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

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

analyze9.0ms (0.2%)

Memory

-32.2MiB live, 7.4MiB 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)

sample1.1s (19.5%)

Memory

-88.5MiB live, 1 372.1MiB allocated

Samples

784.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 443.0ms

ival-mult: 187.0ms (42.3% of total)

ival-sub: 113.0ms (25.5% of total)

ival-div: 71.0ms (16% of total)

ival-add: 58.0ms (13.1% of total)

ival-true: 5.0ms (1.1% of total)

exact: 5.0ms (1.1% of total)

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

Bogosity

explain165.0ms (3%)

Memory

-3.9MiB live, 282.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
134	-	-	`(/.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)))`
24	-	-	`(-.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	123	0
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	overflow	67
↳	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	overflow	123
↳	`(*.f64 x x)`	overflow	80
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	overflow	67
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	overflow	123
↳	`(*.f64 x x)`	overflow	80
`-.f64`	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	nan-rescue	24	0
↳	`(*.f64 x x)`	overflow	80
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	overflow	67
`/.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	11	0
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	underflow	73
↳	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	underflow	11
↳	`(*.f64 x x)`	underflow	40
↳	`(.f64 (.f64 y #s(literal 4 binary64)) y)`	underflow	73
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))`	underflow	11
↳	`(*.f64 x x)`	underflow	40

Confusion

	Predicted +	Predicted -
+	134	0
-	0	122

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	0
-	0	0	122

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	122
1	110
2	24

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms

512×

valid

Compiler

Compiled 176 to 40 computations (77.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 34.0ms (80.4% of total)

ival-div: 3.0ms (7.1% of total)

ival-sub: 2.0ms (4.7% of total)

ival-add: 2.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess181.0ms (3.3%)

Memory

14.9MiB live, 90.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	97
1	89	97
2	240	95
3	621	95
4	1748	95
5	2724	95
6	2963	95
7	2982	95
8	2997	95
9	3002	95
10	3002	95
11	3302	95
12	3438	95
13	3438	95
14	3582	95
15	4457	95
16	4457	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	725	19
8	1248	19
9	2302	19
10	2353	19
11	2391	19
12	2419	19
13	2419	19
0	2419	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)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.7%	(/.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)

simplify65.0ms (1.2%)

Memory

-17.8MiB live, 27.9MiB 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))

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	725	51
8	1248	51
9	2302	51
10	2353	51
11	2391	51
12	2419	51
13	2419	51
0	2419	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))

localize40.0ms (0.7%)

Memory

-4.4MiB live, 35.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y #s(literal 4 binary64))
accuracy	0	(*.f64 x x)
accuracy	5.343727294132265	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
accuracy	32.822359513884614	(/.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

16.0ms

256×

valid

Compiler

Compiled 104 to 20 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 5.0ms (57.9% of total)

ival-sub: 1.0ms (11.6% of total)

ival-div: 1.0ms (11.6% of total)

ival-add: 1.0ms (11.6% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.2%)

Memory

23.7MiB live, 23.7MiB 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>) () ())) ())
#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>) () ())) ())
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#s(alt (- (pow x 2) (* 4 (pow y 2))) (taylor 0 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 (+ (* 4 (pow y 2)) (pow x 2)) (taylor 0 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 (- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1) (taylor 0 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) (+ 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>) () ())) ())
#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 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>) () ())) ())
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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) (+ 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>) () ())) ())
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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>) () ())) ())
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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 (/.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>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	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))

simplify242.0ms (4.4%)

Memory

10.4MiB live, 316.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	990
1	321	990
2	986	844
3	4103	836
0	8221	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 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #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 (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 #s(literal -8 binary64) (*.f64 x x)) 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 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #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 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #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)

rewrite157.0ms (2.9%)

Memory

-18.6MiB live, 219.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	15	43
1	54	43
2	397	43
3	6363	43
0	8342	39

Stop Event

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

Counts

5 → 628

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
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eval102.0ms (1.9%)

Memory: 24.1MiB live, 209.1MiB allocated
Compiler: Compiled 27 924 to 1 612 computations (94.2% saved)

prune20.0ms (0.4%)

