Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze31.0ms (0.6%)

Memory

-27.7MiB live, 11.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
25%	25%	74.9%	0.1%	0%	0%	0%	3
28.6%	25%	62.4%	0.1%	0%	12.5%	0%	4
46.2%	37.5%	43.7%	0.1%	0%	18.7%	0%	5
52.2%	37.5%	34.3%	0.1%	0%	28.1%	0%	6
65.1%	43.7%	23.4%	0.1%	0%	32.8%	0%	7
70.9%	43.7%	18%	0.1%	0%	38.2%	0%	8
79.5%	46.8%	12.1%	0.1%	0%	41%	0%	9
83.6%	46.8%	9.2%	0.1%	0%	43.9%	0%	10
88.7%	48.4%	6.1%	0.1%	0%	45.4%	0%	11
91.3%	48.4%	4.6%	0.1%	0%	46.9%	0%	12

Compiler

Compiled 6 to 6 computations (0% saved)

sample1.1s (19.1%)

Memory

36.9MiB live, 549.5MiB allocated

Samples

798.0ms	8 256×	0	valid
17.0ms	513×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 505.0ms

ival-sqrt: 249.0ms (49.4% of total)

ival-add: 246.0ms (48.8% of total)

ival-true: 7.0ms (1.4% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain110.0ms (2%)

Memory

-6.1MiB live, 76.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(sqrt.f64 (+.f64 x y))`
-	-	`y`
-	-	`(+.f64 x y)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

67.0ms

512×

valid

Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-sqrt: 53.0ms (94.4% of total)

ival-add: 3.0ms (5.3% of total)

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

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

preprocess59.0ms (1.1%)

Memory

-2.2MiB live, 37.4MiB allocated

Algorithm

1×	egg-herbie

Rules

44×	`sub-neg`
28×	`associate--r+`
24×	`neg-mul-1`
22×	`cancel-sign-sub-inv`
22×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x y))

Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))

Symmetry

(sort x y)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory: 0.8MiB live, 0.8MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 x y)
cost-diff	0	(sqrt.f64 (+.f64 x y))

Rules

4×	`lower-+.f32`
2×	`lift-sqrt.f64`
2×	`lift-+.f64`
2×	`lower-+.f64`
2×	`lower-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	7	9
0	7	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
x
y

Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))
(+.f64 x y)
(+.f64 y x)
x
y

localize14.0ms (0.3%)

Memory

3.1MiB live, 42.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.01171875	(sqrt.f64 (+.f64 x y))

Samples

10.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (59.4% of total)

ival-add: 1.0ms (29.7% of total)

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

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

series10.0ms (0.2%)

Memory

-41.6MiB live, 14.2MiB allocated

Counts

2 → 48

Calls

Call 1

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

Outputs
#s(alt (sqrt x) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (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 (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x y)) (patch (sqrt.f64 (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	((sqrt (+ x y)) (+ x y))
1.0ms	y	@	inf	((sqrt (+ x y)) (+ x y))
1.0ms	y	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	inf	((sqrt (+ x y)) (+ x y))

simplify441.0ms (8%)

Memory

1.5MiB live, 312.3MiB allocated

Algorithm

1×	egg-herbie

Rules

27 648×	`lower-fma.f64`
27 648×	`lower-fma.f32`
5 638×	`lower-*.f64`
5 638×	`lower-*.f32`
2 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1426	582
3	4628	570
0	8167	534

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

Inputs
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
x
(+ x y)
(+ x y)
(+ x y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
y
(+ x y)
(+ x y)
(+ x y)
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))

Outputs
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
y
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 (*.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x (sqrt.f64 y))
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(.f64 (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) y) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
x
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (*.f64 y y) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)

rewrite195.0ms (3.5%)

Memory

26.6MiB live, 294.7MiB allocated

Rules

5 128×	`lower-fma.f64`
5 128×	`lower-fma.f32`
4 292×	`lower-/.f64`
4 292×	`lower-/.f32`
3 378×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	22	7
2	145	7
3	1366	7
0	8310	7

Stop Event

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

Counts

2 → 226

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)

Outputs
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eval104.0ms (1.9%)

Memory: -28.5MiB live, 143.8MiB allocated
Compiler: Compiled 5 681 to 881 computations (84.5% saved)

prune5.0ms (0.1%)

Memory

26.2MiB live, 26.2MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	265	4	269

Accuracy

100.0%

Counts

269 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.8%	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	99.3%	#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)))
▶	98.3%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify309.0ms (5.6%)

