Metrics for Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze44.0ms (0.2%)

Memory

-9.6MiB live, 27.8MiB 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
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
68.8%	68.7%	31.2%	0.1%	0%	0%	0%	6
78.1%	78%	21.9%	0.1%	0%	0%	0%	7
82.8%	82.7%	17.2%	0.1%	0%	0%	0%	8
88.3%	88.2%	11.7%	0.1%	0%	0%	0%	9
91%	90.9%	9%	0.1%	0%	0%	0%	10
93.9%	93.9%	6%	0.1%	0%	0%	0%	11
95.4%	95.3%	4.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample847.0ms (3.2%)

Memory

24.9MiB live, 1 216.2MiB allocated

Samples

550.0ms	8 255×	0	valid
0.0ms	1×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 376.0ms

ival-div: 138.0ms (36.7% of total)

ival-mult: 87.0ms (23.2% of total)

ival-sub: 78.0ms (20.8% of total)

ival-add: 57.0ms (15.2% of total)

exact: 7.0ms (1.9% of total)

ival-true: 6.0ms (1.6% of total)

ival-assert: 3.0ms (0.8% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain461.0ms (1.8%)

Memory

-21.8MiB live, 143.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
27	-	-	`(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))`
0	-	-	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 x y)`
0	-	-	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`y`
0	-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

31.0ms

512×

valid

Compiler

Compiled 95 to 31 computations (67.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-div: 7.0ms (42.6% of total)

ival-mult: 4.0ms (24.3% of total)

ival-sub: 2.0ms (12.2% of total)

ival-add: 2.0ms (12.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess172.0ms (0.7%)

Memory

12.1MiB live, 48.7MiB allocated

Algorithm

1×	egg-herbie

Rules

384×	`lower-fma.f64`
384×	`lower-fma.f32`
272×	`lower-*.f32`
270×	`lower-*.f64`
224×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	63
1	57	61
2	121	57
3	253	55
4	541	55
5	888	55
6	995	55
7	1019	55
8	1029	55
9	1033	55
0	9	11
0	14	11
1	22	11
2	33	11
3	48	11
4	90	11
5	163	11
6	284	11
7	379	11
8	589	11
9	679	11
10	801	11
11	837	11
12	1000	11
13	1009	11
0	1009	10

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify284.0ms (1.1%)

Memory

2.5MiB live, 38.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

384×	`lower-fma.f64`
384×	`lower-fma.f32`
272×	`lower-*.f32`
270×	`lower-*.f64`
224×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	14	39
1	22	39
2	33	39
3	48	39
4	90	39
5	163	39
6	284	39
7	379	39
8	589	39
9	679	39
10	801	39
11	837	39
12	1000	39
13	1009	39
0	1009	36

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize75.0ms (0.3%)

Memory

-11.2MiB live, 34.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x y)
accuracy	0.00390625	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
accuracy	0.00390625	(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
accuracy	6.404643624986375	(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))

Samples

15.0ms

256×

valid

Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 3.0ms (37.8% of total)

ival-mult: 2.0ms (25.2% of total)

ival-sub: 1.0ms (12.6% of total)

ival-add: 1.0ms (12.6% 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%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (* x y)))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (/ 2 x) (taylor -inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) (taylor -inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1/2 (* x (pow y 2)))) (taylor 0 x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) (taylor 0 x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2))))) (taylor 0 x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 2 (* 4 (/ 1 (* x y)))) x) (taylor inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) (taylor inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) (taylor inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())

Calls

30 calls:

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

simplify340.0ms (1.3%)

Memory

15.3MiB live, 253.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 558×	`lower-fma.f64`
13 558×	`lower-fma.f32`
4 930×	`lower-*.f64`
4 930×	`lower-*.f32`
1 854×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	231	1053
1	738	1018
2	1942	987
3	6081	981
0	8428	934

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 115

Calls

Call 1

Inputs
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

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

rewrite428.0ms (1.6%)

Memory

-35.6MiB live, 366.6MiB allocated

Rules

5 754×	`lower-fma.f64`
5 754×	`lower-fma.f32`
4 124×	`lower-*.f32`
4 122×	`lower-*.f64`
2 962×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	14	35
1	63	35
2	500	35
3	6873	35
0	8527	32

Stop Event

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

Counts

5 → 279

Calls

Call 1

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

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

eval79.0ms (0.3%)

Memory: 33.0MiB live, 71.2MiB allocated
Compiler: Compiled 11 052 to 1 049 computations (90.5% saved)

prune90.0ms (0.3%)

Memory

9.2MiB live, 83.9MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	386	8	394
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	387	8	395