Memory

-6.8MiB live, 64.5MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	755	4	759
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	756	4	760

Accuracy

99.6%

Counts

760 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.5%	(/.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)))
▶	54.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
▶	56.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
▶	43.7%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 32 to 27 computations (15.6% saved)

simplify187.0ms (3.4%)

Memory

0.2MiB live, 123.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	149
0	38	146
1	67	143
2	115	143
3	194	143
4	310	143
5	437	143
6	607	143
7	895	143
8	1839	143
9	3200	143
10	3525	143
11	3725	143
12	3828	143
13	3840	143
14	3850	143
15	3907	143
16	3947	143
17	4059	143
18	4083	143
19	4083	143
20	4091	143
21	4091	143
22	4091	143
0	4091	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 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64))
(.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y)
(/.f64 #s(literal -8 binary64) (*.f64 x x))
#s(literal -8 binary64)
(*.f64 x x)
x
y
#s(literal 1 binary64)
(/.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)))
(fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x))
#s(literal -4 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(*.f64 #s(literal 4 binary64) y)
#s(literal 4 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 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64))
(.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y)
(/.f64 #s(literal -8 binary64) (*.f64 x x))
#s(literal -8 binary64)
(*.f64 x x)
x
y
#s(literal 1 binary64)
(/.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 (fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x)) (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x)))
(fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x))
(fma.f64 (.f64 y y) #s(literal -4 binary64) (.f64 x x))
#s(literal -4 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
(fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 x x))
(*.f64 #s(literal 4 binary64) y)
#s(literal 4 binary64)

localize82.0ms (1.5%)

Memory

-6.8MiB live, 171.0MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 #s(literal 4 binary64) y)
accuracy	5.347633544132265	(fma.f64 #s(literal -4 binary64) (.f64 y y) (.f64 x x))
accuracy	32.822359513884614	(/.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)))
accuracy	0.47867463003566557	(/.f64 #s(literal -8 binary64) (*.f64 x x))
accuracy	1.0022826938993534	(fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64))
accuracy	8.497932784718868	(.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y)
accuracy	26.58021155480763	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
accuracy	27.555816242628165	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
accuracy	36.0273095263657	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Samples

61.0ms

256×

valid

Compiler

Compiled 233 to 45 computations (80.7% saved)

Precisions

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

ival-mult: 18.0ms (51.7% of total)

ival-add: 10.0ms (28.7% of total)

ival-div: 5.0ms (14.4% of total)

ival-sub: 1.0ms (2.9% of total)

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

exact: 0.0ms (0% of total)

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

series22.0ms (0.4%)

Memory

7.7MiB live, 86.3MiB allocated

Counts

11 → 216

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

Calls

6 calls:

Time	Variable		Point	Expression
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 (* x x)) y) y) 1) (* (/ -8 (* x x)) y) (/ -8 (* x x)) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (* x x) (* 4 y))
3.0ms	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 (* x x)) y) y) 1) (* (/ -8 (* x x)) y) (/ -8 (* x x)) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (* x x) (* 4 y))
2.0ms	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 (* x x)) y) y) 1) (* (/ -8 (* x x)) y) (/ -8 (* x x)) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (* x x) (* 4 y))
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 (* x x)) y) y) 1) (* (/ -8 (* x x)) y) (/ -8 (* x x)) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (* x x) (* 4 y))
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) y)) (+ (* x x) (* (* y 4) y))) (+ (* (* (/ -8 (* x x)) y) y) 1) (* (/ -8 (* x x)) y) (/ -8 (* x x)) (/ (+ (* -4 (* y y)) (* x x)) (+ (* (* 4 y) y) (* x x))) (+ (* -4 (* y y)) (* x x)) (* y y) (* x x) (* 4 y))

simplify208.0ms (3.8%)

Memory

31.4MiB live, 292.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	118	2798
1	317	2798
2	978	2342
3	4010	2326
0	8216	2154

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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

rewrite177.0ms (3.2%)

Memory

-27.1MiB live, 170.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	128
0	38	125
1	149	122
2	1034	122
0	8909	122

Stop Event

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

Counts

11 → 495

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

Outputs
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eval192.0ms (3.5%)

