Metrics for Kahan p9 Example

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze5.0ms (0.1%)

Memory

14.9MiB live, 14.9MiB 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)

sample1.1s (15.6%)

Memory

32.1MiB live, 2 485.8MiB allocated

Samples

662.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 466.0ms

ival-mult: 162.0ms (34.8% of total)

ival-add: 91.0ms (19.5% of total)

ival-<: 69.0ms (14.8% of total)

ival-sub: 59.0ms (12.7% of total)

ival-div: 53.0ms (11.4% of total)

ival-and: 17.0ms (3.7% of total)

exact: 11.0ms (2.4% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain114.0ms (1.7%)

Memory

-42.1MiB live, 249.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
73	-	-	`(/.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	41	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	overflow	41
↳	`(*.f64 y y)`	overflow	41
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	41
`/.f64`	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`	u/u	32	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	underflow	32
↳	`(*.f64 y y)`	underflow	83
↳	`(*.f64 x x)`	underflow	107
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	32

Confusion

	Predicted +	Predicted -
+	73	0
-	0	183

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	73	0	0
-	0	0	183

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	183
1	73

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 105 to 31 computations (70.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 10.0ms (44.3% of total)

ival-add: 5.0ms (22.1% of total)

ival-sub: 3.0ms (13.3% of total)

ival-div: 3.0ms (13.3% of total)

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

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

preprocess377.0ms (5.5%)

Memory

32.7MiB live, 226.2MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 15 to 9 computations (40% saved)

simplify347.0ms (5.1%)

Memory

-33.3MiB live, 219.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize25.0ms (0.4%)

Memory

5.9MiB live, 44.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 (.f64 x x) (.f64 y y))
accuracy	18.07903021872248	(/.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: 11.0ms

ival-mult: 5.0ms (44.8% of total)

ival-div: 2.0ms (17.9% of total)

ival-add: 2.0ms (17.9% of total)

ival-sub: 1.0ms (9% of total)

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

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

series9.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB 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
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))
1.0ms	x	@	0	((+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (* x x) (* y y))

simplify125.0ms (1.8%)

Memory

-17.2MiB live, 134.9MiB 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)

rewrite141.0ms (2.1%)

Memory

33.1MiB live, 146.6MiB 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
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eval81.0ms (1.2%)

Memory: 0.1MiB live, 156.1MiB allocated
Compiler: Compiled 18 891 to 1 857 computations (90.2% saved)

prune16.0ms (0.2%)

Memory

-27.4MiB live, 50.0MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	672	8	680
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	673	8	681

Accuracy

99.8%

Counts

681 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.3%	(/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (+.f64 y x))
▶	71.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	42.3%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
	71.3%	(.f64 (/.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (+.f64 y x))
▶	67.0%	#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)))
▶	31.0%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
	34.4%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
▶	65.3%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 176 to 120 computations (31.8% saved)

simplify189.0ms (2.8%)

Memory

22.9MiB live, 224.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 y x)
cost-diff	0	(/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x x)))
cost-diff	0	(.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x)))
cost-diff	1536	(/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (+.f64 y x))
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	(/.f64 #s(literal -2 binary64) (*.f64 x x))
cost-diff	0	(.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y)
cost-diff	0	(fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 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	128	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Rules

15 872×	`lower-fma.f32`
15 862×	`lower-fma.f64`
3 682×	`lower-*.f32`
3 670×	`lower-*.f64`
2 402×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	232
0	58	224
1	108	224
2	223	224
3	496	224
4	1309	224
5	4001	224
0	8453	224

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

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

localize80.0ms (1.2%)

Memory

12.6MiB live, 122.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 y y (*.f64 x x))
accuracy	0.01953125	(/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (+.f64 y x))
accuracy	17.733229144723204	(/.f64 (+.f64 y x) (fma.f64 y y (*.f64 x x)))
accuracy	17.747258730931414	(.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x)))
accuracy	0	(/.f64 #s(literal 2 binary64) y)
accuracy	0.06478500976844201	(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
accuracy	0.1484375	(*.f64 (/.f64 x y) x)
accuracy	21.12859933652683	#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	0.1171875	(/.f64 #s(literal -2 binary64) (*.f64 x x))
accuracy	5.39571798552481	(fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64))
accuracy	8.048623140984951	(.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y)
accuracy	40.446455216399954	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
accuracy	22.178573434992373	#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	0.00390625	(fma.f64 x x (*.f64 y y))
accuracy	18.07903021872248	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Samples

