Metrics for Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
75%	74.9%	25%	0.1%	0%	0%	0%	3
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	4
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	5
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	6
98.4%	98.3%	1.6%	0.1%	0%	0%	0%	7
99.2%	99.1%	0.8%	0.1%	0%	0%	0%	8
99.6%	99.5%	0.4%	0.1%	0%	0%	0%	9
99.8%	99.7%	0.2%	0.1%	0%	0%	0%	10
99.9%	99.8%	0.1%	0.1%	0%	0%	0%	11
100%	99.9%	0%	0.1%	0%	0%	0%	12

Compiler

Compiled 21 to 11 computations (47.6% saved)

sample892.0ms (14.1%)

Memory

-13.1MiB live, 1 672.3MiB allocated

Samples

611.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 388.0ms

ival-mult: 251.0ms (64.6% of total)

ival-div: 47.0ms (12.1% of total)

ival-sub: 38.0ms (9.8% of total)

ival-add: 37.0ms (9.5% of total)

ival-true: 6.0ms (1.5% of total)

exact: 6.0ms (1.5% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

explain117.0ms (1.8%)

Memory

17.4MiB live, 256.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
117	-	-	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`
19	-	-	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`
0	-	-	`(.f64 (.f64 y #s(literal 4 binary64)) y)`
0	-	-	`(*.f64 y #s(literal 4 binary64))`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`(*.f64 x x)`
0	-	-	`(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`
0	-	-	`y`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`	o/o	102	0
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	overflow	60
↳	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	overflow	102
↳	`(*.f64 x x)`	overflow	61
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	overflow	60
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	overflow	102
↳	`(*.f64 x x)`	overflow	61
`-.f64`	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	nan-rescue	19	0
↳	`(*.f64 x x)`	overflow	61
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	overflow	60
`/.f64`	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`	u/u	15	0
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	underflow	66
↳	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	underflow	15
↳	`(*.f64 x x)`	underflow	60
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	underflow	66
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	underflow	15
↳	`(*.f64 x x)`	underflow	60

Confusion

	Predicted +	Predicted -
+	117	0
-	0	139

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	0
-	0	0	139

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	139
1	98
2	19

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 125 to 31 computations (75.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 10.0ms (45.2% of total)

ival-div: 7.0ms (31.6% of total)

ival-sub: 2.0ms (9% of total)

ival-add: 2.0ms (9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess191.0ms (3%)

Memory

2.0MiB live, 81.7MiB allocated

Algorithm

1×	egg-herbie

Rules

984×	`times-frac`
880×	`lower-fma.f64`
880×	`lower-fma.f32`
784×	`distribute-lft-in`
762×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	97
1	89	97
2	240	95
3	620	95
4	1743	95
5	2721	95
6	2962	95
7	2981	95
8	2996	95
9	3001	95
10	3001	95
11	3301	95
12	3437	95
13	3437	95
14	3581	95
15	4417	95
16	4417	95
0	9	19
0	15	19
1	27	19
2	56	19
3	112	19
4	215	19
5	344	19
6	511	19
7	724	19
8	1191	19
9	2211	19
10	2260	19
11	2298	19
12	2326	19
13	2326	19
0	2326	17

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Outputs

(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))

(/.f64 (fma.f64 (*.f64 y y) #s(literal -4 binary64) (*.f64 x x)) (fma.f64 y (*.f64 y #s(literal 4 binary64)) (*.f64 x x)))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 19 to 9 computations (52.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.3%	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Compiler

Compiled 19 to 9 computations (52.6% saved)

simplify56.0ms (0.9%)

Memory

2.6MiB live, 41.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))
cost-diff	128	(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
cost-diff	128	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))

Rules

880×	`lower-fma.f64`
880×	`lower-fma.f32`
738×	`times-frac`
592×	`lower-*.f32`
586×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	51
0	15	51
1	27	51
2	56	51
3	112	51
4	215	51
5	344	51
6	511	51
7	724	51
8	1191	51
9	2211	51
10	2260	51
11	2298	51
12	2326	51
13	2326	51
0	2326	47

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
(*.f64 x x)
x
(.f64 (.f64 y #s(literal 4 binary64)) y)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))

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

localize27.0ms (0.4%)

Memory

13.3MiB live, 50.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y #s(literal 4 binary64))
accuracy	0	(*.f64 x x)
accuracy	4.3945064799624705	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
accuracy	28.70512540625526	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Samples

20.0ms

256×

valid

Compiler

Compiled 53 to 11 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 7.0ms (52% of total)

ival-sub: 3.0ms (22.3% of total)

ival-div: 1.0ms (7.4% of total)

ival-add: 1.0ms (7.4% of total)

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

exact: 0.0ms (0% of total)

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

series56.0ms (0.9%)

Memory

-38.7MiB live, 6.7MiB allocated

Counts

5 → 96

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())
#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (pow y 2)) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow y 2)) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) (taylor inf y) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (pow y 2)) (taylor -inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
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#s(alt (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4)) (taylor -inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
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#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
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#s(alt 1 (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) 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 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (patch (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) #<representation binary64>) () ())) ())
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#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #<representation binary64>) () ())) ())
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#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
48.0ms	y	@	inf	((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x) (* y 4))
1.0ms	x	@	0	((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x) (* y 4))
1.0ms	y	@	0	((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x) (* y 4))
1.0ms	x	@	inf	((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x) (* y 4))
1.0ms	y	@	-inf	((- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (* x x) (* y 4))

simplify191.0ms (3%)

Memory

35.3MiB live, 189.7MiB allocated

Algorithm

1×	egg-herbie

Rules

18 822×	`lower-fma.f64`
18 822×	`lower-fma.f32`
7 268×	`lower-*.f64`
7 268×	`lower-*.f32`
2 750×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	990
1	321	990
2	960	844
3	4060	836
0	8249	766