Accuracy

100.0%

Counts

395 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
▶	58.0%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y)))
▶	61.5%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 y (.f64 y #s(literal -1/2 binary64))) y)))
▶	57.7%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
	65.1%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)) x))
	55.0%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x))
	73.0%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
▶	29.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 170 to 98 computations (42.4% saved)

simplify18.2s (69.4%)

Memory

-38.2MiB live, 134.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

4 808×	`lower-fma.f32`
4 800×	`lower-fma.f64`
2 312×	`lower-*.f32`
2 300×	`lower-*.f64`
828×	`unsub-neg`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	33	225
0	54	225
1	101	225
2	208	225
3	425	225
4	660	225
5	992	224
6	1714	218
7	2764	218
8	3781	218
9	4437	218
10	4735	218
11	4855	218
12	4988	218
13	5190	218
14	5535	218
15	5535	218
16	5770	218
17	5912	218
18	5932	218
19	5932	218
20	5932	218
21	5932	218
22	5937	218
0	5937	218

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize163.0ms (0.6%)

Memory

7.8MiB live, 170.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y)))
accuracy	0.7215337826339021	(.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
accuracy	4.080061120449537	(fma.f64 x (.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y)
accuracy	29.24072541075659	#s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y))
accuracy	0	(*.f64 y #s(literal -1/2 binary64))
accuracy	0.00390625	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 y (.f64 y #s(literal -1/2 binary64))) y)))
accuracy	5.461238431859488	(fma.f64 x (.f64 y (.f64 y #s(literal -1/2 binary64))) y)
accuracy	29.706987964315022	#s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 y (.f64 y #s(literal -1/2 binary64))) y))
accuracy	0	(/.f64 #s(literal 2 binary64) x)
accuracy	0.00390625	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
accuracy	33.69028013384085	#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
accuracy	0	(neg.f64 y)
accuracy	45.339034446136324	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
accuracy	0	(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0	(*.f64 y #s(literal 1/2 binary64))
accuracy	0.00390625	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
accuracy	6.404643624986375	(/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))

Samples

89.0ms

256×

valid

Compiler

Compiled 178 to 32 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-add: 19.0ms (41.2% of total)

ival-mult: 16.0ms (34.7% of total)

ival-div: 7.0ms (15.2% of total)

ival-sub: 2.0ms (4.3% of total)

exact: 1.0ms (2.2% of total)

ival-neg: 1.0ms (2.2% of total)

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

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

series26.0ms (0.1%)

Memory

0.9MiB live, 42.0MiB allocated

Counts

18 → 372

Calls

Call 1

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

Outputs
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (* x y)))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) (taylor inf y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3)))) (taylor inf x) (#s(alt (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (patch (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3)))) (taylor inf x) (#s(alt (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (patch (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3)))) (taylor inf x) (#s(alt (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (patch (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* x (pow y 3))) (taylor -inf x) (#s(alt (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (patch (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/4 (pow y 3)) (* 1/2 (/ (pow y 2) x))))) (taylor -inf x) (#s(alt (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (patch (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/4 (pow y 3)) (* 1/2 (/ (pow y 2) x))))) (taylor -inf x) (#s(alt (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (patch (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/4 (pow y 3)) (* 1/2 (/ (pow y 2) x))))) (taylor -inf x) (#s(alt (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (patch (.f64 (.f64 y y) (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())

Calls

93 calls:

Time	Variable		Point	Expression
3.0ms	y	@	0	(+ (* x (* y (* y -1/2))) y)
1.0ms	x	@	0	(/ 2 x)
1.0ms	x	@	inf	(+ (* x (* (* y y) (+ (* x (* y 1/4)) -1/2))) y)
0.0ms	x	@	-inf	(+ (* x (* (* y y) (+ (* x (* y 1/4)) -1/2))) y)
0.0ms	x	@	0	(+ (* x (* y (* y -1/2))) y)

simplify313.0ms (1.2%)

Memory

-8.0MiB live, 344.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 034×	`lower-fma.f64`
14 034×	`lower-fma.f32`
4 420×	`lower-*.f64`
4 420×	`lower-*.f32`
2 940×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	296	4330
1	964	4143
2	2762	4004
3	7963	3994
0	8024	3784

