Metrics for Examples.Basics.ProofTests:f4 from sbv-4.4

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample802.0ms (18.2%)

Memory

4.1MiB live, 1 140.2MiB allocated

Samples

578.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 402.0ms

ival-mult: 282.0ms (70.2% of total)

ival-add: 105.0ms (26.1% of total)

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

exact: 5.0ms (1.2% of total)

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

Bogosity

explain127.0ms (2.9%)

Memory

15.2MiB live, 160.3MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	nan-rescue	9	0
↳	`(*.f64 x x)`	overflow	63
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	31
`+.f64`	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`	nan-rescue	4	0
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	73
↳	`(*.f64 x x)`	overflow	63
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	31
↳	`(*.f64 y y)`	overflow	66

Confusion

	Predicted +	Predicted -
+	12	0
-	0	244

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	12	0	0
-	0	0	244

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	244
1	11
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

50.0ms

512×

valid

Compiler

Compiled 97 to 31 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 31.0ms (85.9% of total)

ival-add: 4.0ms (11.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess42.0ms (1%)

Memory

15.1MiB live, 15.1MiB allocated

Algorithm

1×	egg-herbie

Rules

232×	`sub-neg`
230×	`unsub-neg`
190×	`distribute-lft-neg-in`
136×	`cancel-sign-sub-inv`
132×	`cancel-sign-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	77	57
2	250	55
3	638	55
4	1214	55
5	1509	55
6	1539	55
0	9	13
0	15	13
1	23	11
2	43	11
3	51	11
0	51	9

Stop Event

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

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

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

Symmetry

(sort x y)

Compiler

Compiled 15 to 9 computations (40% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.3%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Compiler

Compiled 15 to 9 computations (40% saved)

simplify5.0ms (0.1%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
cost-diff	448	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Rules

64×	`lower-fma.f64`
64×	`lower-fma.f32`
36×	`lower-*.f32`
32×	`lower-+.f32`
28×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	15	39
1	23	35
2	43	35
3	51	35
0	51	32

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (1.2%)

Memory

-23.4MiB live, 22.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	1.1523375574906174	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
accuracy	1.9960937500000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Samples

43.0ms

256×

valid

Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions

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

ival-mult: 6.0ms (68.5% of total)

ival-add: 2.0ms (22.8% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

5 → 96

Calls

Call 1

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

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

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(* (* x 2) y)
1.0ms	y	@	0	(+ (* x x) (* (* x 2) y))
1.0ms	x	@	inf	(+ (* x x) (* (* x 2) y))
1.0ms	x	@	0	(+ (* x x) (* (* x 2) y))
0.0ms	y	@	inf	(+ (* x x) (* (* x 2) y))

simplify281.0ms (6.4%)

Memory

8.8MiB live, 188.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 660×	`lower-fma.f64`
7 660×	`lower-fma.f32`
3 048×	`lower-*.f64`
3 048×	`lower-*.f32`
1 308×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	534
1	166	534
2	468	534
3	1334	534
4	3280	534
5	6441	534
0	8173	486

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite369.0ms (8.4%)

Memory

-9.1MiB live, 451.7MiB allocated

Rules

7 568×	`lower-fma.f64`
7 568×	`lower-fma.f32`
5 064×	`lower-*.f32`
5 056×	`lower-*.f64`
2 536×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	15	33
1	50	29
2	420	29
3	6357	29
0	8219	26

Stop Event

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

Counts

5 → 210

Calls

Call 1

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

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

eval75.0ms (1.7%)

Memory: 7.0MiB live, 126.4MiB allocated
Compiler: Compiled 10 505 to 638 computations (93.9% saved)

prune56.0ms (1.3%)

Memory

-35.9MiB live, 120.9MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	302	4	306
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	303	4	307

Accuracy

100.0%

Counts

307 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.1%	(fma.f64 y y (*.f64 x (fma.f64 #s(literal 2 binary64) y x)))
▶	58.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
▶	56.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
▶	56.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 32 to 17 computations (46.9% saved)

simplify7.0ms (0.2%)

Memory

18.9MiB live, 18.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

64×	`lower-fma.f32`
58×	`lower-fma.f64`
36×	`lower-*.f32`
32×	`lower-+.f64`
32×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	97
0	28	85
1	47	85
2	63	85
3	65	85
0	65	85

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (1.2%)

Memory

-12.4MiB live, 123.7MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 #s(literal 2 binary64) y x)
accuracy	0	(*.f64 x (fma.f64 #s(literal 2 binary64) y x))
accuracy	2.499972476055602	(fma.f64 y y (*.f64 x (fma.f64 #s(literal 2 binary64) y x)))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0.00390625	(*.f64 y (fma.f64 #s(literal 2 binary64) x y))
accuracy	26.404298830244276	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
accuracy	0	(*.f64 y y)
accuracy	27.880648835519093	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
accuracy	0	(*.f64 x x)
accuracy	28.15724883816483	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Samples