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(pow x 2)
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(+ (* -4 (pow y 2)) (pow x 2))
(pow x 2)
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* 4 (pow y 2))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(* 4 (pow y 2))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (pow y 2))
(- (pow x 2) (* 4 (pow y 2)))
(- (pow x 2) (* 4 (pow y 2)))
(- (pow x 2) (* 4 (pow y 2)))
(* 4 (pow y 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
(+ (* 4 (pow y 2)) (pow x 2))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(pow x 2)
(*.f64 x x)
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(+ (* -4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -8 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (pow y 2))
(.f64 (.f64 y y) #s(literal -4 binary64))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* 4 (pow y 2))
(.f64 #s(literal 4 binary64) (.f64 y y))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (.f64 y y))) (.f64 x x) #s(literal -1 binary64)) (/.f64 (.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (pow y 2))
(.f64 (.f64 y y) #s(literal -4 binary64))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* 4 (pow y 2))
(.f64 #s(literal 4 binary64) (.f64 y y))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(+.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (.f64 y y))) (.f64 x x) #s(literal -1 binary64)) (/.f64 (.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/32 binary64)) (pow.f64 y #s(literal 6 binary64))))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (pow y 2))
(.f64 (.f64 y y) #s(literal -4 binary64))
(- (pow x 2) (* 4 (pow y 2)))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(- (pow x 2) (* 4 (pow y 2)))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(- (pow x 2) (* 4 (pow y 2)))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* 4 (pow y 2))
(.f64 #s(literal 4 binary64) (.f64 y y))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(+ (* 4 (pow y 2)) (pow x 2))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 #s(literal 1/2 binary64) (.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) (.f64 x x) (/.f64 #s(literal 1/2 binary64) (.f64 y y))) (.f64 x x) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal -8 binary64) (.f64 y y)) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 16 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 #s(literal -8 binary64) (.f64 y y)) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 16 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite182.0ms (2.9%)

Memory

9.1MiB live, 271.9MiB allocated

Rules

4 732×	`lower-fma.f64`
4 732×	`lower-fma.f32`
4 522×	`lower-*.f32`
4 516×	`lower-*.f64`
2 930×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	15	43
1	54	43
2	397	43
3	6323	43
0	8488	39

Stop Event

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

Counts

5 → 604

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))
(*.f64 x x)
(*.f64 y #s(literal 4 binary64))

Outputs
(.f64 (/.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)))))
(.f64 (/.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64))) (-.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
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(fma.f64 x (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x)) (.f64 (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)))) (.f64 (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (*.f64 #s(literal 4 binary64) y))))
(fma.f64 x (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x)) (neg.f64 (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(literal 2 binary64)))))
(fma.f64 x (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal -1 binary64)) (.f64 #s(literal -4 binary64) (*.f64 y y))))
(fma.f64 x (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x))))))
(fma.f64 x (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal -3 binary64))) (fma.f64 (.f64 (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (.f64 #s(literal 4 binary64) y)) #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal 2 binary64))))) (/.f64 (.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal -3 binary64))) (fma.f64 (.f64 (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (.f64 #s(literal 4 binary64) y)) #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(literal 2 binary64))))))
(-.f64 (/.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal 2 binary64))) (/.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64))) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (fma.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)))) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64)) (.f64 (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (fma.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (fma.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (/.f64 (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64)) (fma.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64) (fma.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)))) (/.f64 (neg.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x))) (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x))) (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))))
(-.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x) (.f64 (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (*.f64 #s(literal 4 binary64) y)))
(exp.f64 (.f64 (log.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) (fma.f64 #s(literal -4 binary64) (.f64 y y) (*.f64 x x)))) #s(literal -1 binary64)))
(+.f64 (.f64 (-.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64))) (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (*.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (-.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64))) (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (*.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))))
(+.f64 (.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x) #s(literal 1 binary64)) (.f64 (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (.f64 (pow.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64)))) (.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (*.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))
(+.f64 (.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x)) (fma.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (.f64 (pow.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(+.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal -1 binary64)) (.f64 #s(literal -4 binary64) (.f64 y y))) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x))
(+.f64 (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)))) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x))) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal 2 binary64))) (.f64 (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)))) (.f64 (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) (*.f64 #s(literal 4 binary64) y))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal 2 binary64))) (neg.f64 (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)) #s(literal 2 binary64)))))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x) (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)) #s(literal -1 binary64)) (.f64 #s(literal -4 binary64) (.f64 y y))))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x) (.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))))))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))) x) (.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 #s(literal 4 binary64) y) y (*.f64 x x)))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 4 binary64) y)
(*.f64 y #s(literal 4 binary64))

eval132.0ms (2.1%)

Memory: 9.5MiB live, 244.8MiB allocated
Compiler: Compiled 26 298 to 1 561 computations (94.1% saved)

prune98.0ms (1.6%)

Memory

-20.2MiB live, 251.9MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	731	4	735
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	732	4	736

Accuracy

99.6%

Counts

736 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
▶	53.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
▶	52.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
▶	48.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 26 to 25 computations (3.8% saved)

simplify282.0ms (4.5%)

Memory

18.8MiB live, 135.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 (*.f64 x x) y)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
cost-diff	0	(/.f64 y x)
cost-diff	0	(*.f64 #s(literal -8 binary64) (/.f64 y x))
cost-diff	0	(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Rules

2 800×	`lower-fma.f32`
2 796×	`lower-fma.f64`
2 224×	`lower-*.f32`
2 220×	`lower-*.f64`
930×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	151
0	33	151
1	64	151
2	122	151
3	222	151
4	362	151
5	519	151
6	698	151
7	1050	151
8	2383	151
9	4117	151
10	4696	151
11	4840	151
12	4884	151
13	4900	151
14	4904	151
15	5170	151
16	5286	151
17	5286	151
18	5468	151
19	5638	151
20	5798	151
21	5805	151
22	5961	151
23	6181	151
24	6213	151
25	6213	151
0	6213	143

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal -8 binary64) (/.f64 y x))
#s(literal -8 binary64)
(/.f64 y x)
y
x
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(/.f64 (*.f64 x x) y)
(*.f64 x x)
x
#s(literal -1 binary64)

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal -8 binary64) (/.f64 y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
#s(literal -8 binary64)
(/.f64 y x)
y
x
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(fma.f64 (/.f64 (*.f64 x x) y) (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(/.f64 (*.f64 x x) y)
(*.f64 x x)
x
#s(literal -1 binary64)

localize85.0ms (1.3%)