58.0ms

256×

valid

Compiler

Compiled 224 to 32 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 14.0ms (36.2% of total)

ival-div: 10.0ms (25.8% of total)

ival-add: 8.0ms (20.7% of total)

ival-neg: 5.0ms (12.9% of total)

ival-sub: 2.0ms (5.2% of total)

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

exact: 0.0ms (0% of total)

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

series42.0ms (0.6%)

Memory

-17.0MiB live, 62.4MiB allocated

Counts

20 → 444

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

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	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))) (+ (* (* (/ -2 (* x x)) y) y) 1) (* (/ -2 (* x x)) y) (/ -2 (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (/ (+ y x) (+ (* y y) (* x x))) (+ y x) (* y y) (* (- x y) (+ x y)) (+ (* y y) (* x x)))
3.0ms	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))) (+ (* (* (/ -2 (* x x)) y) y) 1) (* (/ -2 (* x x)) y) (/ -2 (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (/ (+ y x) (+ (* y y) (* x x))) (+ y x) (* y y) (* (- x y) (+ x y)) (+ (* y y) (* x x)))
3.0ms	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))) (+ (* (* (/ -2 (* x x)) y) y) 1) (* (/ -2 (* x x)) y) (/ -2 (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (/ (+ y x) (+ (* y y) (* x x))) (+ y x) (* y y) (* (- x y) (+ x y)) (+ (* y y) (* x x)))
3.0ms	x	@	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))) (+ (* (* (/ -2 (* x x)) y) y) 1) (* (/ -2 (* x x)) y) (/ -2 (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (/ (+ y x) (+ (* y y) (* x x))) (+ y x) (* y y) (* (- x y) (+ x y)) (+ (* y y) (* x x)))
3.0ms	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))) (+ (* (* (/ -2 (* x x)) y) y) 1) (* (/ -2 (* x x)) y) (/ -2 (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (/ (+ y x) (+ (* y y) (* x x))) (+ y x) (* y y) (* (- x y) (+ x y)) (+ (* y y) (* x x)))

simplify173.0ms (2.5%)

Memory

31.4MiB live, 225.0MiB allocated

Algorithm

1×	egg-herbie

Rules

8 792×	`lower-fma.f64`
8 792×	`lower-fma.f32`
3 478×	`lower-*.f64`
3 478×	`lower-*.f32`
3 172×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	399	4482
1	1249	4126
2	3826	3684
0	8354	3456

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 426

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

rewrite232.0ms (3.4%)

Memory

-4.4MiB live, 285.0MiB allocated

Rules

5 550×	`lower-/.f32`
5 538×	`lower-/.f64`
4 118×	`lower-fma.f32`
4 108×	`lower-fma.f64`
3 664×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	201
0	58	193
1	227	193
2	1931	193
0	8160	193

Stop Event

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

Counts

20 → 1 162

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

Outputs
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eval433.0ms (6.3%)

Memory: 6.4MiB live, 376.6MiB allocated
Compiler: Compiled 43 818 to 3 907 computations (91.1% saved)

prune107.0ms (1.6%)

Memory

-30.9MiB live, 114.4MiB allocated

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	1 639	5	1 644
Fresh	2	1	3
Picked	0	5	5
Done	0	0	0
Total	1 641	11	1 652

Accuracy

99.9%

Counts

1 652 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.3%	(/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (fma.f64 (neg.f64 y) y (*.f64 x x))) (+.f64 y x))
✓	71.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	67.0%	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y))) (+.f64 y x))
▶	64.9%	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y)) (+.f64 y x))
▶	71.3%	(.f64 (/.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (+.f64 y x))
▶	36.8%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
▶	58.6%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
▶	34.4%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) #s(literal 1 binary64))
✓	67.0%	#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)))
✓	31.0%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
✓	65.3%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 190 to 138 computations (27.4% saved)

simplify195.0ms (2.9%)

