Metrics for Numeric.Integration.TanhSinh:everywhere from integration-0.2.1

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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 9 to 8 computations (11.1% saved)

sample944.0ms (13.1%)

Memory

8.7MiB live, 838.5MiB allocated

Samples

569.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 280.0ms

ival-mult: 203.0ms (72.4% of total)

ival-add: 63.0ms (22.5% of total)

ival-true: 6.0ms (2.1% of total)

exact: 5.0ms (1.8% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain240.0ms (3.3%)

Memory

11.4MiB live, 108.4MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`	*no**	16	0

Confusion

	Predicted +	Predicted -
+	16	0
-	0	240

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	16	0	0
-	0	0	240

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	240
1	16

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-mult: 7.0ms (67.5% of total)

ival-add: 2.0ms (19.3% of total)

ival-true: 1.0ms (9.6% of total)

exact: 0.0ms (0% of total)

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

preprocess29.0ms (0.4%)

Memory

-1.0MiB live, 75.4MiB allocated

Algorithm

1×	egg-herbie

Rules

158×	`associate-r`
124×	`distribute-lft-in`
112×	`unsub-neg`
92×	`associate-l`
82×	`distribute-lft-neg-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Stop Event

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

Calls

Call 1

Inputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

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

Symmetry

(abs y)

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.1%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

-27.9MiB live, 9.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

46×	`lower-*.f32`
42×	`lower-*.f64`
22×	`lower-fma.f64`
22×	`lower-fma.f32`
14×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	19	18
2	27	18
3	49	18
4	49	18
0	49	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize21.0ms (0.3%)

Memory

9.0MiB live, 51.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	3.77060462909502	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Samples

15.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 8.0ms (86.2% of total)

ival-add: 1.0ms (10.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

19.6MiB live, 19.6MiB allocated

Counts

3 → 48

Calls

Call 1

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

Inputs

#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())

#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())

#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())

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

Calls

6 calls:

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

simplify243.0ms (3.4%)

Memory

-26.3MiB live, 170.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 064×	`lower-fma.f64`
9 064×	`lower-fma.f32`
6 574×	`lower-*.f64`
6 574×	`lower-*.f32`
2 432×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	246
1	42	246
2	74	246
3	214	246
4	721	246
5	1940	246
6	2658	246
7	3752	246
8	5094	246
9	5986	246
10	6927	246
11	7270	246
12	7376	246
13	7453	246
14	7522	246
15	7669	246
0	8207	216

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

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

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

rewrite305.0ms (4.2%)

Memory

25.5MiB live, 142.2MiB allocated

Rules

5 176×	`lower-fma.f64`
5 176×	`lower-fma.f32`
4 882×	`lower-/.f64`
4 882×	`lower-/.f32`
4 246×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	34	15
2	209	15
3	1404	15
0	8269	13

Stop Event

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

Counts

3 → 368

Calls

Call 1

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

Outputs
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eval76.0ms (1%)

Memory: 5.0MiB live, 76.0MiB allocated
Compiler: Compiled 9 642 to 1 119 computations (88.4% saved)

prune58.0ms (0.8%)

Memory

3.9MiB live, 42.7MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	409	6	415
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	410	6	416

Accuracy

100.0%

Counts

416 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (*.f64 x y) y x)
▶	65.3%	(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
▶	94.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
	37.0%	(.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) #s(literal 2 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x)))
▶	49.4%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
▶	49.1%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 118 to 86 computations (27.1% saved)

simplify158.0ms (2.2%)

Memory

-13.1MiB live, 201.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

9 384×	`lower-fma.f32`
9 378×	`lower-fma.f64`
2 336×	`lower-*.f32`
2 324×	`lower-*.f64`
2 128×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	121
0	38	113
1	68	113
2	110	113
3	241	113
4	477	113
5	1128	113
6	1768	113
7	3328	113
8	5779	113
9	7690	113
0	8086	113

Stop Event

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

Calls

Call 1

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

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

localize80.0ms (1.1%)

Memory

-9.2MiB live, 107.6MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 y #s(literal 4 binary64))
accuracy	0	(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
accuracy	1.6510460885479463	(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
accuracy	17.632797323035902	(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0.12890625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
accuracy	0.3852097047845906	(/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))
accuracy	3.77060462909502	(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
accuracy	0	(*.f64 y y)
accuracy	3.77060462909502	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
accuracy	28.749262572395796	#s(approx (+ 1 (* y y)) (*.f64 y y))
accuracy	3.77060462909502	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
accuracy	32.93850943203693	#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
accuracy	0	(*.f64 x y)
accuracy	0.05078125	(fma.f64 (*.f64 x y) y x)