Memory

-9.2MiB live, 381.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

37 904×	`lower-fma.f32`
37 902×	`lower-fma.f64`
8 976×	`lower-+.f32`
8 974×	`lower-+.f64`
3 160×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	91
0	31	91
1	42	91
2	67	91
3	109	91
4	220	91
5	384	91
6	723	91
7	1372	91
8	2391	91
9	3266	91
10	3666	91
11	3874	91
12	3934	91
13	3944	91
14	3944	91
15	3944	91
16	3944	91
0	9265	91

Stop Event

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

Calls

Call 1

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

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

localize314.0ms (5.7%)

Memory

-1.7MiB live, 173.3MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (+.f64 y x) (-.f64 y x))
accuracy	0.0078125	(sqrt.f64 (-.f64 y x))
accuracy	0.4765625	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
accuracy	30.251702255584604	(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))
accuracy	0	(sqrt.f64 y)
accuracy	0.01953125	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
accuracy	0.14453125	(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
accuracy	0.4323422590460884	#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)))
accuracy	0	(sqrt.f64 y)
accuracy	1.0615504283005368	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Samples

303.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sqrt: 8.0ms (38.2% of total)

ival-add: 4.0ms (19.1% of total)

ival-mult: 4.0ms (19.1% of total)

ival-div: 3.0ms (14.3% of total)

ival-sub: 1.0ms (4.8% of total)

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

exact: 0.0ms (0% of total)

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

series24.0ms (0.4%)

Memory

7.4MiB live, 45.4MiB allocated

Counts

12 → 252

Calls

Call 1

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

Outputs
#s(alt (sqrt x) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x (sqrt (/ 1 y)))) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) (taylor 0 y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) (taylor 0 y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (* y (+ x (* -1 x)))) (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x))))) (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x))))) (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ x y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) (taylor inf y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) (taylor inf y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) (taylor inf y) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (patch (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1 (/ (+ y (* -1 y)) x)) 1)) (taylor -inf x) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1)) (taylor -inf x) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1)) (taylor -inf x) (#s(alt (.f64 (+.f64 y x) (-.f64 y x)) (patch (.f64 (+.f64 y x) (-.f64 y x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	y	@	-inf	((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (+ y x) (- y x) (sqrt (- y x)) (* (+ y x) (- y x)))
2.0ms	y	@	0	((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (+ y x) (- y x) (sqrt (- y x)) (* (+ y x) (- y x)))
2.0ms	x	@	inf	((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (+ y x) (- y x) (sqrt (- y x)) (* (+ y x) (- y x)))
2.0ms	y	@	inf	((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (+ y x) (- y x) (sqrt (- y x)) (* (+ y x) (- y x)))
2.0ms	x	@	-inf	((sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (+ y x) (- y x) (sqrt (- y x)) (* (+ y x) (- y x)))

simplify117.0ms (2.1%)

Memory

5.2MiB live, 157.8MiB allocated

Algorithm

1×	egg-herbie

Rules

7 852×	`lower-fma.f64`
7 852×	`lower-fma.f32`
4 026×	`lower-*.f64`
4 026×	`lower-*.f32`
1 906×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	496	3790
1	1634	3284
2	6729	3202
0	8425	3018

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 241

Calls

Call 1

Inputs
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(* 1/2 (* x (sqrt (/ 1 y))))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(* x (sqrt -1))
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))))
x
(+ x y)
(+ x y)
(+ x y)
(* -1 x)
(- y x)
(- y x)
(- y x)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(* -1 (pow x 2))
(+ (* -1 (pow x 2)) (* y (+ x (* -1 x))))
(+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x)))))
(+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
y
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))))
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7)))))))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (/ x y))))
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y)))))
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y)))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2))))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) y)) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ x (* -1 x))) (/ (pow x 2) y)) y))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y)))
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y)))))
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3))))))))
y
(+ x y)
(+ x y)
(+ x y)
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(pow y 2)
(+ (* x (+ y (* -1 y))) (pow y 2))
(+ (* x (+ y (+ (* -1 x) (* -1 y)))) (pow y 2))
(+ (* x (+ y (+ (* -1 x) (* -1 y)))) (pow y 2))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))))
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (pow x 2))
(* (pow x 2) (- (+ (* -1 (/ y x)) (/ y x)) 1))
(* (pow x 2) (- (+ (* -1 (/ y x)) (+ (/ y x) (/ (pow y 2) (pow x 2)))) 1))
(* (pow x 2) (- (+ (* -1 (/ y x)) (+ (/ y x) (/ (pow y 2) (pow x 2)))) 1))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (pow x 2))
(* (pow x 2) (- (* -1 (/ (+ y (* -1 y)) x)) 1))
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1))
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1))

