	(fma.f64 (/.f64 (*.f64 y #s(literal -2 binary64)) x) (/.f64 y x) #s(literal 1 binary64))
accuracy	38.309762423316975	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 y #s(literal -2 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	0.22452169042460723	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	14.253265272393973	(fma.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64))
accuracy	23.292020032418357	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1 binary64)))

Samples

44.0ms

256×

valid

Compiler

Compiled 136 to 27 computations (80.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 11.0ms (37.9% of total)

ival-div: 8.0ms (27.5% of total)

ival-add: 7.0ms (24.1% of total)

ival-sub: 2.0ms (6.9% of total)

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

exact: 0.0ms (0% of total)

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

series44.0ms (0.7%)

Memory

-12.6MiB live, 48.1MiB allocated

Counts

16 → 324

Calls

Call 1

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

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

Calls

6 calls:

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

simplify163.0ms (2.6%)

Memory

14.1MiB live, 169.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 708×	`lower-fma.f64`
8 708×	`lower-fma.f32`
2 958×	`lower-*.f64`
2 958×	`lower-*.f32`
2 918×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	259	2378
1	769	2327
2	2279	2242
3	6640	2242
0	8211	2112

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 315

Calls

Call 1

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

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

rewrite164.0ms (2.6%)

Memory

-7.8MiB live, 216.3MiB allocated

Rules

4 982×	`lower-/.f32`
4 974×	`lower-/.f64`
4 478×	`lower-*.f32`
4 468×	`lower-*.f64`
4 326×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	154
0	43	152
1	181	148
2	1508	148
0	8255	143

Stop Event

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

Counts

16 → 527

Calls

Call 1

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

Outputs
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 x x)))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(.f64 x (.f64 #s(literal 2 binary64) x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 y #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 y y)))
(*.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -2 binary64)))
(pow.f64 (/.f64 y (pow.f64 y #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (*.f64 (neg.f64 y) y)) #s(literal -1 binary64))
(pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 y y) #s(literal -1 binary64))
(pow.f64 y #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (pow.f64 y #s(literal -1 binary64)))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (pow.f64 y #s(literal -1 binary64))) (neg.f64 y))
(/.f64 (pow.f64 y #s(literal -1 binary64)) y)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 y (pow.f64 y #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (*.f64 (neg.f64 y) y))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 y) y))
(/.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 y #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 y) y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 y y)))
(exp.f64 (neg.f64 (*.f64 (log.f64 y) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 y) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal -1 binary64)))
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal 1 binary64)))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (+.f64 (/.f64 (.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) (-.f64 (/.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))) (/.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))) (fma.f64 (pow.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))) (pow.f64 (fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))) (.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) (fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) y) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -2 binary64) y) y)) (.f64 x x)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) y) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -2 binary64) y) y)) (.f64 x x))))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) (-.f64 (/.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) (-.f64 (/.f64 (pow.f64 (.f64 (*.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal -8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))))
(fma.f64 (/.f64 (/.f64 y x) #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) (/.f64 (neg.f64 y) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) x) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) (/.f64 y (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) x) (/.f64 (*.f64 #s(literal -2 binary64) y) (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) x) (/.f64 y (pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) #s(literal -1 binary64)) (/.f64 (/.f64 y x) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 y) x) (/.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) (/.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) x) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (/.f64 y x) (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (*.f64 y y) x) #s(literal 1 binary64))
(fma.f64 (.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) y) (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 y x) (pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 y x) (/.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 y x) (/.f64 (/.f64 #s(literal -2 binary64) x) (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 y x) (.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal -2 binary64) y) x) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (.f64 (/.f64 y x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -2 binary64) y) (/.f64 (/.f64 y x) x) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal -2 binary64) y) (pow.f64 (.f64 x (/.f64 x y)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))
(fma.f64 y (pow.f64 (.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 x y))) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 y (*.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 y x)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x)))) (/.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64))) (pow.f64 (fma.f64 (/.f64 y x) (/.f64 (.f64 #s(literal -2 binary64) y) x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) y) (/.f64 #s(literal -2 binary64) x)))
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) x))
(*.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) x))
(*.f64 (/.f64 #s(literal -2 binary64) x) y)
(.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 #s(literal -2 binary64) y) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 x #s(literal -1 binary64)) (.f64 #s(literal -2 binary64) y))
(.f64 (.f64 #s(literal 2 binary64) y) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal -2 binary64) y) (pow.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (/.f64 y x))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -2 binary64) y) x))
(*.f64 #s(literal 2 binary64) (/.f64 (neg.f64 y) x))
(*.f64 y (/.f64 #s(literal -2 binary64) x))
(pow.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) y))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal -2 binary64) y) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) y)) (neg.f64 (neg.f64 x)))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)) x)
(/.f64 (*.f64 #s(literal 2 binary64) y) (neg.f64 x))
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(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 (.f64 (pow.f64 y #s(literal -2 binary64)) x) (.f64 #s(literal 2 binary64) x)))) (/.f64 (.f64 (pow.f64 y #s(literal -4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (.f64 (.f64 (pow.f64 y #s(literal -2 binary64)) x) (*.f64 #s(literal 2 binary64) x)))))
(-.f64 (/.f64 (.f64 (pow.f64 y #s(literal -4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 y #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (pow.f64 y #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 (pow.f64 y #s(literal -2 binary64)) x) (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 (pow.f64 y #s(literal -2 binary64)) x) (*.f64 #s(literal 2 binary64) x)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) y)
(*.f64 (neg.f64 y) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 y (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 y))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (*.f64 y #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 x)))
(/.f64 (*.f64 y #s(literal 1 binary64)) x)
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x y) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x y)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 y x)
(neg.f64 (/.f64 (neg.f64 y) x))
(neg.f64 (/.f64 y (neg.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 y (neg.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 (neg.f64 y) (neg.f64 y))
(.f64 (.f64 y y) #s(literal 1 binary64))
(*.f64 y (/.f64 y #s(literal 1 binary64)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (pow.f64 y #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 y) y)) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 y) y) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 y #s(literal -2 binary64))))
(/.f64 (*.f64 y y) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 y y) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval163.0ms (2.6%)