Samples

66.0ms

256×

valid

Compiler

Compiled 118 to 22 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 38.0ms (73.5% of total)

ival-add: 5.0ms (9.7% of total)

ival-div: 4.0ms (7.7% of total)

ival-pow: 3.0ms (5.8% of total)

ival-sub: 1.0ms (1.9% of total)

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

exact: 0.0ms (0% of total)

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

series49.0ms (0.7%)

Memory

4.1MiB live, 47.3MiB allocated

Counts

15 → 288

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	x	@	-inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4))
4.0ms	x	@	inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4))
3.0ms	y	@	inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4))
2.0ms	x	@	0	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4))
2.0ms	y	@	-inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4))

simplify203.0ms (2.8%)

Memory

-8.4MiB live, 223.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18 354×	`lower-fma.f64`
18 354×	`lower-fma.f32`
4 458×	`lower-*.f64`
4 458×	`lower-*.f32`
2 106×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	1868
1	163	1845
2	402	1841
3	1297	1831
4	3601	1815
0	8656	1641

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 282

Calls

Call 1

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

Outputs
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(/.f64 (fma.f64 (neg.f64 y) y #s(literal 1 binary64)) x)
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 y (-.f64 (pow.f64 y #s(literal 3 binary64)) y) #s(literal 1 binary64)))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
(*.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 (neg.f64 y) y #s(literal 1 binary64)) x))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* x (pow y 4)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(+ (* -1 x) (* x (pow y 4)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
(+ (* -1 x) (* x (pow y 4)))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64)) x)
-1
#s(literal -1 binary64)
(- (pow y 4) 1)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(- (pow y 4) 1)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(- (pow y 4) 1)
(-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
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rewrite291.0ms (4%)

Memory

25.6MiB live, 228.5MiB allocated

Rules

5 758×	`lower-fma.f32`
5 752×	`lower-fma.f64`
4 958×	`lower-*.f32`
4 946×	`lower-*.f64`
3 696×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	103
0	38	89
1	151	89
2	926	89
0	8758	89

Stop Event

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

Counts

15 → 1 721

Calls

Call 1

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

Outputs
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eval770.0ms (10.7%)

Memory: 11.2MiB live, 471.7MiB allocated
Compiler: Compiled 41 071 to 3 588 computations (91.3% saved)

prune58.0ms (0.8%)

Memory

-34.5MiB live, 135.8MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1 999	4	2 003
Fresh	0	1	1
Picked	2	3	5
Done	0	0	0
Total	2 001	8	2 009

Accuracy

100.0%

Counts

2 009 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
▶	93.7%	(pow.f64 (pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
▶	94.0%	(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))
▶	20.4%	(/.f64 (*.f64 #s(approx (- (pow y 4) 1) (pow.f64 y #s(literal 4 binary64))) x) (fma.f64 y y #s(literal -1 binary64)))
▶	49.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
▶	37.0%	(.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) #s(literal 2 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x)))
✓	49.4%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	49.1%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 138 to 104 computations (24.6% saved)

simplify120.0ms (1.7%)

Memory

12.9MiB live, 121.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 y y #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
cost-diff	5824	(pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal 1/2 binary64))
cost-diff	7104	(pow.f64 (pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
cost-diff	0	(pow.f64 (.f64 x (.f64 y y)) #s(literal 2 binary64))
cost-diff	128	(-.f64 (.f64 x (.f64 y y)) x)
cost-diff	320	(-.f64 (pow.f64 (.f64 x (.f64 y y)) #s(literal 2 binary64)) (*.f64 x x))
cost-diff	8320	(.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) #s(literal 2 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x)))
cost-diff	0	(pow.f64 y #s(literal 4 binary64))
cost-diff	0	#s(approx (- (pow y 4) 1) (pow.f64 y #s(literal 4 binary64)))
cost-diff	0	(*.f64 #s(approx (- (pow y 4) 1) (pow.f64 y #s(literal 4 binary64))) x)
cost-diff	0	(/.f64 (*.f64 #s(approx (- (pow y 4) 1) (pow.f64 y #s(literal 4 binary64))) x) (fma.f64 y y #s(literal -1 binary64)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* y y) 1) (*.f64 y y))
cost-diff	0	(.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))
cost-diff	1792	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
cost-diff	0	(/.f64 #s(literal -1 binary64) x)
cost-diff	0	(*.f64 y y)
cost-diff	0	(-.f64 #s(literal -1 binary64) (*.f64 y y))
cost-diff	1216	(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))