Memory

32.8MiB live, 147.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

13 320×	`lower-fma.f32`
13 314×	`lower-fma.f64`
3 876×	`lower-*.f32`
3 866×	`lower-*.f64`
1 700×	`lower-+.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	244
0	54	244
1	103	239
2	219	239
3	464	221
4	1378	215
5	3846	215
0	8409	215

Stop Event

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

Calls

Call 1

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

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

localize178.0ms (2.6%)

Memory

-0.9MiB live, 119.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal -2 binary64) x)
accuracy	0.10546875	(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
accuracy	0.203125	(*.f64 y (/.f64 y x))
accuracy	40.446455216399954	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
accuracy	0.45079602267966185	(/.f64 #s(literal 2 binary64) (*.f64 y y))
accuracy	3.515709990986784	(fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64))
accuracy	9.520315804529991	(.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x)
accuracy	21.12859933652683	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
accuracy	0	(+.f64 y x)
accuracy	0	(neg.f64 y)
accuracy	0.01953125	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y)) (+.f64 y x))
accuracy	22.221271668652417	#s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y))
accuracy	41.96354339602946	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(fma.f64 y y (*.f64 x x))
accuracy	0.1953125	(.f64 (/.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (+.f64 y x))
accuracy	17.72541672254457	(/.f64 (-.f64 x y) (fma.f64 y y (*.f64 x x)))

Samples

104.0ms

256×

valid

Compiler

Compiled 226 to 30 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-neg: 42.0ms (47.1% of total)

ival-add: 22.0ms (24.7% of total)

ival-mult: 13.0ms (14.6% of total)

ival-div: 9.0ms (10.1% of total)

ival-sub: 2.0ms (2.2% of total)

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

exact: 0.0ms (0% of total)

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

series39.0ms (0.6%)

Memory

-19.5MiB live, 51.9MiB allocated

Counts

18 → 384

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	y	@	0	((* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (+ (* y y) (* x x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg y) (+ y x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (* (/ 2 (* y y)) x) x) -1) (* (/ 2 (* y y)) x) (/ 2 (* y y)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (/ -2 x) (* y (/ y x))) 1) (/ -2 x) (* y (/ y x)) (* x x))
2.0ms	x	@	-inf	((* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (+ (* y y) (* x x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg y) (+ y x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (* (/ 2 (* y y)) x) x) -1) (* (/ 2 (* y y)) x) (/ 2 (* y y)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (/ -2 x) (* y (/ y x))) 1) (/ -2 x) (* y (/ y x)) (* x x))
2.0ms	x	@	inf	((* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (+ (* y y) (* x x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg y) (+ y x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (* (/ 2 (* y y)) x) x) -1) (* (/ 2 (* y y)) x) (/ 2 (* y y)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (/ -2 x) (* y (/ y x))) 1) (/ -2 x) (* y (/ y x)) (* x x))
2.0ms	y	@	inf	((* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (+ (* y y) (* x x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg y) (+ y x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (* (/ 2 (* y y)) x) x) -1) (* (/ 2 (* y y)) x) (/ 2 (* y y)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (/ -2 x) (* y (/ y x))) 1) (/ -2 x) (* y (/ y x)) (* x x))
2.0ms	x	@	0	((* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (+ (* y y) (* x x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg y) (+ y x) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (* (/ 2 (* y y)) x) x) -1) (* (/ 2 (* y y)) x) (/ 2 (* y y)) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (+ (* (/ -2 x) (* y (/ y x))) 1) (/ -2 x) (* y (/ y x)) (* x x))

simplify256.0ms (3.8%)

Memory

-50.5MiB live, 233.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 772×	`lower-fma.f64`
14 772×	`lower-fma.f32`
4 254×	`lower-+.f64`
4 254×	`lower-+.f32`
3 558×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	374	4674
1	1145	4304
2	3497	3736
0	8177	3484

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 372

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

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

rewrite217.0ms (3.2%)