Memory: 4.2MiB live, 189.3MiB allocated
Compiler: Compiled 20 863 to 1 593 computations (92.4% saved)

prune53.0ms (1%)

Memory

-7.7MiB live, 42.2MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	768	1	769
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	768	5	773

Accuracy

99.8%

Counts

773 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.5%	(/.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)))
▶	58.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64)))
✓	54.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
✓	56.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓	43.7%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 43 to 36 computations (16.3% saved)

simplify197.0ms (3.6%)

Memory

-20.9MiB live, 90.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	59
0	21	59
1	44	59
2	87	59
3	167	59
4	285	59
5	419	59
6	587	59
7	874	59
8	1822	59
9	3117	59
10	3446	59
11	3638	59
12	3741	59
13	3753	59
14	3763	59
15	3820	59
16	3860	59
17	3990	59
18	4014	59
19	4014	59
20	4022	59
21	4022	59
22	4022	59
0	4022	57

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

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

localize50.0ms (0.9%)

Memory

3.8MiB live, 88.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.125	(/.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) x)
accuracy	0.22265625	(*.f64 (/.f64 #s(literal -8 binary64) x) y)
accuracy	1.0022826938993534	(fma.f64 (/.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64))
accuracy	26.58021155480763	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64)))

Samples

41.0ms

256×

valid

Compiler

Compiled 91 to 27 computations (70.3% saved)

Precisions

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

ival-mult: 12.0ms (59.3% of total)

ival-div: 5.0ms (24.7% of total)

ival-add: 2.0ms (9.9% of total)

ival-sub: 1.0ms (4.9% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Memory

-3.4MiB live, 34.3MiB allocated

Counts

4 → 96

Calls

Call 1

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

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

Calls

6 calls:

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

simplify201.0ms (3.7%)

Memory

23.0MiB live, 296.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	1028
1	304	1028
2	927	914
3	3452	910
0	8239	858

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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))))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ 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))))))
(* -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)))))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ 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))))))
(* -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)))))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ 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)
(* -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 (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ 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
(+ 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 (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ 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
(+ 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 (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y (pow x 2)))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))
(* -8 (/ y x))

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

rewrite178.0ms (3.2%)

Memory

-16.4MiB live, 260.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
0	21	52
1	95	52
2	680	52
0	8236	50

Stop Event

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

Counts

4 → 192

Calls

Call 1

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

Outputs
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eval57.0ms (1%)

Memory: 25.9MiB live, 133.8MiB allocated
Compiler: Compiled 5 323 to 782 computations (85.3% saved)

prune14.0ms (0.3%)

Memory

-14.1MiB live, 30.6MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	287	6	293

Accuracy

99.8%

Counts

293 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.5%	(/.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)))
✓	58.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64)))
✓	54.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
▶	29.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* (/ -8 x) y) x) y) 1) (/.f64 (/.f64 (fma.f64 (.f64 y y) #s(literal -8 binary64) (.f64 x x)) x) x)))
✓	56.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓	43.7%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 57 to 46 computations (19.3% saved)

simplify224.0ms (4.1%)

Memory

-15.9MiB live, 203.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	107
0	29	107
1	57	107
2	99	107
3	177	107
4	294	107
5	434	107
6	600	107
7	897	107
8	1904	104
9	3500	103
10	3924	103
11	4541	103
12	5249	103
13	5850	103
14	6188	103
15	6559	103
16	6996	103
0	8028	95

Stop Event

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

Calls

Call 1

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

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

localize70.0ms (1.3%)

Memory

2.4MiB live, 78.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	3.1081996287448805	(/.f64 (/.f64 (fma.f64 (.f64 y y) #s(literal -8 binary64) (.f64 x x)) x) x)
accuracy	5.349918553900706	(fma.f64 (.f64 y y) #s(literal -8 binary64) (.f64 x x))
accuracy	19.800134636817514	(/.f64 (fma.f64 (.f64 y y) #s(literal -8 binary64) (.f64 x x)) x)
accuracy	26.58021155480763	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* (/ -8 x) y) x) y) 1) (/.f64 (/.f64 (fma.f64 (.f64 y y) #s(literal -8 binary64) (.f64 x x)) x) x)))