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 345

Calls

Call 1

Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* -1/2 (* x (pow y 2))))
(* -1/2 (* x (pow y 2)))
(* x (+ (* -1/2 (pow y 2)) (/ y x)))
(* x (+ (* -1/2 (pow y 2)) (/ y x)))
(* x (+ (* -1/2 (pow y 2)) (/ y x)))
(* -1/2 (* x (pow y 2)))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* -1/2 (* x y))))
(* -1/2 (* x (pow y 2)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* -1/2 (* x (pow y 2)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1/2 (pow y 2))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (+ (* -1/2 (pow y 2)) (* 1/4 (* x (pow y 3))))))
(+ y (* x (+ (* -1/2 (pow y 2)) (* 1/4 (* x (pow y 3))))))
(* 1/4 (* (pow x 2) (pow y 3)))
(* (pow x 2) (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3))))
(* (pow x 2) (+ (* -1/2 (/ (pow y 2) x)) (+ (* 1/4 (pow y 3)) (/ y (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ (pow y 2) x)) (+ (* 1/4 (pow y 3)) (/ y (pow x 2)))))
(* 1/4 (* (pow x 2) (pow y 3)))
(* (pow x 2) (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ y x)) (* 1/2 (pow y 2))) x)) (* 1/4 (pow y 3))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ y x)) (* 1/2 (pow y 2))) x)) (* 1/4 (pow y 3))))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (+ (* -1/2 x) (* 1/4 (* (pow x 2) y))))))
(* y (+ 1 (* y (+ (* -1/2 x) (* 1/4 (* (pow x 2) y))))))
(* 1/4 (* (pow x 2) (pow y 3)))
(* (pow y 3) (+ (* -1/2 (/ x y)) (* 1/4 (pow x 2))))
(* (pow y 3) (+ (* -1/2 (/ x y)) (+ (* 1/4 (pow x 2)) (/ 1 (pow y 2)))))
(* (pow y 3) (+ (* -1/2 (/ x y)) (+ (* 1/4 (pow x 2)) (/ 1 (pow y 2)))))
(* 1/4 (* (pow x 2) (pow y 3)))
(* -1 (* (pow y 3) (+ (* -1/4 (pow x 2)) (* 1/2 (/ x y)))))
(* -1 (* (pow y 3) (+ (* -1 (/ (+ (* -1/2 x) (/ 1 y)) y)) (* -1/4 (pow x 2)))))
(* -1 (* (pow y 3) (+ (* -1 (/ (+ (* -1/2 x) (/ 1 y)) y)) (* -1/4 (pow x 2)))))
(* -1/2 (pow y 2))
(* (pow y 2) (- (* 1/4 (* x y)) 1/2))
(* (pow y 2) (- (* 1/4 (* x y)) 1/2))
(* (pow y 2) (- (* 1/4 (* x y)) 1/2))
(* 1/4 (* x (pow y 3)))
(* (pow y 3) (- (* 1/4 x) (* 1/2 (/ 1 y))))
(* (pow y 3) (- (* 1/4 x) (* 1/2 (/ 1 y))))
(* (pow y 3) (- (* 1/4 x) (* 1/2 (/ 1 y))))
(* 1/4 (* x (pow y 3)))
(* -1 (* (pow y 3) (+ (* -1/4 x) (* 1/2 (/ 1 y)))))
(* -1 (* (pow y 3) (+ (* -1/4 x) (* 1/2 (/ 1 y)))))
(* -1 (* (pow y 3) (+ (* -1/4 x) (* 1/2 (/ 1 y)))))
(* -1/2 (pow y 2))
(+ (* -1/2 (pow y 2)) (* 1/4 (* x (pow y 3))))
(+ (* -1/2 (pow y 2)) (* 1/4 (* x (pow y 3))))
(+ (* -1/2 (pow y 2)) (* 1/4 (* x (pow y 3))))
(* 1/4 (* x (pow y 3)))
(* x (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3))))
(* x (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3))))
(* x (+ (* -1/2 (/ (pow y 2) x)) (* 1/4 (pow y 3))))
(* 1/4 (* x (pow y 3)))
(* -1 (* x (+ (* -1/4 (pow y 3)) (* 1/2 (/ (pow y 2) x)))))
(* -1 (* x (+ (* -1/4 (pow y 3)) (* 1/2 (/ (pow y 2) x)))))
(* -1 (* x (+ (* -1/4 (pow y 3)) (* 1/2 (/ (pow y 2) x)))))
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)
(* -1/2 y)

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

rewrite684.0ms (2.6%)

Memory

14.3MiB live, 404.0MiB allocated

Rules

4 796×	`lower-fma.f32`
4 788×	`lower-fma.f64`
4 682×	`lower-*.f32`
4 670×	`lower-*.f64`
3 874×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	199
0	54	199
1	237	192
2	1906	192
0	8216	192