Memory

12.4MiB live, 131.9MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	1.469013455108363	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
accuracy	8.39964082469946	(/.f64 (*.f64 x x) y)
accuracy	32.1052613562466	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
accuracy	0	(/.f64 y x)
accuracy	0.010097509768442016	(*.f64 #s(literal -8 binary64) (/.f64 y x))
accuracy	0.08984375	(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
accuracy	29.50777204383162	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
accuracy	30.402940140238716	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
accuracy	33.00215845324568	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Samples

70.0ms

256×

valid

Compiler

Compiled 129 to 23 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-div: 27.0ms (66.8% of total)

ival-mult: 9.0ms (22.3% of total)

ival-add: 3.0ms (7.4% of total)

ival-sub: 1.0ms (2.5% of total)

exact: 1.0ms (2.5% of total)

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

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

series36.0ms (0.6%)

Memory

8.5MiB live, 46.6MiB allocated

Counts

11 → 240

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())
#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor 0 y) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor 0 y) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor 0 y) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor 0 y) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4)))))) (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2))))) (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x 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>) () ())) ())
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#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -8 (/ y x)) (taylor -inf x) (#s(alt (.f64 #s(literal -8 binary64) (/.f64 y x)) (patch (.f64 #s(literal -8 binary64) (/.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor -inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor -inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor -inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor -inf x) (#s(alt (/.f64 (.f64 x x) y) (patch (/.f64 (.f64 x 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
17.0ms	y	@	-inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 y) (/ (* x x) y)) -1) (/ 1/2 y) (/ (* x x) y) (* x x))
3.0ms	y	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 y) (/ (* x x) y)) -1) (/ 1/2 y) (/ (* x x) y) (* x x))
2.0ms	y	@	0	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 y) (/ (* x x) y)) -1) (/ 1/2 y) (/ (* x x) y) (* x x))
2.0ms	x	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 y) (/ (* x x) y)) -1) (/ 1/2 y) (/ (* x x) y) (* x x))
2.0ms	x	@	0	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* -8 (/ y x)) (/ y x)) 1) (* -8 (/ y x)) (/ y x) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 y) (/ (* x x) y)) -1) (/ 1/2 y) (/ (* x x) y) (* x x))

simplify221.0ms (3.5%)

Memory

-7.1MiB live, 280.8MiB allocated

Algorithm

1×	egg-herbie

Rules

20 234×	`lower-fma.f64`
20 234×	`lower-fma.f32`
6 946×	`lower-*.f64`
6 946×	`lower-*.f32`
3 028×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	120	2840
1	316	2610
2	943	2474
3	3616	2398
0	8083	2226

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
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(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
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(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
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(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
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(/ y x)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
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(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
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(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(* -8 (/ (pow y 2) (pow x 2)))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (/.f64 x y))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(/ 1/2 y)
(/.f64 #s(literal 1/2 binary64) y)
(/ 1/2 y)
(/.f64 #s(literal 1/2 binary64) y)
(/ 1/2 y)
(/.f64 #s(literal 1/2 binary64) y)
(/ 1/2 y)
(/.f64 #s(literal 1/2 binary64) y)
(/ (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)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
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(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (/.f64 x y))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(* -8 (/ y x))
(*.f64 (/.f64 y x) #s(literal -8 binary64))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (/.f64 x y))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) y) y) (*.f64 x x) #s(literal -1 binary64))
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite177.0ms (2.8%)

Memory

-18.4MiB live, 175.4MiB allocated

Rules

7 902×	`lower-fma.f32`
7 898×	`lower-fma.f64`
5 586×	`lower-*.f32`
5 582×	`lower-*.f64`
3 730×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	141
0	33	141
1	135	139
2	1030	137
0	8960	125

Stop Event

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

Counts

11 → 257

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal -8 binary64) (/.f64 y x))
(/.f64 y x)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 (*.f64 x x) y)
(*.f64 x x)

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))))
(*.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal -512 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))))))
(*.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))
(.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal -512 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64) (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
(.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal -512 binary64) #s(literal 1 binary64)) (pow.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64)) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal -1 binary64))) (/.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64)) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))) (+.f64 (/.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal 64 binary64)) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
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(.f64 (/.f64 (.f64 x x) y) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) y))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 x y) (neg.f64 x)))
(.f64 (.f64 x x) (pow.f64 y #s(literal -1 binary64)))
(*.f64 x (/.f64 x y))
(pow.f64 (/.f64 (/.f64 y x) x) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 y x) x))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 y) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 y x) x)))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (neg.f64 x))))
(neg.f64 (.f64 (.f64 (/.f64 x y) (neg.f64 x)) #s(literal 1 binary64)))
(neg.f64 (*.f64 (/.f64 x y) (neg.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 y)) (*.f64 (/.f64 x y) (neg.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 x y) (neg.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 y x) x)) #s(literal -1 binary64)))
(.f64 (.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval114.0ms (1.8%)

Memory: -5.5MiB live, 153.0MiB allocated
Compiler: Compiled 8 180 to 1 010 computations (87.7% saved)

prune95.0ms (1.5%)

Memory

1.3MiB live, 146.0MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	539	2	541
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	540	5	545

Accuracy

99.6%

Counts

545 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
✓	53.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
▶	53.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))))
✓	52.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓	48.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify170.0ms (2.7%)

Memory

-6.7MiB live, 74.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
cost-diff	320	(/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))

Rules

1 928×	`lower-fma.f32`
1 924×	`lower-fma.f64`
1 508×	`lower-*.f32`
1 502×	`lower-*.f64`
620×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	142
0	38	134
1	68	128
2	137	128
3	307	128
4	591	128
5	838	128
6	1074	128
7	1499	128
8	2756	128
9	3830	128
10	4100	128
11	4123	128
12	4137	128
13	4141	128
14	4263	128
15	4321	128
16	4321	128
17	4321	128
18	4333	128
19	4337	128
0	4337	124