Samples

60.0ms

256×

valid

Compiler

Compiled 140 to 33 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-add: 28.0ms (58.1% of total)

ival-mult: 11.0ms (22.8% of total)

ival-div: 8.0ms (16.6% of total)

ival-sub: 1.0ms (2.1% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Memory

16.2MiB live, 16.2MiB allocated

Counts

5 → 120

Calls

Call 1

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

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

Calls

6 calls:

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

simplify227.0ms (4.2%)

Memory

-1.4MiB live, 237.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	1412
1	348	1412
2	1068	1298
3	4427	1282
0	8243	1182

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 117

Calls

Call 1

Inputs
x
(+ x (* -8 (/ (pow y 2) x)))
(+ x (* -8 (/ (pow y 2) x)))
(+ x (* -8 (/ (pow y 2) 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
(+ 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 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(pow x 2)
(+ (* -8 (pow y 2)) (pow x 2))
(+ (* -8 (pow y 2)) (pow x 2))
(+ (* -8 (pow y 2)) (pow x 2))
(* -8 (/ (pow y 2) x))
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x))))
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x))))
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 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)))))
(* -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)))))
(* -8 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8))
(* -8 (/ (pow y 2) x))
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x))))
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 x))))
(* (pow y 2) (- (/ x (pow y 2)) (* 8 (/ 1 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)))))
(* -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)))))
(* -8 (pow y 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 8))
(* -8 (/ (pow y 2) x))
(/ (+ (* -8 (pow y 2)) (pow x 2)) x)
(/ (+ (* -8 (pow y 2)) (pow x 2)) x)
(/ (+ (* -8 (pow y 2)) (pow x 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))
(* -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 (pow y 2))
(+ (* -8 (pow y 2)) (pow x 2))
(+ (* -8 (pow y 2)) (pow x 2))
(+ (* -8 (pow y 2)) (pow x 2))
x
(* x (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))
(* x (+ 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 (* -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 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))
x
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1)))
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1)))
(* -1 (* x (- (* 8 (/ (pow y 2) (pow x 2))) 1)))
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 (* -8 (/ (pow y 2) (pow x 2))))
(+ 1 (* -8 (/ (pow y 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (pow y 2) (pow x 2)))))

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

rewrite165.0ms (3%)

Memory

-5.1MiB live, 221.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	98
0	29	98
1	129	98
2	951	98
0	8373	94

Stop Event

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

Counts

5 → 199

Calls

Call 1

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

Outputs
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eval86.0ms (1.6%)

Memory: -6.5MiB live, 125.1MiB allocated
Compiler: Compiled 6 461 to 1 084 computations (83.2% saved)

prune8.0ms (0.2%)

Memory

27.3MiB live, 27.3MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	316	6	322

Accuracy

99.8%

Counts

322 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.5%	(/.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)))
✓	58.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64)))
✓	54.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal -8 binary64) (.f64 x x)) y) y #s(literal 1 binary64)))
✓	29.4%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(approx (+ (* (/ (* (/ -8 x) y) x) y) 1) (/.f64 (/.f64 (fma.f64 (.f64 y y) #s(literal -8 binary64) (.f64 x x)) x) x)))
✓	56.9%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓	43.7%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 133 to 80 computations (39.8% saved)

regimes15.0ms (0.3%)

Memory

-12.6MiB live, 26.1MiB allocated

Counts

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

(/.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)))

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

Calls

5 calls:

4.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)
3.0ms	x
3.0ms	y
3.0ms	(*.f64 x x)
2.0ms	(/.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
81.5%	3	`x`
83.3%	3	`y`
77.8%	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)))`
81.5%	3	`(*.f64 x x)`
83.3%	3	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 29 to 21 computations (27.6% saved)

regimes5.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

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

Outputs

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (*.f64 (/.f64 #s(literal -8 binary64) x) y) x) 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
80.0%	2	`y`
80.0%	2	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes10.0ms (0.2%)

Memory

-29.9MiB live, 15.2MiB allocated

Counts

3 → 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 (/.f64 #s(literal -8 binary64) (*.f64 x x)) y) y #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

4 calls:

4.0ms	y
2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)