Stop Event

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

Counts

18 → 355

Calls

Call 1

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

Outputs
(+.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(+.f64 (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x)
(-.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x))) (/.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (*.f64 x x))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(fma.f64 y (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) x)
(fma.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x)
(fma.f64 #s(literal -1 binary64) (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x)
(fma.f64 (/.f64 y (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x y)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))) x)
(fma.f64 (/.f64 y (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) (.f64 x y)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))) x)
(fma.f64 (/.f64 y (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) (.f64 x y))))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x y))))) x)
(fma.f64 (/.f64 y (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) (.f64 x y)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x y)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) (.f64 x y)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) (.f64 x y)) #s(literal -1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) (.f64 x y))))) (/.f64 y (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x y))))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x)))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (fma.f64 x x (-.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (neg.f64 (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (neg.f64 (fma.f64 x x (-.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (neg.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (neg.f64 (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x))) (.f64 (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (.f64 (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x)) (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))) (neg.f64 (neg.f64 (fma.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (neg.f64 (neg.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (+.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (.f64 x (.f64 x x))) (+.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x x) (.f64 (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x))))
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(fma.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (.f64 y y) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (*.f64 y y))))
(fma.f64 (.f64 y #s(literal -1/2 binary64)) y (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (*.f64 y y))))
(fma.f64 (.f64 y y) #s(literal -1/2 binary64) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (*.f64 y y))))
(fma.f64 (.f64 y y) (.f64 x (.f64 y #s(literal 1/4 binary64))) (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 y y)) (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 (.f64 x (.f64 y #s(literal 1/4 binary64))) (.f64 y y) (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 (.f64 x (.f64 y y)) (.f64 y #s(literal 1/4 binary64)) (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 (.f64 (.f64 x (.f64 y #s(literal 1/4 binary64))) y) y (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 (.f64 (.f64 y y) (.f64 x y)) #s(literal 1/4 binary64) (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 (.f64 (.f64 y y) (.f64 y #s(literal 1/4 binary64))) x (.f64 y (*.f64 y #s(literal -1/2 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)))) (fma.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (-.f64 (.f64 (.f64 y (.f64 y #s(literal -1/2 binary64))) (.f64 y (.f64 y #s(literal -1/2 binary64)))) (.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 y (*.f64 y #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (.f64 y (.f64 y #s(literal -1/2 binary64))) (.f64 y (.f64 y #s(literal -1/2 binary64))))) (-.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 y (.f64 y #s(literal -1/2 binary64)))))
(/.f64 (.f64 (.f64 y y) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) #s(literal -1/8 binary64))) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) #s(literal -1/8 binary64)))))
(/.f64 (.f64 (.f64 y y) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) #s(literal -1/4 binary64))) (fma.f64 (.f64 x y) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) #s(literal -1/8 binary64)) (.f64 y y)) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) #s(literal -1/8 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) #s(literal -1/4 binary64)) (.f64 y y)) (fma.f64 (.f64 x y) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (-.f64 (.f64 (.f64 y (.f64 y #s(literal -1/2 binary64))) (.f64 y (.f64 y #s(literal -1/2 binary64)))) (.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 y (*.f64 y #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (.f64 y (.f64 y #s(literal -1/2 binary64))) (.f64 y (.f64 y #s(literal -1/2 binary64)))))) (neg.f64 (-.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 y (.f64 y #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 y y) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 y y) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 (.f64 x y) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) #s(literal -1/8 binary64)) (.f64 y y))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x y) #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x y) (.f64 x y)) #s(literal -1/4 binary64)) (.f64 y y))) (neg.f64 (fma.f64 (.f64 x y) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))))) (fma.f64 (.f64 y (.f64 y #s(literal -1/2 binary64))) (.f64 y (.f64 y #s(literal -1/2 binary64))) (-.f64 (.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (.f64 y (.f64 y #s(literal -1/2 binary64))) (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (*.f64 y y)))))))
(.f64 y (.f64 y (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (*.f64 y y))
(.f64 (.f64 y (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y)
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) y)

eval307.0ms (1.2%)

Memory: 11.7MiB live, 170.7MiB allocated
Compiler: Compiled 17 371 to 1 300 computations (92.5% saved)

prune541.0ms (2.1%)

Memory

7.8MiB live, 213.0MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	696	4	700
Fresh	3	0	3
Picked	1	4	5
Done	0	0	0
Total	700	8	708

Accuracy

100.0%

Counts

708 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
▶	65.1%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y)))
✓	58.0%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y)))
✓	57.7%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
▶	65.1%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x))
▶	55.0%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x))
▶	73.0%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y))
✓	29.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 85 to 49 computations (42.4% saved)

simplify195.0ms (0.7%)