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
(/.f64 x y)
x
y
#s(literal -2 binary64)
#s(literal -8 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 x x)
x
(/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(literal 1 binary64)
(.f64 (.f64 y y) #s(literal 2 binary64))
(*.f64 y y)
y
#s(literal 2 binary64)
#s(literal -1 binary64)

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

localize55.0ms (0.9%)

Memory

16.1MiB live, 127.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (.f64 y y) #s(literal 2 binary64))
accuracy	0.27976812389204053	(/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64)))
accuracy	11.393997865435798	(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))
accuracy	32.1052613562466	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
accuracy	0.0703125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))
accuracy	0.23246005861065208	(pow.f64 (/.f64 x y) #s(literal -2 binary64))
accuracy	0.2834789014369884	(/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))
accuracy	29.50777204383162	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))))

Samples

42.0ms

256×

valid

Compiler

Compiled 122 to 27 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 10.0ms (39.8% of total)

ival-div: 7.0ms (27.8% of total)

ival-add: 3.0ms (11.9% of total)

ival-pow: 2.0ms (8% of total)

ival-sub: 1.0ms (4% of total)

exact: 1.0ms (4% of total)

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

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

series30.0ms (0.5%)

Memory

-13.5MiB live, 63.9MiB allocated

Counts

10 → 204

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)) (patch (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 x y) #s(literal -2 binary64)) (patch (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 y y) #s(literal 2 binary64)) (patch (.f64 (.f64 y y) #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ (pow y 2) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (/.f64 x y) #s(literal -2 binary64)) (patch (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow y 2) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (/.f64 x y) #s(literal -2 binary64)) (patch (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow y 2) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (/.f64 x y) #s(literal -2 binary64)) (patch (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow y 2) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (/.f64 x y) #s(literal -2 binary64)) (patch (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	y	@	inf	((/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (pow (/ x y) -2) -8) 1) (/ 1 (* (* y y) 2)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y y) 2))) -1) (* x x) (pow (/ x y) -2) (* (* y y) 2))
3.0ms	x	@	-inf	((/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (pow (/ x y) -2) -8) 1) (/ 1 (* (* y y) 2)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y y) 2))) -1) (* x x) (pow (/ x y) -2) (* (* y y) 2))
2.0ms	y	@	0	((/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (pow (/ x y) -2) -8) 1) (/ 1 (* (* y y) 2)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y y) 2))) -1) (* x x) (pow (/ x y) -2) (* (* y y) 2))
2.0ms	x	@	inf	((/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (pow (/ x y) -2) -8) 1) (/ 1 (* (* y y) 2)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y y) 2))) -1) (* x x) (pow (/ x y) -2) (* (* y y) 2))
1.0ms	y	@	-inf	((/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (pow (/ x y) -2) -8) 1) (/ 1 (* (* y y) 2)) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* x x) (/ 1 (* (* y y) 2))) -1) (* x x) (pow (/ x y) -2) (* (* y y) 2))

simplify211.0ms (3.3%)

Memory

-9.6MiB live, 357.2MiB allocated

Algorithm

1×	egg-herbie

Rules

18 590×	`lower-fma.f64`
18 590×	`lower-fma.f32`
6 284×	`lower-*.f64`
6 284×	`lower-*.f32`
1 958×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	190	2648
1	525	2504
2	1569	2356
3	5411	2276
0	8147	2118

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (+ (* 64 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 512 (/ (pow y 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 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) (pow x 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -1/8 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1/8 (pow x 2)) (* -1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/512 (/ (pow x 6) (pow y 4)))) (* 1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/4096 (/ (pow x 8) (pow y 6)))) (+ (* 1/512 (/ (pow x 6) (pow y 4))) (* 1/64 (/ (pow x 4) (pow y 2))))) (pow y 2))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -1/8 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1/8 (pow x 2)) (* -1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/512 (/ (pow x 6) (pow y 4)))) (* 1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/4096 (/ (pow x 8) (pow y 6)))) (+ (* 1/512 (/ (pow x 6) (pow y 4))) (* 1/64 (/ (pow x 4) (pow y 2))))) (pow y 2))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* -8 (/ (pow y 2) (pow x 2)))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(* -1/8 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* -1/64 (/ (pow x 2) (pow y 4))) (* 1/8 (/ 1 (pow y 2)))))
(* (pow x 2) (- (* (pow x 2) (- (* -1/512 (/ (pow x 2) (pow y 6))) (* 1/64 (/ 1 (pow y 4))))) (* 1/8 (/ 1 (pow y 2)))))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1/4096 (/ (pow x 2) (pow y 8))) (* 1/512 (/ 1 (pow y 6))))) (* 1/64 (/ 1 (pow y 4))))) (* 1/8 (/ 1 (pow y 2)))))
(* -8 (/ (pow y 2) (pow x 2)))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 64 (/ (pow y 4) (pow x 4)))) (* -8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 512 (/ (pow y 6) (pow x 6)))) (+ (* -64 (/ (pow y 4) (pow x 4))) (* -8 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 64 (/ (pow y 4) (pow x 4)))) (* -8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 512 (/ (pow y 6) (pow x 6)))) (+ (* -64 (/ (pow y 4) (pow x 4))) (* -8 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (pow y 2) (pow x 2))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -8 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (+ (* 64 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 #s(literal 8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 512 (/ (pow y 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (.f64 #s(literal 8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 512 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -8 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
(* 1/2 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* -8 (/ (pow y 2) (pow x 2)))
(.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
(* -1/8 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x y)) (/.f64 x y))
(/ (+ (* -1/8 (pow x 2)) (* -1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1/64 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (*.f64 y y))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/512 (/ (pow x 6) (pow y 4)))) (* 1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1/64 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/512 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))) (*.f64 y y))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/4096 (/ (pow x 8) (pow y 6)))) (+ (* 1/512 (/ (pow x 6) (pow y 4))) (* 1/64 (/ (pow x 4) (pow y 2))))) (pow y 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1/64 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (fma.f64 (pow.f64 x #s(literal 8 binary64)) (/.f64 #s(literal -1/4096 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/512 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))))) (*.f64 y y))
(* -8 (/ (pow y 2) (pow x 2)))
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(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 (fma.f64 (.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -8 binary64) (.f64 x x))) y) y (+.f64 (/.f64 (.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -128 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(- (+ 1 (* 64 (/ (pow y 4) (pow x 4)))) (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal 8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (* 512 (/ (pow y 6) (pow x 6)))) (+ (* -64 (/ (pow y 4) (pow x 4))) (* -8 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 512 binary64) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 (fma.f64 (.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -8 binary64) (.f64 x x))) y) y (+.f64 (/.f64 (.f64 (pow.f64 (*.f64 y y) #s(literal 3 binary64)) #s(literal -128 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)))
(* 1/2 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)
(/ (pow y 2) (pow x 2))
(*.f64 (/.f64 (/.f64 y x) x) y)

rewrite365.0ms (5.8%)