Outputs
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64)))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64)))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(* -1 x)
(neg.f64 x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) y (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(+ (* -1 (pow x 2)) (* y (+ x (* -1 x))))
(*.f64 (neg.f64 x) x)
(+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x)))))
(fma.f64 y y (*.f64 (neg.f64 x) x))
(+ (* -1 (pow x 2)) (* y (+ x (+ y (* -1 x)))))
(fma.f64 y y (*.f64 (neg.f64 x) x))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 (+.f64 (fma.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 (+.f64 (fma.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
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(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* -1 (/ (+ y (* -1 y)) x)) 1))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal -1 binary64)) x) x)
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal -1 binary64)) x) x)

rewrite202.0ms (3.6%)

Memory

1.2MiB live, 276.9MiB allocated

Rules

6 500×	`lower-fma.f32`
6 498×	`lower-fma.f64`
5 378×	`lower-*.f32`
5 374×	`lower-*.f64`
3 736×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	79
0	31	78
1	106	67
2	746	67
0	8635	65

Stop Event

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

Counts

12 → 877

Calls

Call 1

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

Outputs
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eval205.0ms (3.7%)

Memory: 21.0MiB live, 325.0MiB allocated
Compiler: Compiled 32 222 to 4 143 computations (87.1% saved)

prune25.0ms (0.4%)

Memory

11.0MiB live, 88.4MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1 309	2	1 311
Fresh	0	0	0
Picked	2	1	3
Done	0	1	1
Total	1 311	4	1 315

Accuracy

100.0%

Counts

1 315 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	99.3%	#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))
✓	98.3%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify316.0ms (5.7%)

Memory

-0.8MiB live, 274.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

24 624×	`lower-fma.f32`
24 622×	`lower-fma.f64`
4 520×	`lower-+.f64`
4 520×	`lower-+.f32`
3 448×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	64
0	24	64
1	32	64
2	55	64
3	96	64
4	207	64
5	371	64
6	716	64
7	1341	64
8	2333	64
9	3339	64
10	3912	64
11	4388	64
12	4838	64
13	6072	64
14	6279	64
15	6296	64
16	6329	64
17	6337	64
18	6339	64
19	6406	64
20	6406	64
0	8486	64

Stop Event

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

Calls

Call 1

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

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

localize80.0ms (1.5%)

Memory

-13.1MiB live, 119.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 y x)
accuracy	0.0078125	(sqrt.f64 (-.f64 y x))
accuracy	0.4621179847067789	#s(approx (sqrt (* (+ y x) (- y x))) y)
accuracy	0.4765625	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x)))
accuracy	0	(sqrt.f64 y)
accuracy	0.0234375	(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
accuracy	0.21484375	(/.f64 x (sqrt.f64 y))
accuracy	0.4323422590460884	#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))

Samples

71.0ms

256×

valid

Compiler

Compiled 54 to 17 computations (68.5% saved)

Precisions

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

ival-div: 35.0ms (67.5% of total)

ival-add: 6.0ms (11.6% of total)

ival-sqrt: 6.0ms (11.6% of total)

ival-mult: 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)

series13.0ms (0.2%)

Memory

0.7MiB live, 39.5MiB allocated

Counts

8 → 180

Calls

Call 1

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

Outputs
#s(alt (sqrt x) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x (sqrt (/ 1 y)))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) (taylor 0 y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor 0 y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor 0 y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor 0 y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor 0 y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor inf y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor inf y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor inf y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor inf y) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
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#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) (taylor inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) (patch #s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x (sqrt (/ 1 y)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) (patch (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (/ 1 y))) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 y)) (patch (/.f64 x (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	y	@	-inf	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x))
1.0ms	x	@	-inf	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x))
1.0ms	x	@	0	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x))
1.0ms	x	@	inf	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x))
1.0ms	y	@	0	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x))

simplify303.0ms (5.5%)

Memory

-26.1MiB live, 94.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 768×	`lower-fma.f64`
6 768×	`lower-fma.f32`
4 172×	`lower-*.f64`
4 172×	`lower-*.f32`
1 870×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	438	2854
1	1454	2570
2	5968	2441
0	8524	2304

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 175

Calls

Call 1

Inputs
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(* 1/2 (* x (sqrt (/ 1 y))))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(* x (sqrt -1))
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(* -1 x)
(- y x)
(- y x)
(- y x)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
y
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7)))))))))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y)))
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y)))))
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3))))))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* x (sqrt (/ 1 y)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))