Memory

-14.3MiB live, 219.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 x y) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y)
cost-diff	0	#s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y))
cost-diff	0	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y)))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))
cost-diff	0	(fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x)
cost-diff	0	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal -2 binary64) (*.f64 x x))
cost-diff	0	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x))
cost-diff	512	(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)
cost-diff	0	(-.f64 x y)
cost-diff	0	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y))

Rules

2 714×	`lower-*.f32`
2 706×	`lower-*.f64`
2 704×	`lower-fma.f32`
2 696×	`lower-fma.f64`
1 818×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	158
0	47	158
1	93	158
2	165	152
3	247	152
4	369	152
5	755	152
6	1522	152
7	2721	152
8	5902	152
0	8291	147

Stop Event

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

Calls

Call 1

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

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

localize77.0ms (0.3%)

Memory

-12.2MiB live, 183.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x y)
accuracy	0.00390625	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y)))
accuracy	0.05859375	(fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y)
accuracy	29.706987964315022	#s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y))
accuracy	0	(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.03125	(fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x)
accuracy	22.313144652415534	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 y (fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) x))
accuracy	0	(*.f64 x x)
accuracy	0.40194297842287247	(/.f64 #s(literal -2 binary64) (*.f64 x x))
accuracy	15.000776967726694	(fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x)
accuracy	27.093044483986393	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x))
accuracy	0	(-.f64 x y)
accuracy	17.300437472802233	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y))

Samples

49.0ms

256×

valid

Compiler

Compiled 124 to 33 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 16.0ms (47.8% of total)

ival-add: 7.0ms (20.9% of total)

ival-div: 6.0ms (17.9% of total)

ival-sub: 3.0ms (9% of total)

exact: 1.0ms (3% of total)

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

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

series28.0ms (0.1%)

Memory

7.0MiB live, 52.5MiB allocated

Counts

15 → 312

Calls

Call 1

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

Outputs
#s(alt (* -1 y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y)) #<representation binary64>) () ())) ())
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#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())

Calls

78 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(+ (* y (+ (* y (* x 1/2)) -1)) x)
0.0ms	x	@	0	(/ -2 (* x x))
0.0ms	x	@	-inf	(+ (* y (+ (* y (* x 1/2)) -1)) x)
0.0ms	x	@	inf	(+ (* y (+ (* y (* x 1/2)) -1)) x)
0.0ms	x	@	0	(* (* x y) -1/2)

simplify227.0ms (0.9%)

Memory

37.0MiB live, 464.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 304×	`lower-fma.f64`
10 304×	`lower-fma.f32`
3 698×	`lower-*.f64`
3 698×	`lower-*.f32`
3 502×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	276	2907
1	873	2873
2	2369	2590
3	7173	2494
0	8231	2369

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 290

Calls

Call 1

Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* -1 y)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(* x (+ 1 (* 1/2 (pow y 2))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(* 1/2 (* x y))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(* 1/2 (* x y))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* -1/2 (* x (pow y 2))))
(* -1/2 (* x (pow y 2)))
(* x (+ (* -1/2 (pow y 2)) (/ y x)))
(* x (+ (* -1/2 (pow y 2)) (/ y x)))
(* x (+ (* -1/2 (pow y 2)) (/ y x)))
(* -1/2 (* x (pow y 2)))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* -1/2 (* x y))))
(* -1/2 (* x (pow y 2)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* -1/2 (* x (pow y 2)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1/2 x) (/ 1 y)))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

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

rewrite318.0ms (1.2%)

Memory

-9.0MiB live, 582.6MiB allocated

Rules

5 480×	`lower-fma.f32`
5 472×	`lower-fma.f64`
5 464×	`lower-*.f32`
5 456×	`lower-*.f64`
5 036×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	147
0	47	147
1	225	147
2	1600	141
0	9196	136

Stop Event

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

Counts

15 → 342

Calls

Call 1

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

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

eval85.0ms (0.3%)

Memory: -6.9MiB live, 188.3MiB allocated
Compiler: Compiled 13 189 to 1 070 computations (91.9% saved)

prune98.0ms (0.4%)

Memory

6.6MiB live, 262.7MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	630	2	632
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	631	9	640

Accuracy

100.0%

Counts

640 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
✓	65.1%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)) y y)))
✓	58.0%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y)))
✓	57.7%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	55.0%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x))
✓	73.0%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y))
▶	30.1%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* y (+ (* y (* x 1/2)) -1)) x) (.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
▶	13.9%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)))
✓	29.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 92 to 53 computations (42.4% saved)

simplify173.0ms (0.7%)