34.0ms

256×

valid

Compiler

Compiled 90 to 18 computations (80% saved)

Precisions

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

ival-mult: 16.0ms (71.3% of total)

ival-add: 6.0ms (26.7% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.3%)

Memory

39.7MiB live, 39.7MiB allocated

Counts

10 → 216

Calls

Call 1

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

Calls

54 calls:

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

simplify241.0ms (5.5%)

Memory

-42.8MiB live, 251.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 438×	`lower-fma.f64`
8 438×	`lower-fma.f32`
2 840×	`lower-*.f64`
2 840×	`lower-*.f32`
1 688×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	1464
1	269	1464
2	747	1464
3	2260	1344
4	4721	1344
5	7693	1344
0	8166	1152

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 210

Calls

Call 1

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

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

rewrite488.0ms (11.1%)

Memory

37.3MiB live, 758.6MiB allocated

Rules

17 172×	`lower-fma.f32`
17 166×	`lower-fma.f64`
6 394×	`lower-*.f32`
6 386×	`lower-*.f64`
3 472×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	89
0	28	77
1	110	77
2	839	77
0	8707	77

Stop Event

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

Counts

10 → 352

Calls

Call 1

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

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

eval63.0ms (1.4%)

Memory: 0.3MiB live, 141.0MiB allocated
Compiler: Compiled 11 752 to 959 computations (91.8% saved)

prune112.0ms (2.5%)

Memory

-18.2MiB live, 128.0MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	561	1	562
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	562	4	566

Accuracy

100.0%

Counts

566 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.8%	(fma.f64 y y (.f64 x #s(approx (+ ( 2 y) x) (*.f64 y #s(literal 2 binary64)))))
✓	58.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
✓	56.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	56.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 32 to 17 computations (46.9% saved)

simplify5.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

10×	`lower-fma.f32`
10×	`lower-*.f32`
8×	`lower-fma.f64`
8×	`lower-+.f64`
8×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	40
0	13	40
1	17	40
0	17	37

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize44.0ms (1%)

Memory

0.2MiB live, 45.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	0	(.f64 x #s(approx (+ ( 2 y) x) (*.f64 y #s(literal 2 binary64))))
accuracy	2.499972476055602	(fma.f64 y y (.f64 x #s(approx (+ ( 2 y) x) (*.f64 y #s(literal 2 binary64)))))
accuracy	30.502110075686986	#s(approx (+ (* 2 y) x) (*.f64 y #s(literal 2 binary64)))

Samples

36.0ms

256×

valid

Compiler

Compiled 31 to 11 computations (64.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 26.0ms (87.6% of total)

ival-add: 3.0ms (10.1% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify267.0ms (6.1%)

Memory

1.2MiB live, 342.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 382×	`lower-fma.f64`
9 382×	`lower-fma.f32`
3 624×	`lower-*.f64`
3 624×	`lower-*.f32`
1 104×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	534
1	209	492
2	566	492
3	1661	480
4	3683	480
5	6225	480
0	8043	414

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

Calls

Call 1

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

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

rewrite278.0ms (6.3%)

Memory

41.3MiB live, 533.4MiB allocated

Rules

5 762×	`lower-fma.f32`
5 760×	`lower-fma.f64`
4 410×	`lower-*.f32`
4 406×	`lower-*.f64`
4 004×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	37
0	13	37
1	43	37
2	320	37
3	3159	37
0	8933	34

Stop Event

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

Counts

4 → 136

Calls

Call 1

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

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

eval31.0ms (0.7%)

Memory: -20.0MiB live, 82.7MiB allocated
Compiler: Compiled 9 983 to 413 computations (95.9% saved)

prune27.0ms (0.6%)

Memory

7.5MiB live, 97.1MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	217	4	221

Accuracy

100.0%

Counts

221 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.8%	(fma.f64 y y (.f64 x #s(approx (+ ( 2 y) x) (*.f64 y #s(literal 2 binary64)))))
✓	58.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y (fma.f64 #s(literal 2 binary64) x y)))
✓	56.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	56.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 80 to 34 computations (57.5% saved)

regimes53.0ms (1.2%)

Memory

-43.1MiB live, 83.9MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

3 calls:

47.0ms	y
3.0ms	x
2.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
96.1%	1	`x`
100.0%	2	`y`
99.3%	2	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`

Compiler

Compiled 21 to 13 computations (38.1% saved)

regimes8.0ms (0.2%)

Memory

-11.9MiB live, 33.7MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
2.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
2.0ms	y

Results

Accuracy	Segments	Branch
88.7%	2	`x`
61.3%	2	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
88.6%	2	`y`

Compiler

Compiled 21 to 13 computations (38.1% saved)

regimes2.0ms (0%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
88.7%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes3.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