Rules

9 944×	`lower-fma.f32`
9 940×	`lower-fma.f64`
3 454×	`lower-*.f32`
3 440×	`lower-*.f64`
2 074×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	223
0	57	208
1	100	208
2	191	206
3	433	194
4	1519	192
5	5260	192
0	8501	192

Stop Event

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

Calls

Call 1

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

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

localize96.0ms (1.3%)

Memory

2.9MiB live, 169.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0.3125	(pow.f64 (pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
accuracy	3.77060462909502	(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
accuracy	12.403260711726062	(pow.f64 (*.f64 (fma.f64 y y #s(literal 1 binary64)) x) #s(literal 1/2 binary64))
accuracy	0.3930222047845906	(/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x))
accuracy	8.182658029653798	(.f64 x (.f64 y y))
accuracy	9.91405630749062	(-.f64 (pow.f64 (.f64 x (.f64 y y)) #s(literal 2 binary64)) (*.f64 x x))
accuracy	34.25441692310098	(.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) #s(literal 2 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x)))
accuracy	0	(pow.f64 y #s(literal 4 binary64))
accuracy	1.6510460885479463	(*.f64 #s(approx (- (pow y 4) 1) (pow.f64 y #s(literal 4 binary64))) x)
accuracy	17.632797323035902	(/.f64 (*.f64 #s(approx (- (pow y 4) 1) (pow.f64 y #s(literal 4 binary64))) x) (fma.f64 y y #s(literal -1 binary64)))
accuracy	28.892899325216714	#s(approx (- (pow y 4) 1) (pow.f64 y #s(literal 4 binary64)))
accuracy	0.12890625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
accuracy	0.3852097047845906	(/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y))))
accuracy	3.77060462909502	(.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))
accuracy	28.749262572395796	#s(approx (+ (* y y) 1) (*.f64 y y))
accuracy	0	(/.f64 #s(literal -1 binary64) x)
accuracy	0	(-.f64 #s(literal -1 binary64) (*.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	3.84482337909502	(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (/.f64 #s(literal -1 binary64) x))

Samples

75.0ms

256×

valid

Compiler

Compiled 207 to 32 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 11.0ms (24.9% of total)

ival-div: 9.0ms (20.4% of total)

ival-sub: 9.0ms (20.4% of total)

ival-pow2: 7.0ms (15.9% of total)

ival-pow: 3.0ms (6.8% of total)

ival-add: 2.0ms (4.5% of total)

ival-sqrt: 2.0ms (4.5% of total)

exact: 1.0ms (2.3% of total)

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

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

series37.0ms (0.5%)

Memory

19.1MiB live, 57.4MiB allocated

Counts

22 → 444

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	-inf	((/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4) (* (- (pow (* x (* y y)) 2) (* x x)) (/ 1 (- (* x (* y y)) x))) (- (pow (* x (* y y)) 2) (* x x)) (- (* x (* y y)) x) (pow (* x (* y y)) 2) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (+ (* y y) 1) x) (+ (* y y) 1) (/ 1 (* x (+ (* y y) 1))) (* x (* y y)) (/ 1 (- (* x (* y y)) x)))
3.0ms	x	@	inf	((/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4) (* (- (pow (* x (* y y)) 2) (* x x)) (/ 1 (- (* x (* y y)) x))) (- (pow (* x (* y y)) 2) (* x x)) (- (* x (* y y)) x) (pow (* x (* y y)) 2) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (+ (* y y) 1) x) (+ (* y y) 1) (/ 1 (* x (+ (* y y) 1))) (* x (* y y)) (/ 1 (- (* x (* y y)) x)))
3.0ms	x	@	0	((/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4) (* (- (pow (* x (* y y)) 2) (* x x)) (/ 1 (- (* x (* y y)) x))) (- (pow (* x (* y y)) 2) (* x x)) (- (* x (* y y)) x) (pow (* x (* y y)) 2) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (+ (* y y) 1) x) (+ (* y y) 1) (/ 1 (* x (+ (* y y) 1))) (* x (* y y)) (/ 1 (- (* x (* y y)) x)))
3.0ms	y	@	inf	((/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4) (* (- (pow (* x (* y y)) 2) (* x x)) (/ 1 (- (* x (* y y)) x))) (- (pow (* x (* y y)) 2) (* x x)) (- (* x (* y y)) x) (pow (* x (* y y)) 2) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (+ (* y y) 1) x) (+ (* y y) 1) (/ 1 (* x (+ (* y y) 1))) (* x (* y y)) (/ 1 (- (* x (* y y)) x)))
3.0ms	y	@	0	((/ (- -1 (* y y)) (/ -1 x)) (- -1 (* y y)) (* y y) (/ -1 x) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ (* (- (pow y 4) 1) x) (+ (* y y) -1)) (* (- (pow y 4) 1) x) (- (pow y 4) 1) (pow y 4) (* (- (pow (* x (* y y)) 2) (* x x)) (/ 1 (- (* x (* y y)) x))) (- (pow (* x (* y y)) 2) (* x x)) (- (* x (* y y)) x) (pow (* x (* y y)) 2) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (+ (* y y) 1) x) (+ (* y y) 1) (/ 1 (* x (+ (* y y) 1))) (* x (* y y)) (/ 1 (- (* x (* y y)) x)))