Memory

16.9MiB live, 257.6MiB allocated

Rules

10 234×	`lower-fma.f32`
10 230×	`lower-fma.f64`
6 182×	`lower-*.f32`
6 176×	`lower-*.f64`
3 050×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	126
0	38	116
1	151	112
2	982	110
0	8319	104

Stop Event

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

Counts

10 → 401

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))
(fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 x x)
(pow.f64 (/.f64 x y) #s(literal -2 binary64))
(.f64 (.f64 y y) #s(literal 2 binary64))

Outputs
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))))
(*.f64 (neg.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))
(.f64 (neg.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))))))
(.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
(.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(*.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))))
(*.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
(pow.f64 (*.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)))) (.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 (*.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))))
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(.f64 y (.f64 #s(literal 2 binary64) y))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 y y)))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) #s(literal -1 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 y y) #s(literal -2 binary64)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (pow.f64 y #s(literal -2 binary64)))
(/.f64 #s(literal -2 binary64) (neg.f64 (pow.f64 y #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 y y)))
(neg.f64 (.f64 (.f64 y y) #s(literal -2 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 y y) #s(literal -2 binary64)))
(exp.f64 (neg.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 y y))) #s(literal -1 binary64))))

eval394.0ms (6.2%)

Memory: -12.9MiB live, 142.9MiB allocated
Compiler: Compiled 11 332 to 1 544 computations (86.4% saved)

prune109.0ms (1.7%)

Memory

7.2MiB live, 125.6MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	603	2	605
Fresh	0	0	0
Picked	2	0	2
Done	0	3	3
Total	605	5	610

Accuracy

99.6%

Counts

610 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
✓	53.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
▶	53.3%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))
✓	52.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓	48.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 40 to 36 computations (10% saved)

simplify313.0ms (5%)

Memory

-28.7MiB live, 62.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y y)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))

Rules

2 804×	`lower-fma.f32`
2 800×	`lower-fma.f64`
2 228×	`lower-*.f32`
2 222×	`lower-*.f64`
930×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	170
0	43	170
1	75	170
2	145	170
3	252	170
4	387	170
5	541	170
6	717	170
7	1066	170
8	2401	170
9	4125	170
10	4705	170
11	4860	170
12	4904	170
13	4920	170
14	4924	170
15	5190	170
16	5306	170
17	5306	170
18	5482	170
19	5646	170
20	5752	170
21	5759	170
22	5915	170
23	6148	170
24	6180	170
25	6180	170
0	6180	163

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(/.f64 #s(literal 8 binary64) x)
#s(literal 8 binary64)
x
(*.f64 y (/.f64 y x))
y
(/.f64 y x)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
#s(literal 1/2 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
#s(literal -1 binary64)

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

localize82.0ms (1.3%)

Memory

30.7MiB live, 68.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.27976812389204053	(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
accuracy	11.393997865435798	(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))
accuracy	32.1052613562466	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
accuracy	0.1328125	(*.f64 y (/.f64 y x))
accuracy	3.603153513045182	(fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
accuracy	29.50777204383162	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))
accuracy	30.263508564938448	#s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))

Samples

68.0ms

256×

valid

Compiler

Compiled 116 to 32 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-div: 18.0ms (47.2% of total)

ival-mult: 11.0ms (28.8% of total)

ival-add: 4.0ms (10.5% of total)

ival-pow: 3.0ms (7.9% of total)

ival-sub: 1.0ms (2.6% of total)

exact: 1.0ms (2.6% of total)

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

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

series31.0ms (0.5%)

Memory

-20.8MiB live, 17.6MiB allocated

Counts

10 → 204

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<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
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (+ (* 64 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 512 (/ (pow y 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 8 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))))) (patch #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (- (+ 1 (* 64 (/ (pow y 4) (pow x 4)))) (* -8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* 512 (/ (pow y 6) (pow x 6)))) (+ (* -64 (/ (pow y 4) (pow x 4))) (* -8 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (patch #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* 8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 8 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 8 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) (patch #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) (pow y 2))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)) #<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
4.0ms	y	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (/ 8 x) (* y (/ y x))) 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) (* y y) (* y (/ y x)) (* x x))
1.0ms	x	@	-inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (/ 8 x) (* y (/ y x))) 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) (* y y) (* y (/ y x)) (* x x))
1.0ms	y	@	-inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (/ 8 x) (* y (/ y x))) 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) (* y y) (* y (/ y x)) (* x x))
1.0ms	y	@	0	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (/ 8 x) (* y (/ y x))) 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) (* y y) (* y (/ y x)) (* x x))
1.0ms	x	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/ 1 (/ 1 (+ (* (pow (/ x y) -2) -8) 1))) (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (+ (* (/ 8 x) (* y (/ y x))) 1) (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) (* y y) (* y (/ y x)) (* x x))

simplify235.0ms (3.7%)

Memory

31.7MiB live, 109.4MiB allocated

Algorithm

1×	egg-herbie

Rules

19 654×	`lower-fma.f64`
19 654×	`lower-fma.f32`
6 400×	`lower-*.f64`
6 400×	`lower-*.f32`
1 974×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	195	2576
1	536	2432
2	1586	2236
3	5444	2204
0	8205	2046