Memory

38.5MiB live, 266.1MiB allocated

Rules

6 278×	`lower-/.f32`
6 268×	`lower-/.f64`
4 120×	`lower-*.f32`
4 110×	`lower-*.f64`
4 012×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	222
0	54	222
1	210	193
2	1730	193
0	8713	193

Stop Event

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

Counts

18 → 797

Calls

Call 1

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

Outputs
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eval181.0ms (2.6%)

Memory: 24.0MiB live, 366.7MiB allocated
Compiler: Compiled 28 894 to 2 871 computations (90.1% saved)

prune114.0ms (1.7%)

Memory

-49.7MiB live, 87.6MiB allocated

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	1 229	2	1 231
Fresh	0	1	1
Picked	0	5	5
Done	1	4	5
Total	1 230	12	1 242

Accuracy

99.9%

Counts

1 242 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
▶	67.0%	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y))) (+.f64 y x))
✓	64.9%	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y)) (+.f64 y x))
✓	71.3%	(.f64 (/.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (+.f64 y x))
▶	71.3%	(.f64 (/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (fma.f64 y y (*.f64 x x))) (+.f64 y x))
▶	65.4%	(.f64 #s(approx (/ (- x y) (+ ( y y) (* x x))) (/.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)) (+.f64 y x))
✓	36.8%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
✓	58.6%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
✓	34.4%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) #s(literal 1 binary64))
✓	67.0%	#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)))
✓	31.0%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
✓	65.3%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 145 to 105 computations (27.6% saved)

simplify176.0ms (2.6%)

Memory

14.6MiB live, 201.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64))
cost-diff	0	(fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y))
cost-diff	0	#s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y)))
cost-diff	0	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y))) (+.f64 y x))
cost-diff	0	#s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
cost-diff	0	(/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (fma.f64 y y (.f64 x x)))
cost-diff	0	(.f64 (/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (fma.f64 y y (*.f64 x x))) (+.f64 y x))
cost-diff	1024	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
cost-diff	0	(/.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)
cost-diff	0	#s(approx (/ (- x y) (+ (* y y) (* x x))) (/.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))
cost-diff	0	(.f64 #s(approx (/ (- x y) (+ ( y y) (* x x))) (/.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)) (+.f64 y x))
cost-diff	6208	(-.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)))

Rules

11 682×	`lower-fma.f32`
11 672×	`lower-fma.f64`
3 272×	`lower-*.f32`
3 264×	`lower-*.f64`
2 718×	`lower--.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	329
0	65	329
1	140	327
2	311	327
3	793	327
4	2281	311
5	4207	307
6	6847	307
0	8154	307

Stop Event

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

Calls

Call 1

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

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

localize147.0ms (2.2%)

Memory

7.3MiB live, 251.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.06640625	(fma.f64 x (/.f64 x y) x)
accuracy	0.08356373993272953	(fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64))
accuracy	2.0986240870799477	(fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y))
accuracy	21.142830878009455	#s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y)))
accuracy	0.00390625	(fma.f64 y y (*.f64 x x))
accuracy	0.03125	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
accuracy	0.1953125	(.f64 (/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (fma.f64 y y (*.f64 x x))) (+.f64 y x))
accuracy	17.72541672254457	(/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (fma.f64 y y (.f64 x x)))
accuracy	0.1953125	(.f64 #s(approx (/ (- x y) (+ ( y y) (* x x))) (/.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)) (+.f64 y x))
accuracy	0.2673226074528622	(pow.f64 (/.f64 x y) #s(literal 3 binary64))
accuracy	7.757748510736381	(-.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)))
accuracy	22.04223911444347	#s(approx (/ (- x y) (+ (* y y) (* x x))) (/.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))

Samples

117.0ms

256×

valid

Compiler

Compiled 253 to 37 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 31.0ms (54.2% of total)

ival-div: 9.0ms (15.7% of total)

ival-add: 9.0ms (15.7% of total)

ival-sub: 4.0ms (7% of total)

ival-pow: 2.0ms (3.5% of total)

exact: 1.0ms (1.7% of total)

ival-neg: 1.0ms (1.7% of total)

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

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

series71.0ms (1%)