simplify267.0ms (3.7%)

Memory

3.5MiB live, 209.0MiB allocated

Algorithm

1×	egg-herbie

Rules

21 102×	`lower-fma.f64`
21 102×	`lower-fma.f32`
5 278×	`lower-*.f64`
5 278×	`lower-*.f32`
3 448×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	145	3412
1	414	3323
2	1260	3279
3	4169	3244
0	8233	3004

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 437

Calls

Call 1

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

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

rewrite226.0ms (3.1%)

Memory

-4.4MiB live, 224.3MiB allocated

Rules

4 692×	`lower-/.f32`
4 680×	`lower-/.f64`
3 976×	`lower-*.f32`
3 962×	`lower-*.f64`
3 562×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	191
0	57	176
1	236	164
2	1498	164
0	8276	164

Stop Event

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

Counts

22 → 2 010

Calls

Call 1

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

Outputs
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eval433.0ms (6%)

Memory: 28.4MiB live, 555.1MiB allocated
Compiler: Compiled 63 922 to 4 465 computations (93% saved)

prune50.0ms (0.7%)

Memory

-0.7MiB live, 156.4MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	2 551	5	2 556
Fresh	0	0	0
Picked	4	1	5
Done	0	3	3
Total	2 555	9	2 564

Accuracy

100.0%

Counts

2 564 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
▶	94.0%	(fma.f64 (sqrt.f64 (.f64 x (.f64 y y))) (sqrt.f64 (.f64 x (.f64 y y))) x)
▶	99.5%	(pow.f64 (pow.f64 (fma.f64 (*.f64 x y) y x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
▶	55.1%	(pow.f64 #s(approx (pow (* (+ (* y y) 1) x) 1/2) (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64))
▶	49.4%	(/.f64 (neg.f64 #s(approx (+ (* y y) 1) (*.f64 y y))) (/.f64 #s(literal -1 binary64) x))
✓	49.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
▶	36.0%	(.f64 (fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 y y)) x (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x)))
✓	49.4%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	49.1%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 156 to 104 computations (33.3% saved)

simplify163.0ms (2.3%)

Memory

14.4MiB live, 169.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 (sqrt.f64 x) y)
cost-diff	0	#s(approx (pow (* (+ (* y y) 1) x) 1/2) (*.f64 (sqrt.f64 x) y))
cost-diff	0	(pow.f64 #s(approx (pow (* (+ (* y y) 1) x) 1/2) (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64))
cost-diff	0	(.f64 x (.f64 y y))
cost-diff	128	(-.f64 (.f64 x (.f64 y y)) x)
cost-diff	320	(fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 y y)) x (*.f64 (neg.f64 x) x))
cost-diff	8704	(.f64 (fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 y y)) x (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(.f64 x (.f64 y y))
cost-diff	0	(sqrt.f64 (.f64 x (.f64 y y)))
cost-diff	2240	(fma.f64 (sqrt.f64 (.f64 x (.f64 y y))) (sqrt.f64 (.f64 x (.f64 y y))) x)
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* y y) 1) (*.f64 y y))
cost-diff	0	(neg.f64 #s(approx (+ (* y y) 1) (*.f64 y y)))
cost-diff	1216	(/.f64 (neg.f64 #s(approx (+ (* y y) 1) (*.f64 y y))) (/.f64 #s(literal -1 binary64) x))
cost-diff	0	(*.f64 x y)
cost-diff	0	(fma.f64 (*.f64 x y) y x)
cost-diff	5824	(pow.f64 (fma.f64 (*.f64 x y) y x) #s(literal 1/2 binary64))
cost-diff	7104	(pow.f64 (pow.f64 (fma.f64 (*.f64 x y) y x) #s(literal 1/2 binary64)) #s(literal 2 binary64))