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (+ (* 64 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 512 (/ (pow y 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(/ (pow y 2) x)
(/ (pow y 2) x)
(/ (pow y 2) x)
(/ (pow y 2) x)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* -1/8 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1/8 (pow x 2)) (* -1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/512 (/ (pow x 6) (pow y 4)))) (* 1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/4096 (/ (pow x 8) (pow y 6)))) (+ (* 1/512 (/ (pow x 6) (pow y 4))) (* 1/64 (/ (pow x 4) (pow y 2))))) (pow y 2))
(* 8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(/ (pow y 2) x)
(/ (pow y 2) x)
(/ (pow y 2) x)
(/ (pow y 2) x)
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(* -8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(* -1/8 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1/8 (pow x 2)) (* -1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/512 (/ (pow x 6) (pow y 4)))) (* 1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/4096 (/ (pow x 8) (pow y 6)))) (+ (* 1/512 (/ (pow x 6) (pow y 4))) (* 1/64 (/ (pow x 4) (pow y 2))))) (pow y 2))
(* 8 (/ (pow y 2) (pow x 2)))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
-1
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(/ 1/2 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(/ (pow y 2) x)
(/ (pow y 2) x)
(/ (pow y 2) x)
(/ (pow y 2) x)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
(* -8 (/ (pow y 2) (pow x 2)))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -8 (pow y 2)) (pow x 2)) (pow x 2))
(* -1/8 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* -1/64 (/ (pow x 2) (pow y 4))) (* 1/8 (/ 1 (pow y 2)))))
(* (pow x 2) (- (* (pow x 2) (- (* -1/512 (/ (pow x 2) (pow y 6))) (* 1/64 (/ 1 (pow y 4))))) (* 1/8 (/ 1 (pow y 2)))))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1/4096 (/ (pow x 2) (pow y 8))) (* 1/512 (/ 1 (pow y 6))))) (* 1/64 (/ 1 (pow y 4))))) (* 1/8 (/ 1 (pow y 2)))))
(* 8 (/ (pow y 2) (pow x 2)))
(/ (+ (* 8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* 8 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* 8 (pow y 2)) (pow x 2)) (pow x 2))
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)
-1
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(/ (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 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 64 (/ (pow y 4) (pow x 4)))) (* -8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 512 (/ (pow y 6) (pow x 6)))) (+ (* -64 (/ (pow y 4) (pow x 4))) (* -8 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ (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 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 64 (/ (pow y 4) (pow x 4)))) (* -8 (/ (pow y 2) (pow x 2))))
(- (+ 1 (* 512 (/ (pow y 6) (pow x 6)))) (+ (* -64 (/ (pow y 4) (pow x 4))) (* -8 (/ (pow y 2) (pow x 2)))))
1
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
1
(- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))
(- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))
(* 1/2 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ (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 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -8 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) (.f64 x x)) (.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (+ (* 64 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal 8 binary64) x) y) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (* 512 (/ (pow y 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 8 binary64) x) y) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 512 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) (.f64 x x)) (.f64 y y) #s(literal 1 binary64))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) (.f64 x x)) (.f64 y y) #s(literal 1 binary64))
(+ 1 (* 8 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) (.f64 x x)) (.f64 y y) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -128 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -8 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
(* 1/2 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.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) x)
(/.f64 (*.f64 y y) x)
(/ (pow y 2) x)
(/.f64 (*.f64 y y) x)
(/ (pow y 2) x)
(/.f64 (*.f64 y y) x)
(/ (pow y 2) x)
(/.f64 (*.f64 y y) x)
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
(* -8 (/ (pow y 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(* -1/8 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x y)) (/.f64 x y))
(/ (+ (* -1/8 (pow x 2)) (* -1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1/64 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (*.f64 y y))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/512 (/ (pow x 6) (pow y 4)))) (* 1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1/64 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/512 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x)))) (*.f64 y y))
(/ (- (+ (* -1/8 (pow x 2)) (* -1/4096 (/ (pow x 8) (pow y 6)))) (+ (* 1/512 (/ (pow x 6) (pow y 4))) (* 1/64 (/ (pow x 4) (pow y 2))))) (pow y 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1/64 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (fma.f64 (pow.f64 x #s(literal 8 binary64)) (/.f64 #s(literal -1/4096 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/512 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))))) (*.f64 y y))
(* 8 (/ (pow y 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 8 binary64) x) y) (/.f64 y x))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) (.f64 x x)) (.f64 y y) #s(literal 1 binary64))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) (.f64 x x)) (.f64 y y) #s(literal 1 binary64))
(* (pow y 2) (+ (* 8 (/ 1 (pow x 2))) (/ 1 (pow y 2))))
(fma.f64 (/.f64 #s(literal 8 binary64) (.f64 x x)) (.f64 y y) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (* 1/2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(/ 1/2 (pow y 2))
(/.f64 #s(literal 1/2 binary64) (*.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) x)
(/.f64 (*.f64 y y) x)
(/ (pow y 2) x)
(/.f64 (*.f64 y y) x)
(/ (pow y 2) x)
(/.f64 (*.f64 y y) x)
(/ (pow y 2) x)
(/.f64 (*.f64 y y) x)
-1
#s(literal -1 binary64)
(- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (/.f64 x y) (fma.f64 (fma.f64 (.f64 #s(literal 1/32 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
(* -8 (/ (pow y 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(* (pow y 2) (- (/ 1 (pow y 2)) (* 8 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) (/.f64 y x) #s(literal 1 binary64))
(* -1/8 (/ (pow x 2) (pow y 2)))
(.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x y)) (/.f64 x y))
(/ (+ (* -1/8 (pow x 2)) (* -1/64 (/ (pow x 4) (pow y 2)))) (pow y 2))
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(/ (pow y 2) x)
(/.f64 (*.f64 y 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)

rewrite286.0ms (4.5%)

Memory

-7.7MiB live, 184.8MiB allocated

Rules

5 786×	`lower-fma.f32`
5 782×	`lower-fma.f64`
4 382×	`lower-*.f32`
4 376×	`lower-*.f64`
3 908×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	156
0	43	156
1	178	156
2	1217	150
0	8536	137