Results

Accuracy	Segments	Branch
75.0%	2	`x`
75.0%	2	`(*.f64 x x)`
79.6%	2	`y`
79.6%	2	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 10 to 12 computations (-20% saved)

regimes6.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB 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:

1.0ms	x
1.0ms	y
1.0ms	(.f64 (.f64 y #s(literal 4 binary64)) 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
43.7%	1	`x`
43.7%	1	`(*.f64 x x)`
43.7%	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)))`
43.7%	1	`y`
43.7%	1	`(.f64 (.f64 y #s(literal 4 binary64)) y)`

Compiler

Compiled 29 to 21 computations (27.6% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.718030841637427e+215	2.4282069481820626e+219
0.0ms	2.014818263394239e-154	1.627095510017558e-151

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	61044187548.24677	847171109602742.6

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	61044187548.24677	847171109602742.6

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify105.0ms (1.9%)

Memory

-3.4MiB live, 35.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	214
1	55	214
2	81	214
3	138	214
4	249	214
5	400	214
6	698	214
7	5000	214

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64))) (if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 1000000000000000021421546958041957442493134746744949294176709095342291740583330369404881029347127449862957279318330932090828950478869943421594604148335480073467842242942440201823873880805647866312652703956229962072064 binary64)) (/.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))) #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 100000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) x) 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 y #s(literal 4 binary64)) y) #s(literal 100000000000 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 3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64))) (if (<=.f64 (.f64 (.f64 y #s(literal 4 binary64)) y) #s(literal 1000000000000000021421546958041957442493134746744949294176709095342291740583330369404881029347127449862957279318330932090828950478869943421594604148335480073467842242942440201823873880805647866312652703956229962072064 binary64)) (/.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))) #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 3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) x) y #s(literal 1 binary64))) (if (<=.f64 (.f64 (.f64 #s(literal 4 binary64) y) y) #s(literal 1000000000000000021421546958041957442493134746744949294176709095342291740583330369404881029347127449862957279318330932090828950478869943421594604148335480073467842242942440201823873880805647866312652703956229962072064 binary64)) (/.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))) #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 100000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) x) 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 100000000000 binary64)) #s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 (.f64 (/.f64 #s(literal -8 binary64) x) y) x) 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 y #s(literal 4 binary64)) y) #s(literal 100000000000 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 100000000000 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))

soundness647.0ms (11.8%)

Memory

12.6MiB live, 362.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	990
1	321	990
2	986	844
3	4103	836
0	8221	766
0	25	128
0	38	125
1	149	122
2	1034	122
0	8909	122
0	9	43
0	15	43
1	54	43
2	397	43
3	6363	43
0	8342	39

Stop Event

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

Compiler

Compiled 199 to 98 computations (50.8% saved)

preprocess206.0ms (3.8%)

Memory

-20.1MiB live, 108.7MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 546 to 230 computations (57.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze9.0ms (0.2%)

sample1.1s (19.5%)

explain165.0ms (3%)

preprocess181.0ms (3.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify65.0ms (1.2%)

localize40.0ms (0.7%)

series10.0ms (0.2%)

simplify242.0ms (4.4%)

rewrite157.0ms (2.9%)

eval102.0ms (1.9%)

prune20.0ms (0.4%)

simplify187.0ms (3.4%)

localize82.0ms (1.5%)

series22.0ms (0.4%)

simplify208.0ms (3.8%)

rewrite177.0ms (3.2%)

eval192.0ms (3.5%)

prune53.0ms (1%)

simplify197.0ms (3.6%)

localize50.0ms (0.9%)

series12.0ms (0.2%)

simplify201.0ms (3.7%)

rewrite178.0ms (3.2%)

eval57.0ms (1%)

prune14.0ms (0.3%)

simplify224.0ms (4.1%)

localize70.0ms (1.3%)

series11.0ms (0.2%)

simplify227.0ms (4.2%)

rewrite165.0ms (3%)

eval86.0ms (1.6%)

prune8.0ms (0.2%)

regimes15.0ms (0.3%)

regimes5.0ms (0.1%)

regimes10.0ms (0.2%)

regimes6.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify105.0ms (1.9%)

soundness647.0ms (11.8%)

preprocess206.0ms (3.8%)

end0.0ms (0%)

Profiling