Rules

8 250×	`lower-fma.f32`
8 244×	`lower-fma.f64`
4 146×	`lower-*.f32`
4 132×	`lower-*.f64`
2 224×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	224
0	57	201
1	97	186
2	205	181
3	493	175
4	1947	175
5	6168	175
0	8407	170

Stop Event

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

Calls

Call 1

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

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

localize97.0ms (1.3%)

Memory

-33.7MiB live, 175.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.1875	(*.f64 (sqrt.f64 x) y)
accuracy	0.3125	(pow.f64 #s(approx (pow (* (+ (* y y) 1) x) 1/2) (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64))
accuracy	28.39385574134657	#s(approx (pow (* (+ (* y y) 1) x) 1/2) (*.f64 (sqrt.f64 x) y))
accuracy	0.3930222047845906	(/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x))
accuracy	8.182658029653798	(.f64 x (.f64 y y))
accuracy	10.978495577043478	(fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 y y)) x (*.f64 (neg.f64 x) x))
accuracy	34.25441692310098	(.f64 (fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 y y)) x (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 y y)) x)))
accuracy	0	(*.f64 y y)
accuracy	0.12109375	(fma.f64 (sqrt.f64 (.f64 x (.f64 y y))) (sqrt.f64 (.f64 x (.f64 y y))) x)
accuracy	8.182658029653798	(.f64 x (.f64 y y))
accuracy	23.464919388291893	(sqrt.f64 (.f64 x (.f64 y y)))
accuracy	0	(*.f64 y y)
accuracy	0	(neg.f64 #s(approx (+ (* y y) 1) (*.f64 y y)))
accuracy	3.84482337909502	(/.f64 (neg.f64 #s(approx (+ (* y y) 1) (*.f64 y y))) (/.f64 #s(literal -1 binary64) x))
accuracy	28.749262572395796	#s(approx (+ (* y y) 1) (*.f64 y y))
accuracy	0	(*.f64 x y)
accuracy	0.05078125	(fma.f64 (*.f64 x y) y x)
accuracy	0.3125	(pow.f64 (pow.f64 (fma.f64 (*.f64 x y) y x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
accuracy	12.403260711726062	(pow.f64 (fma.f64 (*.f64 x y) y x) #s(literal 1/2 binary64))

Samples

75.0ms

256×

valid

Compiler

Compiled 210 to 35 computations (83.3% saved)

Precisions

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

ival-sqrt: 22.0ms (38.6% of total)

ival-mult: 16.0ms (28.1% of total)

ival-div: 5.0ms (8.8% of total)

ival-add: 5.0ms (8.8% of total)

ival-pow2: 5.0ms (8.8% of total)

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

ival-sub: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series32.0ms (0.4%)