Stop Event

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

Counts

10 → 288

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))))
#s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
(*.f64 y y)
(*.f64 y (/.f64 y x))
(*.f64 x x)

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1/2 binary64)) (pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1/2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(.f64 (pow.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))) #s(literal -1 binary64))
(pow.f64 (.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))
(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(exp.f64 (.f64 (log.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(.f64 (neg.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))
(pow.f64 (pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))))
(neg.f64 (/.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))))
(exp.f64 (neg.f64 (.f64 (log.f64 #s(approx (/ 1 (+ ( (pow (/ x y) -2) -8) 1)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)))) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (*.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
(.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))))
(.f64 (-.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
(.f64 (+.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)))) (.f64 (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))))) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64))))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64)))) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)))) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 512 binary64) (pow.f64 (/.f64 y x) #s(literal 6 binary64)))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 64 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)) (.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 8 binary64) (pow.f64 (/.f64 x y) #s(literal -2 binary64)))))))
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(*.f64 (/.f64 y (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 y (pow.f64 y #s(literal -1 binary64))) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 (neg.f64 y) x))
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 (neg.f64 y) x))
(*.f64 (/.f64 (neg.f64 y) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 y (/.f64 #s(literal -1 binary64) y)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 y (pow.f64 y #s(literal -1 binary64))))
(.f64 (.f64 (neg.f64 y) y) (/.f64 #s(literal -1 binary64) x))
(.f64 (.f64 y y) (pow.f64 x #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 y x) y) #s(literal 1 binary64))
(*.f64 (/.f64 y x) y)
(.f64 #s(literal 1 binary64) (.f64 (/.f64 y x) y))
(*.f64 y (/.f64 y x))
(pow.f64 (*.f64 x (pow.f64 y #s(literal -2 binary64))) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 y) y) (neg.f64 x))
(/.f64 (neg.f64 y) (/.f64 (neg.f64 x) y))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x (pow.f64 y #s(literal -2 binary64)))))
(/.f64 (*.f64 y y) x)
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (pow.f64 y #s(literal -2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) y))
(/.f64 #s(literal 1 binary64) (*.f64 x (pow.f64 y #s(literal -2 binary64))))
(/.f64 y (/.f64 x y))
(neg.f64 (/.f64 (*.f64 (neg.f64 y) y) x))
(neg.f64 (/.f64 y (/.f64 (neg.f64 x) y)))
(neg.f64 (*.f64 y (/.f64 (neg.f64 y) x)))
(neg.f64 (*.f64 (/.f64 (neg.f64 y) x) y))
(neg.f64 (/.f64 (*.f64 y y) (neg.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (*.f64 y y) (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval106.0ms (1.7%)

Memory: 13.3MiB live, 96.5MiB allocated
Compiler: Compiled 8 457 to 1 399 computations (83.5% saved)

prune74.0ms (1.2%)

Memory

-1.4MiB live, 75.5MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	492	0	492
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	492	5	497

Accuracy

99.6%

Counts

497 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
✓	53.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
✓	53.3%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))
✓	52.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓	48.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 136 to 82 computations (39.7% saved)

regimes58.0ms (0.9%)

Memory

-13.8MiB live, 25.5MiB allocated

Counts

9 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))))

Outputs

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64)))))

(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Calls

5 calls:

45.0ms	(*.f64 x x)
3.0ms	y
3.0ms	x
3.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)
3.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Results

Accuracy	Segments	Branch
81.3%	3	`x`
86.2%	3	`y`
77.7%	2	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`
81.3%	3	`(*.f64 x x)`
86.2%	3	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 29 to 21 computations (27.6% saved)

regimes7.0ms (0.1%)

Memory

19.6MiB live, 19.6MiB allocated

Counts

8 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Outputs

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))

(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Calls

2 calls:

3.0ms	y
3.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)

Results

Accuracy	Segments	Branch
86.2%	3	`y`
86.2%	3	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes95.0ms (1.5%)

Memory

-12.5MiB live, 32.6MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) #s(literal 2 binary64))) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (*.f64 x x) y) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* (pow (/ x y) -2) -8) 1)) (fma.f64 (/.f64 #s(literal 8 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64)))))

Outputs

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (*.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Calls

4 calls:

86.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)
3.0ms	y
3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
74.5%	2	`x`
74.5%	2	`(*.f64 x x)`
78.9%	2	`y`
78.9%	2	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 10 to 12 computations (-20% saved)

regimes5.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Calls

2 calls:

2.0ms	y
2.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)

Results

Accuracy	Segments	Branch
78.3%	2	`y`
78.3%	2	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes74.0ms (1.2%)

Memory

-24.0MiB live, 13.9MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Calls

5 calls:

69.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)
1.0ms	x
1.0ms	y
1.0ms	(*.f64 x x)
1.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Results

Accuracy	Segments	Branch
48.4%	1	`(*.f64 x x)`
48.4%	1	`x`
48.4%	1	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`
48.4%	1	`y`
48.4%	1	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 29 to 21 computations (27.6% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.09206372114771e+223	8.535897799050146e+229
0.0ms	4.734778918758588e-288	1.2009137290023491e-287

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.09206372114771e+223	8.535897799050146e+229
0.0ms	4.734778918758588e-288	1.2009137290023491e-287

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.3768436933775405e+111	1.0533743233658457e+113

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.3497091281206424e+74	1.9282142689819076e+78

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify78.0ms (1.2%)

Memory

5.3MiB live, 44.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`-commutative-binary64-.f64`
12×	`+-commutative-binary64-+.f64`
10×	`sub-neg-binary64-neg.f64-+.f64--.f64`
8×	`neg-sub0-binary64--.f64-neg.f64`
8×	`distribute-rgt-neg-in-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	304
1	56	304
2	71	304
3	79	304
4	85	304
5	87	304