Memory: 13.2MiB live, 270.9MiB allocated
Compiler: Compiled 16 901 to 2 052 computations (87.9% saved)

prune55.0ms (0.9%)

Memory

-20.4MiB live, 58.8MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	871	1	872
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	873	6	879

Accuracy

100.0%

Counts

879 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.1%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
✓	40.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
✓	40.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 y #s(literal -2 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))
▶	56.3%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64)))
✓	38.5%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
✓	62.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 52 to 42 computations (19.2% saved)

simplify155.0ms (2.5%)

Memory

-0.2MiB live, 157.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

13 222×	`lower-fma.f32`
13 220×	`lower-fma.f64`
2 592×	`lower-*.f32`
2 588×	`lower-*.f64`
1 964×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	55
0	21	55
1	43	55
2	93	55
3	194	55
4	323	55
5	653	55
6	1441	55
7	3511	55
8	7008	55
0	8098	54

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

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

localize31.0ms (0.5%)

Memory

26.8MiB live, 26.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64))
accuracy	4.03895749525198	(fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))
accuracy	9.388546108890024	(/.f64 x (*.f64 y y))
accuracy	23.292020032418357	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64)))

Samples

23.0ms

256×

valid

Compiler

Compiled 47 to 17 computations (63.8% saved)

Precisions

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

ival-mult: 7.0ms (45.3% of total)

ival-div: 3.0ms (19.4% of total)

ival-add: 3.0ms (19.4% of total)

ival-sub: 1.0ms (6.5% of total)

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

exact: 0.0ms (0% of total)

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

series62.0ms (1%)

Memory

-17.8MiB live, 20.7MiB allocated

Counts

4 → 96

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
51.0ms	y	@	0	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x (* (/ x (* y y)) 2)) -1) (* (/ x (* y y)) 2) (/ x (* y y)))
3.0ms	x	@	0	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x (* (/ x (* y y)) 2)) -1) (* (/ x (* y y)) 2) (/ x (* y y)))
1.0ms	x	@	-inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x (* (/ x (* y y)) 2)) -1) (* (/ x (* y y)) 2) (/ x (* y y)))
1.0ms	x	@	inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x (* (/ x (* y y)) 2)) -1) (* (/ x (* y y)) 2) (/ x (* y y)))
1.0ms	y	@	inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x (* (/ x (* y y)) 2)) -1) (* (/ x (* y y)) 2) (/ x (* y y)))

simplify202.0ms (3.3%)