Memory

-15.4MiB live, 59.7MiB allocated

Counts

19 → 408

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((pow (pow (+ (* (* x y) y) x) 1/2) 2) (pow (+ (* (* x y) y) x) 1/2) (+ (* (* x y) y) x) (* x y) (/ (neg (+ (* y y) 1)) (/ -1 x)) (neg (+ (* y y) 1)) (+ (* y y) 1) (* y y) (+ (* (sqrt (* x (* y y))) (sqrt (* x (* y y)))) x) (sqrt (* x (* y y))) (* x (* y y)) (* (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (/ 1 (- (* x (* y y)) x))) (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (- (* x (* y y)) x) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (sqrt x) y) (sqrt x) (/ 1 (- (* x (* y y)) x)))
4.0ms	y	@	0	((pow (pow (+ (* (* x y) y) x) 1/2) 2) (pow (+ (* (* x y) y) x) 1/2) (+ (* (* x y) y) x) (* x y) (/ (neg (+ (* y y) 1)) (/ -1 x)) (neg (+ (* y y) 1)) (+ (* y y) 1) (* y y) (+ (* (sqrt (* x (* y y))) (sqrt (* x (* y y)))) x) (sqrt (* x (* y y))) (* x (* y y)) (* (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (/ 1 (- (* x (* y y)) x))) (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (- (* x (* y y)) x) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (sqrt x) y) (sqrt x) (/ 1 (- (* x (* y y)) x)))
3.0ms	x	@	inf	((pow (pow (+ (* (* x y) y) x) 1/2) 2) (pow (+ (* (* x y) y) x) 1/2) (+ (* (* x y) y) x) (* x y) (/ (neg (+ (* y y) 1)) (/ -1 x)) (neg (+ (* y y) 1)) (+ (* y y) 1) (* y y) (+ (* (sqrt (* x (* y y))) (sqrt (* x (* y y)))) x) (sqrt (* x (* y y))) (* x (* y y)) (* (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (/ 1 (- (* x (* y y)) x))) (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (- (* x (* y y)) x) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (sqrt x) y) (sqrt x) (/ 1 (- (* x (* y y)) x)))
2.0ms	x	@	0	((pow (pow (+ (* (* x y) y) x) 1/2) 2) (pow (+ (* (* x y) y) x) 1/2) (+ (* (* x y) y) x) (* x y) (/ (neg (+ (* y y) 1)) (/ -1 x)) (neg (+ (* y y) 1)) (+ (* y y) 1) (* y y) (+ (* (sqrt (* x (* y y))) (sqrt (* x (* y y)))) x) (sqrt (* x (* y y))) (* x (* y y)) (* (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (/ 1 (- (* x (* y y)) x))) (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (- (* x (* y y)) x) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (sqrt x) y) (sqrt x) (/ 1 (- (* x (* y y)) x)))
2.0ms	y	@	-inf	((pow (pow (+ (* (* x y) y) x) 1/2) 2) (pow (+ (* (* x y) y) x) 1/2) (+ (* (* x y) y) x) (* x y) (/ (neg (+ (* y y) 1)) (/ -1 x)) (neg (+ (* y y) 1)) (+ (* y y) 1) (* y y) (+ (* (sqrt (* x (* y y))) (sqrt (* x (* y y)))) x) (sqrt (* x (* y y))) (* x (* y y)) (* (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (/ 1 (- (* x (* y y)) x))) (+ (* (* (* x (* y y)) (* y y)) x) (* (neg x) x)) (- (* x (* y y)) x) (pow (pow (* (+ (* y y) 1) x) 1/2) 2) (pow (* (+ (* y y) 1) x) 1/2) (* (sqrt x) y) (sqrt x) (/ 1 (- (* x (* y y)) x)))

simplify321.0ms (4.4%)

Memory

11.4MiB live, 278.0MiB allocated

Algorithm

1×	egg-herbie

Rules

17 138×	`lower-fma.f64`
17 138×	`lower-fma.f32`
5 462×	`lower-*.f64`
5 462×	`lower-*.f32`
2 614×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	136	3001
1	381	2890
2	1162	2823
3	4120	2811
0	8452	2593

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 402

Calls

Call 1

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

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

rewrite266.0ms (3.7%)

Memory

-1.3MiB live, 288.6MiB allocated

Rules

7 774×	`lower-fma.f32`
7 768×	`lower-fma.f64`
4 334×	`lower-*.f32`
4 320×	`lower-*.f64`
3 506×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	180
0	57	155
1	209	137
2	1119	133
0	8539	128

Stop Event

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

Counts

19 → 2 350

Calls

Call 1

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

Outputs
#<batchref>
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eval610.0ms (8.4%)

Memory: 29.1MiB live, 780.9MiB allocated
Compiler: Compiled 92 349 to 5 651 computations (93.9% saved)

prune246.0ms (3.4%)

Memory

-180.8MiB live, 249.4MiB allocated

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	3 293	4	3 297
Fresh	0	0	0
Picked	3	2	5
Done	0	4	4
Total	3 296	10	3 306