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/1371531017198422170813984062796802317518598158983083017528000497114049345439918236791293924884090698403321181334468027936239545965686161975806025929561417574903624675177501566133897549447983506160378135315589948797898488482227042247573189625097864053065113149143877397460535018451535921515162325512880128 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 99999999999999996954903517948319502092964807244749211214842475260109694882873713352688654575305085714037182409224841134505892881183378706080253249519082903930108094789640533388351546084948006950326015738792668900564521713664 binary64)) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))))
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/1371531017198422170813984062796802317518598158983083017528000497114049345439918236791293924884090698403321181334468027936239545965686161975806025929561417574903624675177501566133897549447983506160378135315589948797898488482227042247573189625097864053065113149143877397460535018451535921515162325512880128 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 99999999999999996954903517948319502092964807244749211214842475260109694882873713352688654575305085714037182409224841134505892881183378706080253249519082903930108094789640533388351546084948006950326015738792668900564521713664 binary64)) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))))
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 3999999999999999827279090566567263033620417909033513127181584862491530430484445952615771723789729288178995560448 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 399999999999999980659275247211168791540784363212053420668827279054600142848 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Outputs
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/1371531017198422170813984062796802317518598158983083017528000497114049345439918236791293924884090698403321181334468027936239545965686161975806025929561417574903624675177501566133897549447983506160378135315589948797898488482227042247573189625097864053065113149143877397460535018451535921515162325512880128 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 99999999999999996954903517948319502092964807244749211214842475260109694882873713352688654575305085714037182409224841134505892881183378706080253249519082903930108094789640533388351546084948006950326015738792668900564521713664 binary64)) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))))
(if (<=.f64 (.f64 (.f64 #s(literal 4 binary64) y) y) #s(literal 6857655085992111/1371531017198422170813984062796802317518598158983083017528000497114049345439918236791293924884090698403321181334468027936239545965686161975806025929561417574903624675177501566133897549447983506160378135315589948797898488482227042247573189625097864053065113149143877397460535018451535921515162325512880128 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal -8 binary64) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 #s(literal 4 binary64) y) y) #s(literal 99999999999999996954903517948319502092964807244749211214842475260109694882873713352688654575305085714037182409224841134505892881183378706080253249519082903930108094789640533388351546084948006950326015738792668900564521713664 binary64)) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) y) y)) (+.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) y) y))) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))))
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 6857655085992111/1371531017198422170813984062796802317518598158983083017528000497114049345439918236791293924884090698403321181334468027936239545965686161975806025929561417574903624675177501566133897549447983506160378135315589948797898488482227042247573189625097864053065113149143877397460535018451535921515162325512880128 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 99999999999999996954903517948319502092964807244749211214842475260109694882873713352688654575305085714037182409224841134505892881183378706080253249519082903930108094789640533388351546084948006950326015738792668900564521713664 binary64)) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y))) #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))))
(if (<=.f64 (.f64 (.f64 #s(literal 4 binary64) y) y) #s(literal 6857655085992111/1371531017198422170813984062796802317518598158983083017528000497114049345439918236791293924884090698403321181334468027936239545965686161975806025929561417574903624675177501566133897549447983506160378135315589948797898488482227042247573189625097864053065113149143877397460535018451535921515162325512880128 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))) (if (<=.f64 (.f64 (.f64 #s(literal 4 binary64) y) y) #s(literal 99999999999999996954903517948319502092964807244749211214842475260109694882873713352688654575305085714037182409224841134505892881183378706080253249519082903930108094789640533388351546084948006950326015738792668900564521713664 binary64)) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) y) y)) (+.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) y) y))) #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))))
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 3999999999999999827279090566567263033620417909033513127181584862491530430484445952615771723789729288178995560448 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
(if (<=.f64 (.f64 (.f64 #s(literal 4 binary64) y) y) #s(literal 3999999999999999827279090566567263033620417909033513127181584862491530430484445952615771723789729288178995560448 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 y x) #s(literal -8 binary64)) (/.f64 y x) #s(literal 1 binary64))) #s(approx (/ (- ( x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 399999999999999980659275247211168791540784363212053420668827279054600142848 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
(if (<=.f64 (.f64 (.f64 #s(literal 4 binary64) y) y) #s(literal 399999999999999980659275247211168791540784363212053420668827279054600142848 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

soundness516.0ms (8.2%)

Memory

-2.0MiB live, 346.0MiB allocated

Rules

18 822×	`lower-fma.f64`
18 822×	`lower-fma.f32`
7 902×	`lower-fma.f32`
7 898×	`lower-fma.f64`
7 268×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	141
0	33	141
1	135	139
2	1030	137
0	8960	125
0	116	990
1	321	990
2	960	844
3	4060	836
0	8249	766

Stop Event

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

Compiler

Compiled 180 to 85 computations (52.8% saved)

preprocess58.0ms (0.9%)

Memory

29.0MiB live, 152.1MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 666 to 244 computations (63.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample892.0ms (14.1%)

explain117.0ms (1.8%)

preprocess191.0ms (3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify56.0ms (0.9%)

localize27.0ms (0.4%)

series56.0ms (0.9%)

simplify191.0ms (3%)

rewrite182.0ms (2.9%)

eval132.0ms (2.1%)

prune98.0ms (1.6%)

simplify282.0ms (4.5%)

localize85.0ms (1.3%)

series36.0ms (0.6%)

simplify221.0ms (3.5%)

rewrite177.0ms (2.8%)

eval114.0ms (1.8%)

prune95.0ms (1.5%)

simplify170.0ms (2.7%)

localize55.0ms (0.9%)

series30.0ms (0.5%)

simplify211.0ms (3.3%)

rewrite365.0ms (5.8%)

eval394.0ms (6.2%)

prune109.0ms (1.7%)

simplify313.0ms (5%)

localize82.0ms (1.3%)

series31.0ms (0.5%)

simplify235.0ms (3.7%)

rewrite286.0ms (4.5%)

eval106.0ms (1.7%)

prune74.0ms (1.2%)

regimes58.0ms (0.9%)

regimes7.0ms (0.1%)

regimes95.0ms (1.5%)

regimes5.0ms (0.1%)

regimes74.0ms (1.2%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify78.0ms (1.2%)

soundness516.0ms (8.2%)

preprocess58.0ms (0.9%)

end0.0ms (0%)

Profiling