Memory

-8.8MiB live, 187.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

3 250×	`lower-fma.f32`
3 248×	`lower-fma.f64`
2 652×	`lower-*.f32`
2 648×	`lower-*.f64`
1 856×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	116
0	33	114
1	69	114
2	118	106
3	167	106
4	253	106
5	490	106
6	1032	106
7	2175	106
8	5484	106
0	8289	102

Stop Event

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

Calls

Call 1

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

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

localize83.0ms (0.3%)

Memory

8.6MiB live, 90.5MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y #s(literal 1/2 binary64))
accuracy	0.06640625	(.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))
accuracy	22.313144652415534	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* y (+ (* y (* x 1/2)) -1)) x) (.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
accuracy	22.656766674448665	#s(approx (+ (* y (+ (* y (* x 1/2)) -1)) x) (.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))
accuracy	0	(/.f64 #s(literal -2 binary64) x)
accuracy	27.093044483986393	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)))
accuracy	28.526172702860578	#s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))

Samples

66.0ms

256×

valid

Compiler

Compiled 72 to 26 computations (63.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 14.0ms (53.3% of total)

ival-add: 6.0ms (22.9% of total)

ival-div: 5.0ms (19.1% of total)

ival-sub: 1.0ms (3.8% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0%)

Memory

-21.5MiB live, 17.0MiB allocated

Counts

8 → 156

Calls

Call 1

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

Outputs
#s(alt (* -1 y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y) (taylor 0 x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) (patch (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

39 calls:

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

simplify271.0ms (1%)

Memory

6.7MiB live, 318.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 640×	`lower-fma.f64`
12 640×	`lower-fma.f32`
4 146×	`lower-*.f64`
4 146×	`lower-*.f32`
2 410×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	179	1518
1	540	1511
2	1512	1363
3	4611	1323
0	8207	1227

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 147

Calls

Call 1

Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* -1 y)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(* x (+ 1 (* 1/2 (pow y 2))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 y)
(* y (- (* 1/2 (* x y)) 1))
(* y (- (* 1/2 (* x y)) 1))
(* y (- (* 1/2 (* x y)) 1))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* -1 y)
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(* 1/2 (* x (pow y 2)))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* 1/2 (* x (pow y 2)))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(* 1/2 (* x y))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(* 1/2 (* x y))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)

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

rewrite312.0ms (1.2%)

Memory

50.3MiB live, 434.8MiB allocated

Rules

14 010×	`lower-fma.f32`
14 008×	`lower-fma.f64`
5 902×	`lower-*.f32`
5 898×	`lower-*.f64`
3 160×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	110
0	33	108
1	165	108
2	1026	100
0	9218	96