Accuracy

100.0%

Counts

3 306 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (.f64 (sqrt.f64 (.f64 y x)) (sqrt.f64 (*.f64 y x))) y x)
✓	99.9%	(fma.f64 (*.f64 x y) y x)
✓	94.0%	(fma.f64 (sqrt.f64 (.f64 x (.f64 y y))) (sqrt.f64 (.f64 x (.f64 y y))) x)
	99.1%	(pow.f64 (.f64 (sqrt.f64 (pow.f64 (fma.f64 (.f64 y x) y x) #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (*.f64 y x) y x) #s(literal 1/4 binary64)))) #s(literal 2 binary64))
✓	49.4%	(/.f64 (neg.f64 #s(approx (+ (* y y) 1) (*.f64 y y))) (/.f64 #s(literal -1 binary64) x))
✓	49.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
	8.1%	(.f64 (fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 y y)) x (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) #s(approx (- (* x (* y y)) x) (.f64 (.f64 y y) x))))
	55.1%	(.f64 #s(approx (pow ( (+ (* y y) 1) x) 1/2) (.f64 (sqrt.f64 x) y)) #s(approx (pow ( (+ (* y y) 1) x) 1/2) (*.f64 (sqrt.f64 x) y)))
✓	49.4%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	49.1%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 356 to 152 computations (57.3% saved)

regimes103.0ms (1.4%)

Memory

12.4MiB live, 51.4MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs
(fma.f64 (*.f64 x y) y x)

Calls

5 calls:

80.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
6.0ms	y
6.0ms	x
5.0ms	(*.f64 y y)
5.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

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

Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes11.0ms (0.2%)

Memory

-20.3MiB live, 18.2MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))

Outputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))

Calls

5 calls:

5.0ms	x
2.0ms	y
1.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
1.0ms	(*.f64 y y)
1.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

Accuracy	Segments	Branch
55.4%	2	`x`
93.7%	2	`y`
77.4%	2	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
93.7%	2	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
93.7%	2	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes6.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Outputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
49.1%	1	`x`
49.1%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
49.1%	1	`y`
49.1%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
49.1%	1	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

bsearch12.0ms (0.2%)

Memory

19.3MiB live, 19.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	2.864472934963278e-10	11381681.672975821

Samples

6.0ms

160×

valid

Compiler

Compiled 90 to 121 computations (-34.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 1.0ms (44.4% of total)

ival-mult: 1.0ms (44.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify25.0ms (0.4%)

Memory

-23.4MiB live, 52.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	20	41

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 (*.f64 x y) y x)

(if (<=.f64 (*.f64 y y) #s(literal 1 binary64)) (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))))

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

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

soundness512.0ms (7.1%)

Memory

5.6MiB live, 248.6MiB allocated

Rules

9 064×	`lower-fma.f64`
9 064×	`lower-fma.f32`
6 574×	`lower-*.f64`
6 574×	`lower-*.f32`
5 176×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	34	15
2	209	15
3	1404	15
0	8269	13
0	15	246
1	42	246
2	74	246
3	214	246
4	721	246
5	1940	246
6	2658	246
7	3752	246
8	5094	246
9	5986	246
10	6927	246
11	7270	246
12	7376	246
13	7453	246
14	7522	246
15	7669	246
0	8207	216

Stop Event

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

Compiler

Compiled 50 to 32 computations (36% saved)

preprocess56.0ms (0.8%)

Memory

19.3MiB live, 129.0MiB allocated

Remove

(negabs x)

(abs y)

Compiler

Compiled 152 to 94 computations (38.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

start0.0ms (0%)

analyze0.0ms (0%)

sample944.0ms (13.1%)

explain240.0ms (3.3%)

preprocess29.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize21.0ms (0.3%)

series5.0ms (0.1%)

simplify243.0ms (3.4%)

rewrite305.0ms (4.2%)

eval76.0ms (1%)

prune58.0ms (0.8%)

simplify158.0ms (2.2%)

localize80.0ms (1.1%)

series49.0ms (0.7%)

simplify203.0ms (2.8%)

rewrite291.0ms (4%)

eval770.0ms (10.7%)

prune58.0ms (0.8%)

simplify120.0ms (1.7%)

localize96.0ms (1.3%)

series37.0ms (0.5%)

simplify267.0ms (3.7%)

rewrite226.0ms (3.1%)

eval433.0ms (6%)

prune50.0ms (0.7%)

simplify163.0ms (2.3%)

localize97.0ms (1.3%)

series32.0ms (0.4%)

simplify321.0ms (4.4%)

rewrite266.0ms (3.7%)

eval610.0ms (8.4%)

prune246.0ms (3.4%)

regimes103.0ms (1.4%)

regimes11.0ms (0.2%)

regimes6.0ms (0.1%)

bsearch12.0ms (0.2%)

simplify25.0ms (0.4%)

soundness512.0ms (7.1%)

preprocess56.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6