Memory

18.5MiB live, 131.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 252×	`lower-fma.f64`
10 252×	`lower-fma.f32`
4 324×	`lower-*.f64`
4 324×	`lower-*.f32`
1 768×	`lower-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	139	809
1	426	786
2	1394	786
3	5002	740
0	8126	702

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite343.0ms (5.5%)

Memory

-39.5MiB live, 262.0MiB allocated

Rules

7 502×	`lower-fma.f32`
7 500×	`lower-fma.f64`
6 254×	`lower-*.f32`
6 250×	`lower-*.f64`
4 712×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
0	21	48
1	98	48
2	790	48
0	8567	47

Stop Event

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

Counts

4 → 151

Calls

Call 1

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

Outputs
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (*.f64 y y))) x))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x (.f64 y y)) x) #s(literal 2 binary64)) #s(literal 4 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -2 binary64) (.f64 (/.f64 x (*.f64 y y)) x) #s(literal -1 binary64))))
(.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x (.f64 y y)) x) #s(literal 2 binary64)) #s(literal 4 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x))))))
(.f64 (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x (.f64 y y)) x) #s(literal 2 binary64)) #s(literal 4 binary64) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (*.f64 y y))) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (*.f64 y y))) x #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 x (.f64 y y)) x) (-.f64 (.f64 #s(literal 4 binary64) (.f64 (/.f64 x (*.f64 y y)) x)) #s(literal -2 binary64))))))
(.f64 (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x (.f64 y y)) x) #s(literal 2 binary64)) #s(literal 4 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x))) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x #s(literal 1 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 (.f64 (/.f64 x (.f64 y y)) x) #s(literal 2 binary64)) #s(literal 4 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x #s(literal 1 binary64)) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x (.f64 y y)) x) #s(literal 2 binary64)) #s(literal 4 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (*.f64 y y))) x))) #s(literal -1 binary64))) (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 3 binary64)) #s(literal 512 binary64) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x (.f64 y y)) x) #s(literal 2 binary64)) #s(literal 4 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 y y))) x) #s(literal 6 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -8 binary64))))
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(/.f64 (/.f64 x y) (neg.f64 (neg.f64 y)))
(/.f64 (/.f64 x y) y)
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 y y) x))
(/.f64 (neg.f64 x) (*.f64 (neg.f64 y) y))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 y) (/.f64 y x)))
(/.f64 x (*.f64 y y))
(neg.f64 (/.f64 (/.f64 (neg.f64 x) y) y))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 y y) x)))
(neg.f64 (/.f64 (/.f64 x y) (neg.f64 y)))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) (pow.f64 y #s(literal -2 binary64)))))
(neg.f64 (*.f64 (neg.f64 x) (pow.f64 y #s(literal -2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 y) y)) (.f64 (neg.f64 x) (pow.f64 y #s(literal -2 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (pow.f64 y #s(literal -2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 y y) x)) #s(literal -1 binary64)))

eval55.0ms (0.9%)

Memory: 14.2MiB live, 52.4MiB allocated
Compiler: Compiled 4 006 to 627 computations (84.3% saved)

prune27.0ms (0.4%)

Memory

-12.6MiB live, 24.8MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	247	6	253

Accuracy

100.0%

Counts

253 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.1%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
✓	40.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
✓	40.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 y #s(literal -2 binary64)) x) (/.f64 y x) #s(literal 1 binary64)))
✓	56.3%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64)))
✓	38.5%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
✓	62.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 155 to 82 computations (47.1% saved)

regimes97.0ms (1.6%)

Memory

23.9MiB live, 104.7MiB allocated

Counts

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

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

Calls

3 calls:

60.0ms	y
33.0ms	x
4.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Results

Accuracy	Segments	Branch
88.3%	2	`x`
95.0%	4	`y`
93.7%	2	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes38.0ms (0.6%)