Stop Event

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

Counts

8 → 199

Calls

Call 1

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

Outputs
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)))
#s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) x))
(neg.f64 (/.f64 #s(literal 2 binary64) x))
(neg.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) x))
(neg.f64 (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x))))
(/.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x))
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 2 binary64) (neg.f64 x))
(/.f64 (neg.f64 x) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 x #s(literal -2 binary64)) (.f64 x x))
(/.f64 (.f64 x #s(literal 2 binary64)) (.f64 x (neg.f64 x)))
(/.f64 (neg.f64 (.f64 x #s(literal 2 binary64))) (.f64 x x))
(pow.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(.f64 x (/.f64 #s(literal -2 binary64) (.f64 x x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal -2 binary64) (/.f64 x (.f64 x x)))
(.f64 #s(literal -2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x)
(*.f64 (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal -2 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) x) x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x))
(.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x #s(literal -2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))
(.f64 (.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 x (neg.f64 x)))
(.f64 (.f64 x #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 (/.f64 x (.f64 x x)) #s(literal -2 binary64))
(*.f64 (/.f64 x (neg.f64 x)) (/.f64 #s(literal 2 binary64) x))
(.f64 (pow.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 (.f64 (.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -2 binary64))
#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* y (+ (* y (* x 1/2)) -1)) x) (.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
#s(approx (+ (* y (+ (* y (* x 1/2)) -1)) x) (.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(+.f64 (neg.f64 y) (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))))
(+.f64 (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))) (neg.f64 y))
(-.f64 #s(literal 0 binary64) (-.f64 y (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64))))))
(-.f64 (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))) y)
(-.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 x y))) (.f64 y y)) (fma.f64 x (.f64 y (.f64 y #s(literal 1/2 binary64))) y)) (/.f64 (.f64 y y) (fma.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64))) y)))
(-.f64 (fma.f64 x (.f64 y (.f64 y #s(literal 1/2 binary64))) #s(literal 0 binary64)) y)
(fma.f64 x (.f64 y (.f64 y #s(literal 1/2 binary64))) (neg.f64 y))
(fma.f64 y #s(literal -1 binary64) (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))))
(fma.f64 y (.f64 x (.f64 y #s(literal 1/2 binary64))) (neg.f64 y))
(fma.f64 #s(literal 1/2 binary64) (.f64 y (.f64 x y)) (neg.f64 y))
(fma.f64 #s(literal 1/2 binary64) (.f64 x (.f64 y y)) (neg.f64 y))
(fma.f64 #s(literal 1 binary64) (neg.f64 y) (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))) (neg.f64 y))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 y y) (neg.f64 y))
(fma.f64 #s(literal -1 binary64) y (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))))
(fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x y) (neg.f64 y))
(fma.f64 (.f64 x (.f64 y #s(literal 1/2 binary64))) y (neg.f64 y))
(fma.f64 (neg.f64 y) #s(literal 1 binary64) (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))))
(fma.f64 (.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64)))) #s(literal 1 binary64) (neg.f64 y))
(fma.f64 (.f64 x y) (.f64 y #s(literal 1/2 binary64)) (neg.f64 y))
(fma.f64 (.f64 y y) (.f64 x #s(literal 1/2 binary64)) (neg.f64 y))
(fma.f64 (.f64 y (.f64 y #s(literal 1/2 binary64))) x (neg.f64 y))
(fma.f64 (.f64 y (.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))
(/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 x y) (.f64 #s(literal 1/4 binary64) (.f64 x y))) (.f64 y y) (.f64 (neg.f64 y) (-.f64 (neg.f64 y) (.f64 x (.f64 y (.f64 y #s(literal 1/2 binary64))))))) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (.f64 y (.f64 y y)) (neg.f64 (.f64 y (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 y (.f64 y #s(literal 1/2 binary64))) y) (.f64 (.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))) (fma.f64 x (.f64 y (*.f64 y #s(literal 1/2 binary64))) y))))
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eval96.0ms (0.4%)

Memory: -38.7MiB live, 123.2MiB allocated
Compiler: Compiled 6 547 to 599 computations (90.9% saved)

prune53.0ms (0.2%)

Memory

26.4MiB live, 112.6MiB allocated

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	344	2	346
Fresh	0	0	0
Picked	0	2	2
Done	1	6	7
Total	345	10	355

Accuracy

100.0%

Counts

355 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
✓	58.0%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (fma.f64 x (.f64 (.f64 y y) (fma.f64 x (*.f64 y #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) y)))
✓	57.7%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	55.0%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (fma.f64 x (/.f64 #s(literal -2 binary64) (*.f64 x x)) x))
✓	73.0%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) (-.f64 x y))
	30.1%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* y (+ (* y (* x 1/2)) -1)) x) (fma.f64 (.f64 y (.f64 x y)) #s(literal 1/2 binary64) (neg.f64 y))))
✓	30.1%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* y (+ (* y (* x 1/2)) -1)) x) (.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
✓	13.9%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)))
	11.3%	#s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x)))
✓	29.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 254 to 108 computations (57.5% saved)

regimes18.0ms (0.1%)

Memory

-3.4MiB live, 34.6MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
5.0ms	x
5.0ms	y

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes16.0ms (0.1%)

Memory

-8.0MiB live, 29.7MiB allocated

Counts

14 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

3 calls:

6.0ms	y
5.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
5.0ms	x

Results

Accuracy	Segments	Branch
87.7%	3	`x`
91.6%	3	`y`
84.2%	3	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes7.0ms (0%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

4 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

3 calls:

2.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
73.0%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
73.0%	1	`x`
78.3%	3	`y`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes32.0ms (0.1%)

Memory

-26.2MiB live, 14.1MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

30.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
2.0ms	y

Results

Accuracy	Segments	Branch
73.0%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
73.0%	1	`y`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes4.0ms (0%)

Memory

11.5MiB live, 11.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
29.2%	1	`x`
29.2%	1	`y`
29.2%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch122.0ms (0.5%)

Memory

2.5MiB live, 41.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
108.0ms	2.2966710157669615e+150	8.321153178008413e+160
11.0ms	-3.581689677260411e+112	-5.108848309433554e+108

Samples

109.0ms

288×

valid

Compiler

Compiled 304 to 194 computations (36.2% saved)

Precisions

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

ival-div: 4.0ms (44% of total)

ival-mult: 2.0ms (22% of total)

ival-sub: 1.0ms (11% of total)

ival-add: 1.0ms (11% of total)

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

exact: 0.0ms (0% of total)