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

Calls

2 calls:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
88.6%	2	`y`
88.6%	2	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

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

Calls

3 calls:

1.0ms	x
1.0ms	y
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
56.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
56.0%	1	`x`
56.0%	1	`y`

Compiler

Compiled 21 to 13 computations (38.1% saved)

bsearch3.0ms (0.1%)

Memory

-40.9MiB live, 6.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
3.0ms	2.1877137334703568e+151	1.9951515528786048e+157

Samples

2.0ms

16×

valid

Compiler

Compiled 37 to 25 computations (32.4% saved)

Precisions

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch14.0ms (0.3%)

Memory

35.6MiB live, 35.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-6.534697060671456e-97	-2.4283867057155153e-105

Samples

7.0ms

144×

valid

Compiler

Compiled 189 to 113 computations (40.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 3.0ms (62.9% of total)

ival-add: 1.0ms (21% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-6.534697060671456e-97	-2.4283867057155153e-105

Compiler

Compiled 171 to 104 computations (39.2% saved)

bsearch27.0ms (0.6%)

Memory

-24.1MiB live, 27.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
26.0ms	7.180865751000327e-80	5.2664593773339985e-76

Samples

21.0ms

128×

valid

Compiler

Compiled 130 to 78 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 18.0ms (95.8% of total)

ival-add: 1.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

simplify7.0ms (0.2%)

Memory

13.3MiB live, 13.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	161
1	39	161

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 y #s(literal 40000000000000000687101295488708764721572416337221820430929313780800125051127541680330506971444692730890183838174171339147724505780692024998538197860352 binary64)) (fma.f64 y y (.f64 x (fma.f64 #s(literal 2 binary64) y x))) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
(if (<=.f64 x #s(literal -3126379886188527/4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) (fma.f64 y y (.f64 x #s(approx (+ (* 2 y) x) (*.f64 y #s(literal 2 binary64))))))
(if (<=.f64 x #s(literal -3126379886188527/4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y (fma.f64 #s(literal 2 binary64) x y))))
(if (<=.f64 y #s(literal 1018517988167243/2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Outputs
(if (<=.f64 y #s(literal 40000000000000000687101295488708764721572416337221820430929313780800125051127541680330506971444692730890183838174171339147724505780692024998538197860352 binary64)) (fma.f64 y y (.f64 x (fma.f64 #s(literal 2 binary64) y x))) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
(if (<=.f64 x #s(literal -3126379886188527/4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) (fma.f64 y y (.f64 x #s(approx (+ (* 2 y) x) (*.f64 y #s(literal 2 binary64))))))
(if (<=.f64 x #s(literal -3126379886188527/4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y (fma.f64 #s(literal 2 binary64) x y))))
(if (<=.f64 y #s(literal 1018517988167243/2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

soundness729.0ms (16.5%)

Memory

3.9MiB live, 508.2MiB allocated

Rules

8 438×	`lower-fma.f64`
8 438×	`lower-fma.f32`
7 660×	`lower-fma.f64`
7 660×	`lower-fma.f32`
7 568×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	1464
1	269	1464
2	747	1464
3	2260	1344
4	4721	1344
5	7693	1344
0	8166	1152
0	56	534
1	166	534
2	468	534
3	1334	534
4	3280	534
5	6441	534
0	8173	486
0	9	33
0	15	33
1	50	29
2	420	29
3	6357	29
0	8219	26

Stop Event

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

Compiler

Compiled 187 to 78 computations (58.3% saved)

preprocess116.0ms (2.6%)

Memory: -21.5MiB live, 136.3MiB allocated
Remove: (sort x y)
Compiler: Compiled 232 to 102 computations (56% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample802.0ms (18.2%)

explain127.0ms (2.9%)

preprocess42.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize51.0ms (1.2%)

series8.0ms (0.2%)

simplify281.0ms (6.4%)

rewrite369.0ms (8.4%)

eval75.0ms (1.7%)

prune56.0ms (1.3%)

simplify7.0ms (0.2%)

localize51.0ms (1.2%)

series11.0ms (0.3%)

simplify241.0ms (5.5%)

rewrite488.0ms (11.1%)

eval63.0ms (1.4%)

prune112.0ms (2.5%)

simplify5.0ms (0.1%)

localize44.0ms (1%)

series3.0ms (0.1%)

simplify267.0ms (6.1%)

rewrite278.0ms (6.3%)

eval31.0ms (0.7%)

prune27.0ms (0.6%)

regimes53.0ms (1.2%)

regimes8.0ms (0.2%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch3.0ms (0.1%)

bsearch14.0ms (0.3%)

bsearch1.0ms (0%)

bsearch27.0ms (0.6%)

simplify7.0ms (0.2%)

soundness729.0ms (16.5%)

preprocess116.0ms (2.6%)

end0.0ms (0%)

Profiling