Memory

-7.5MiB live, 67.7MiB allocated

Counts

15 → 360

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	y	@	-inf	((- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (/ (- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) y) (* (- (/ x y) 1) y) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ (* (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) x) (neg y)) (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) (pow (/ x y) 3) (+ (* y y) (* x x)) (+ (* x (/ x y)) x))
3.0ms	x	@	-inf	((- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (/ (- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) y) (* (- (/ x y) 1) y) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ (* (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) x) (neg y)) (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) (pow (/ x y) 3) (+ (* y y) (* x x)) (+ (* x (/ x y)) x))
3.0ms	y	@	0	((- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (/ (- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) y) (* (- (/ x y) 1) y) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ (* (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) x) (neg y)) (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) (pow (/ x y) 3) (+ (* y y) (* x x)) (+ (* x (/ x y)) x))
3.0ms	x	@	inf	((- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (/ (- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) y) (* (- (/ x y) 1) y) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ (* (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) x) (neg y)) (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) (pow (/ x y) 3) (+ (* y y) (* x x)) (+ (* x (/ x y)) x))
2.0ms	y	@	inf	((- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (/ (- (+ (* (+ (/ x y) 1) (/ x y)) -1) (pow (/ x y) 3)) y) (* (- (/ x y) 1) y) (* (/ (- x y) (+ (* y y) (* x x))) (+ y x)) (/ (- x y) (+ (* y y) (* x x))) (- x y) (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ (* (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) x) (neg y)) (+ (* (/ 2 y) (+ (* x (/ x y)) x)) -1) (pow (/ x y) 3) (+ (* y y) (* x x)) (+ (* x (/ x y)) x))

simplify155.0ms (2.3%)

Memory

21.5MiB live, 149.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 612×	`lower-fma.f64`
9 612×	`lower-fma.f32`
4 788×	`lower-*.f64`
4 788×	`lower-*.f32`
2 502×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	577	4345
1	1790	4045
2	5584	3685
0	8689	3501

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 348

Calls

Call 1

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

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

rewrite300.0ms (4.4%)

Memory

-31.2MiB live, 216.4MiB allocated

Rules

5 352×	`lower-/.f32`
5 342×	`lower-/.f64`
3 956×	`lower-fma.f32`
3 946×	`lower-fma.f64`
3 944×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	271
0	65	271
1	296	269
2	2716	269
0	8500	269

Stop Event

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

Counts

15 → 634

Calls

Call 1

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

Outputs
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eval192.0ms (2.8%)

Memory: 33.2MiB live, 342.6MiB allocated
Compiler: Compiled 28 443 to 3 392 computations (88.1% saved)

prune32.0ms (0.5%)

Memory

-16.7MiB live, 96.3MiB allocated

Pruning

13 alts after pruning (1 fresh and 12 done)

	Pruned	Kept	Total
New	981	1	982
Fresh	0	0	0
Picked	0	3	3
Done	0	9	9
Total	981	13	994

Accuracy

99.9%

Counts

994 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.5%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
✓	67.0%	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal 2 binary64) y) (fma.f64 x (/.f64 x y) x) #s(literal -1 binary64)) x (neg.f64 y))) (+.f64 y x))
✓	64.9%	(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y)) (+.f64 y x))
✓	71.3%	(.f64 (/.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (+.f64 y x))
✓	71.3%	(.f64 (/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (fma.f64 y y (*.f64 x x))) (+.f64 y x))
	65.3%	(.f64 #s(approx (/ (- x y) (+ ( y y) (* x x))) (fma.f64 (/.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) (/.f64 x y) #s(literal 1 binary64)) y) (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 x y) x x) y) #s(literal 1 binary64)) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) (/.f64 x y) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) y)))) (+.f64 y x))
✓	65.4%	(.f64 #s(approx (/ (- x y) (+ ( y y) (* x x))) (/.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)) (+.f64 y x))
✓	36.8%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
✓	58.6%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
✓	34.4%	#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) #s(literal 1 binary64))
✓	67.0%	#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)))
✓	31.0%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
✓	65.3%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 435 to 203 computations (53.3% saved)

regimes21.0ms (0.3%)