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

bsearch28.0ms (0.1%)

Memory

9.9MiB live, 48.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	5.929605135474797e+165	7.821910894086297e+167
14.0ms	-1.3845436382175139e+132	-1.3302026552554572e+120

Samples

16.0ms

272×

valid

Compiler

Compiled 271 to 167 computations (38.4% saved)

Precisions

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

ival-div: 5.0ms (50.4% of total)

ival-mult: 2.0ms (20.2% of total)

ival-sub: 1.0ms (10.1% of total)

ival-add: 1.0ms (10.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify10.0ms (0%)

Memory

-20.4MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
14×	`sub-neg_binary64`
10×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	165
1	58	165
2	70	165
3	77	165
4	81	165
5	82	165

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -5999999999999999682512740336388509484941752085476579057104675510547571467487249965034836958870203892578123776 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 46999999999999998917563339030654883119605688687423849686874405905413190203200343604726196596612913310699234154069380865516020118000250502183318148087808 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))))
(if (<=.f64 y #s(literal -1359999999999999943397964727249519408861263123815332018609057445142729778163126892478210006144820650918680858848023258802562319515648 binary64)) #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (if (<=.f64 y #s(literal 100000000000000003860899428741951440279402051491350438954423829568577391016492742670197391754543170343555750902863155030391327289536708508823166797373630632400726786048 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)))))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Outputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -5999999999999999682512740336388509484941752085476579057104675510547571467487249965034836958870203892578123776 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 46999999999999998917563339030654883119605688687423849686874405905413190203200343604726196596612913310699234154069380865516020118000250502183318148087808 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))))
(if (<=.f64 y #s(literal -1359999999999999943397964727249519408861263123815332018609057445142729778163126892478210006144820650918680858848023258802562319515648 binary64)) #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x))) (if (<=.f64 y #s(literal 100000000000000003860899428741951440279402051491350438954423829568577391016492742670197391754543170343555750902863155030391327289536708508823166797373630632400726786048 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #s(approx (- x (/ y (+ (* (* y 1/2) x) 1))) #s(approx (+ (* x (/ -2 (* x x))) x) (/.f64 #s(literal -2 binary64) x)))))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

soundness859.0ms (3.3%)

Memory

-8.4MiB live, 526.3MiB allocated

Rules

14 034×	`lower-fma.f64`
14 034×	`lower-fma.f32`
13 558×	`lower-fma.f64`
13 558×	`lower-fma.f32`
10 304×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	276	2907
1	873	2873
2	2369	2590
3	7173	2494
0	8231	2369
0	296	4330
1	964	4143
2	2762	4004
3	7963	3994
0	8024	3784
0	9	35
0	14	35
1	63	35
2	500	35
3	6873	35
0	8527	32
0	231	1053
1	738	1018
2	1942	987
3	6081	981
0	8428	934

Stop Event

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

Compiler

Compiled 149 to 80 computations (46.3% saved)

preprocess37.0ms (0.1%)

Memory: 14.1MiB live, 85.1MiB allocated
Compiler: Compiled 156 to 72 computations (53.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze44.0ms (0.2%)

sample847.0ms (3.2%)

explain461.0ms (1.8%)

preprocess172.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify284.0ms (1.1%)

localize75.0ms (0.3%)

series11.0ms (0%)

simplify340.0ms (1.3%)

rewrite428.0ms (1.6%)

eval79.0ms (0.3%)

prune90.0ms (0.3%)

simplify18.2s (69.4%)

localize163.0ms (0.6%)

series26.0ms (0.1%)

simplify313.0ms (1.2%)

rewrite684.0ms (2.6%)

eval307.0ms (1.2%)

prune541.0ms (2.1%)

simplify195.0ms (0.7%)

localize77.0ms (0.3%)

series28.0ms (0.1%)

simplify227.0ms (0.9%)

rewrite318.0ms (1.2%)

eval85.0ms (0.3%)

prune98.0ms (0.4%)

simplify173.0ms (0.7%)

localize83.0ms (0.3%)

series9.0ms (0%)

simplify271.0ms (1%)

rewrite312.0ms (1.2%)

eval96.0ms (0.4%)

prune53.0ms (0.2%)

regimes18.0ms (0.1%)

regimes16.0ms (0.1%)

regimes7.0ms (0%)

regimes32.0ms (0.1%)

regimes4.0ms (0%)

bsearch122.0ms (0.5%)

bsearch28.0ms (0.1%)

simplify10.0ms (0%)

soundness859.0ms (3.3%)

preprocess37.0ms (0.1%)

end0.0ms (0%)

Profiling