Outputs
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64)))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64)))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) y (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(* -1 x)
(neg.f64 x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 (+.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 (+.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
y
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))
y
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))
(fma.f64 (neg.f64 y) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) y) y) y)
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))))
(fma.f64 (neg.f64 y) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) y) y) y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
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(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (/.f64 y (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (/.f64 y (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ y x) 1))
(fma.f64 (/.f64 y x) x (neg.f64 x))
(* x (- (/ y x) 1))
(fma.f64 (/.f64 y x) x (neg.f64 x))
(* x (- (/ y x) 1))
(fma.f64 (/.f64 y x) x (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 y y) x) #s(literal 0 binary64)) x)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (fma.f64 (.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) #s(literal 0 binary64)) (neg.f64 x)) x)) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(fma.f64 (/.f64 y x) x (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(fma.f64 (/.f64 y x) x (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(fma.f64 (/.f64 y x) x (neg.f64 x))

rewrite142.0ms (2.6%)

Memory

34.1MiB live, 193.6MiB allocated

Rules

5 468×	`lower-fma.f32`
5 466×	`lower-fma.f64`
5 382×	`lower-*.f64`
5 382×	`lower-*.f32`
4 222×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	59
0	24	59
1	90	59
2	700	59
0	8708	59

Stop Event

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

Counts

8 → 340

Calls

Call 1

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

Outputs
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eval114.0ms (2.1%)

Memory: -21.8MiB live, 133.3MiB allocated
Compiler: Compiled 10 835 to 1 656 computations (84.7% saved)

prune11.0ms (0.2%)

Memory

-6.1MiB live, 32.3MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	542	2	544
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	543	5	548

Accuracy

100.0%

Counts

548 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x)))
▶	97.6%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
▶	98.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.3%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 29 to 28 computations (3.4% saved)

simplify363.0ms (6.6%)

Memory

18.3MiB live, 300.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (- y x)) (sqrt.f64 y))
cost-diff	0	#s(approx (sqrt (* (+ y x) (- y x))) y)
cost-diff	0	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
cost-diff	0	(-.f64 y x)
cost-diff	0	(sqrt.f64 (-.f64 y x))
cost-diff	0	(/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)))

Rules

37 776×	`lower-fma.f64`
37 776×	`lower-fma.f32`
8 740×	`lower-+.f64`
8 740×	`lower-+.f32`
3 276×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	90
0	22	90
1	30	90
2	51	88
3	93	88
4	218	88
5	386	88
6	732	88
7	1335	88
8	2273	88
9	2876	88
10	3044	88
11	3086	88
12	3124	88
13	3124	88
14	3124	88
15	3126	88
0	8257	88

Stop Event

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

Calls

Call 1

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

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

localize35.0ms (0.6%)

Memory

-17.0MiB live, 58.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 y)
accuracy	0.4621179847067789	#s(approx (sqrt (* (+ y x) (- y x))) y)
accuracy	0.4765625	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
accuracy	1.0587190955114654	#s(approx (sqrt (- y x)) (sqrt.f64 y))
accuracy	0.0078125	(sqrt.f64 (-.f64 y x))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)))
accuracy	0.26953125	(/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))
accuracy	0.4621179847067789	#s(approx (sqrt (* (+ y x) (- y x))) y)

Samples

24.0ms

256×

valid

Compiler

Compiled 76 to 14 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-sqrt: 5.0ms (32.7% of total)

ival-div: 4.0ms (26.2% of total)

ival-add: 3.0ms (19.6% of total)

ival-sub: 2.0ms (13.1% of total)

ival-mult: 1.0ms (6.5% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.2%)

Memory

25.2MiB live, 25.2MiB allocated

Counts

8 → 180

Calls

Call 1

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

Outputs
#s(alt (sqrt x) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y))))) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5))))))))) (taylor 0 y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1))))))) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1))))))))) (taylor 0 y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) (taylor inf y) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y)))) (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))) (taylor inf y) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) (taylor inf y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) (taylor inf y) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) (taylor inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) (taylor inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) (taylor inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))) (taylor inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) (patch (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) (patch (/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (* (+ y x) (- y x))) y) (patch #s(approx (sqrt (* (+ y x) (- y x))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- y x)) (sqrt.f64 y)) (patch #s(approx (sqrt (- y x)) (sqrt.f64 y)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify273.0ms (4.9%)

Memory

-5.4MiB live, 147.8MiB allocated

Algorithm

1×	egg-herbie

Rules

7 704×	`lower-fma.f64`
7 704×	`lower-fma.f32`
4 596×	`lower-*.f64`
4 596×	`lower-*.f32`
2 026×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	503	3680
1	1668	3332
2	6672	3184
0	8609	2992