Memory

9.0MiB live, 51.2MiB allocated

Counts

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

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:

10.0ms	x
5.0ms	y
4.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Results

Accuracy	Segments	Branch
87.3%	2	`x`
92.3%	3	`y`
95.9%	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)

regimes3.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB 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 (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) #s(literal 1 binary64))
(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y)) (+.f64 y x))
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
(/.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 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))
#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (+.f64 y x))

Outputs

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

#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:

3.0ms

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

Results

Accuracy	Segments	Branch
94.8%	2	`(/.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

-22.6MiB live, 15.3MiB allocated

Counts

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

Outputs

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

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

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
95.3%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes3.0ms (0%)

Memory

10.0MiB live, 10.0MiB 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 (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) #s(literal 1 binary64))
(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y)) (+.f64 y x))
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
(/.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 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))

Outputs

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

2.0ms

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

Results

Accuracy	Segments	Branch
94.9%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes3.0ms (0%)

Memory

7.7MiB live, 7.7MiB 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 (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) #s(literal 1 binary64))
(/.f64 #s(approx (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (neg.f64 y)) (+.f64 y x))
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
#s(approx (/ (* (/ (+ y x) (+ (* y y) (* x x))) (+ (* (neg y) y) (* x x))) (+ y x)) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))

Outputs

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

2.0ms

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

Results

Accuracy	Segments	Branch
94.3%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes2.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

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

2.0ms

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

Results

Accuracy	Segments	Branch
94.1%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
65.3%	1	`x`
65.3%	1	`y`
65.3%	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)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch35.0ms (0.5%)

Memory

-36.7MiB live, 1.1MiB 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

1.1MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.7547482778685656	0.9999997279804196

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.7547482778685656	0.9999997279804196

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	-0.7547482778685656	0.9999997279804196

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.7547482778685656	0.9999997279804196

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify39.0ms (0.6%)

Memory

28.0MiB live, 65.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`-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	62	571
1	74	571
2	77	571
3	79	571
4	80	571

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

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

soundness781.0ms (11.5%)

Memory

-21.2MiB live, 519.7MiB allocated

Rules

13 120×	`lower-fma.f64`
13 120×	`lower-fma.f32`
8 792×	`lower-fma.f64`
8 792×	`lower-fma.f32`
5 274×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	399	4482
1	1249	4126
2	3826	3684
0	8354	3456
0	160	628
1	504	603
2	1609	563
3	6170	563
0	8190	525
0	9	34
0	16	34
1	66	34
2	551	34
0	8160	32

Stop Event

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

Compiler

Compiled 473 to 149 computations (68.5% saved)

preprocess113.0ms (1.7%)

Memory

-18.6MiB live, 133.7MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 906 to 234 computations (74.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze5.0ms (0.1%)

sample1.1s (15.6%)

explain114.0ms (1.7%)

preprocess377.0ms (5.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify347.0ms (5.1%)

localize25.0ms (0.4%)

series9.0ms (0.1%)

simplify125.0ms (1.8%)

rewrite141.0ms (2.1%)

eval81.0ms (1.2%)

prune16.0ms (0.2%)

simplify189.0ms (2.8%)

localize80.0ms (1.2%)

series42.0ms (0.6%)

simplify173.0ms (2.5%)

rewrite232.0ms (3.4%)

eval433.0ms (6.3%)

prune107.0ms (1.6%)

simplify195.0ms (2.9%)

localize178.0ms (2.6%)

series39.0ms (0.6%)

simplify256.0ms (3.8%)

rewrite217.0ms (3.2%)

eval181.0ms (2.6%)

prune114.0ms (1.7%)

simplify176.0ms (2.6%)

localize147.0ms (2.2%)

series71.0ms (1%)

simplify155.0ms (2.3%)

rewrite300.0ms (4.4%)

eval192.0ms (2.8%)

prune32.0ms (0.5%)

regimes21.0ms (0.3%)

regimes3.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

bsearch1.0ms (0%)

bsearch35.0ms (0.5%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify39.0ms (0.6%)

soundness781.0ms (11.5%)

preprocess113.0ms (1.7%)

end0.0ms (0%)

Profiling