Memory

-31.1MiB live, 91.6MiB allocated

Counts

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

Outputs

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

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

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

Calls

2 calls:

31.0ms	y
7.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Results

Accuracy	Segments	Branch
86.9%	4	`y`
93.2%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes5.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

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

Outputs

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
93.1%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes5.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

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

Outputs

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
92.8%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

2 → 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))

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:

4.0ms

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

Results

Accuracy	Segments	Branch
92.5%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes8.0ms (0.1%)

Memory

-18.9MiB live, 20.1MiB 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:

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
62.1%	1	`y`
62.1%	1	`x`
62.1%	1	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 17 to 13 computations (23.5% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.9796035880541963	-0.2786611233824196

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.2786611233824196	1.0

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.2786611233824196	1.0

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch34.0ms (0.5%)

Memory

-4.2MiB live, 34.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	predicate-failed
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1.0	NaN
13.0ms	-0.2786611233824196	1.0

Samples

8.0ms	416×	0	valid
2.0ms	101×	0	invalid

Compiler

Compiled 122 to 274 computations (-124.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

simplify24.0ms (0.4%)

Memory

27.8MiB live, 27.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`-commutative-binary64-.f64`
8×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	477
1	67	477
2	70	477
3	72	477
4	73	477

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 x x (.f64 y y))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #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 x (.f64 (/.f64 x (.f64 y y)) #s(literal 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))) (fma.f64 (/.f64 (.f64 y #s(literal -2 binary64)) x) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 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 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 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))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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 +inf.0 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 x x (.f64 y y))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal 2 binary64)) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (fma.f64 x x (.f64 y y))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #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 x (.f64 (/.f64 x (.f64 y y)) #s(literal 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))) (fma.f64 (/.f64 (.f64 y #s(literal -2 binary64)) x) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -1/2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal 2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 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 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #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 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 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))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 x (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)) #s(literal -1 binary64))) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #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))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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 +inf.0 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))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal +inf.0 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))

soundness889.0ms (14.4%)

Memory

4.3MiB live, 748.5MiB allocated

Rules

13 120×	`lower-fma.f64`
13 120×	`lower-fma.f32`
12 974×	`lower-fma.f64`
12 974×	`lower-fma.f32`
8 068×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	139
0	38	139
1	128	139
2	938	139
0	9271	139
0	160	628
1	504	603
2	1609	563
3	6170	563
0	8190	525
0	195	2930
1	611	2679
2	1999	2395
0	8133	2234
0	29	154
0	43	152
1	181	148
2	1508	148
0	8255	143
0	9	34
0	16	34
1	66	34
2	551	34
0	8160	32

Stop Event

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

Compiler

Compiled 413 to 169 computations (59.1% saved)

preprocess95.0ms (1.5%)

Memory

-5.3MiB live, 206.1MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 820 to 240 computations (70.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze5.0ms (0.1%)

sample937.0ms (15.1%)

explain109.0ms (1.8%)

preprocess403.0ms (6.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify320.0ms (5.2%)

localize24.0ms (0.4%)

series10.0ms (0.2%)

simplify132.0ms (2.1%)

rewrite199.0ms (3.2%)

eval195.0ms (3.1%)

prune17.0ms (0.3%)

simplify149.0ms (2.4%)

localize117.0ms (1.9%)

series25.0ms (0.4%)

simplify163.0ms (2.6%)

rewrite216.0ms (3.5%)

eval255.0ms (4.1%)

prune46.0ms (0.7%)

simplify145.0ms (2.3%)

localize60.0ms (1%)

series44.0ms (0.7%)

simplify163.0ms (2.6%)

rewrite164.0ms (2.6%)

eval163.0ms (2.6%)

prune55.0ms (0.9%)

simplify155.0ms (2.5%)

localize31.0ms (0.5%)

series62.0ms (1%)

simplify202.0ms (3.3%)

rewrite343.0ms (5.5%)

eval55.0ms (0.9%)

prune27.0ms (0.4%)

regimes97.0ms (1.6%)

regimes38.0ms (0.6%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch34.0ms (0.5%)

simplify24.0ms (0.4%)

soundness889.0ms (14.4%)

preprocess95.0ms (1.5%)

end0.0ms (0%)

Profiling