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 175

Calls

Call 1

Inputs
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y)))))
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5)))))))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(* -1 x)
(- y x)
(- y x)
(- y x)
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(* x (sqrt -1))
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7)))))))))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
y
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7)))))))))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ x (* -1 x)))) y)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* x (sqrt (/ 1 (pow y 5))))))))
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y)))
(+ y (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y)))))
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* x (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3))))))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow x 2) (sqrt -1))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))

Outputs
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))
(fma.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y)))))
(fma.f64 (fma.f64 (.f64 y #s(literal 3/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -5/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal 3/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) y (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) y (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(* -1 x)
(neg.f64 x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
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(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(fma.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (*.f64 y y) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (fma.f64 (.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (/.f64 (.f64 y y) #s(literal -1 binary64)) x) #s(literal -1/4 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) y) y)) (pow.f64 x #s(literal 3 binary64))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 y y) x) #s(literal 0 binary64)) x)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (fma.f64 (.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) #s(literal 0 binary64)) (neg.f64 x)) x)) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))

rewrite137.0ms (2.5%)

Memory

8.9MiB live, 164.6MiB allocated

Rules

3 190×	`lower-*.f64`
3 190×	`lower-*.f32`
2 442×	`lower-fma.f64`
2 442×	`lower-fma.f32`
2 120×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	76
0	22	76
1	74	74
2	434	74
3	5061	74
0	8552	74

Stop Event

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

Counts

8 → 350

Calls

Call 1

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

Outputs
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eval113.0ms (2%)

Memory: -11.0MiB live, 135.1MiB allocated
Compiler: Compiled 10 532 to 1 795 computations (83% saved)

prune12.0ms (0.2%)

Memory

-1.1MiB live, 35.3MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	565	0	565
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	565	5	570

Accuracy

100.0%

Counts

570 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x)))
✓	97.6%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
✓	98.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) #s(approx (sqrt (* (+ y x) (- y x))) y)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.3%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 91 to 56 computations (38.5% saved)

regimes15.0ms (0.3%)

Memory

-22.9MiB live, 23.6MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 x y))

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 x y))
3.0ms	(+.f64 x y)
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(sqrt.f64 (+.f64 x y))`
100.0%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes5.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Calls

4 calls:

1.0ms	(+.f64 x y)
1.0ms	(sqrt.f64 (+.f64 x y))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`y`
98.3%	1	`(sqrt.f64 (+.f64 x y))`
98.3%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify23.0ms (0.4%)

Memory

7.6MiB live, 45.1MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x y))
#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))
#s(approx (sqrt (+ x y)) (sqrt.f64 y))

soundness247.0ms (4.5%)

Memory

-29.2MiB live, 91.0MiB allocated

Rules

27 648×	`lower-fma.f64`
27 648×	`lower-fma.f32`
5 638×	`lower-*.f64`
5 638×	`lower-*.f32`
2 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1426	582
3	4628	570
0	8167	534

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 9 to 9 computations (0% saved)

preprocess96.0ms (1.7%)

Memory: 2.8MiB live, 41.1MiB allocated
Remove: (sort x y)
Compiler: Compiled 38 to 36 computations (5.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

start0.0ms (0%)

analyze31.0ms (0.6%)

sample1.1s (19.1%)

explain110.0ms (2%)

preprocess59.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize14.0ms (0.3%)

series10.0ms (0.2%)

simplify441.0ms (8%)

rewrite195.0ms (3.5%)

eval104.0ms (1.9%)

prune5.0ms (0.1%)

simplify309.0ms (5.6%)

localize314.0ms (5.7%)

series24.0ms (0.4%)

simplify117.0ms (2.1%)

rewrite202.0ms (3.6%)

eval205.0ms (3.7%)

prune25.0ms (0.4%)

simplify316.0ms (5.7%)

localize80.0ms (1.5%)

series13.0ms (0.2%)

simplify303.0ms (5.5%)

rewrite142.0ms (2.6%)

eval114.0ms (2.1%)

prune11.0ms (0.2%)

simplify363.0ms (6.6%)

localize35.0ms (0.6%)

series14.0ms (0.2%)

simplify273.0ms (4.9%)

rewrite137.0ms (2.5%)

eval113.0ms (2%)

prune12.0ms (0.2%)

regimes15.0ms (0.3%)

regimes5.0ms (0.1%)

simplify23.0ms (0.4%)

soundness247.0ms (4.5%)

preprocess96.0ms (1.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4