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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze23.0ms (0.4%)

Memory

-24.1MiB live, 22.4MiB 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)

sample788.0ms (15.2%)

Memory

-156.8MiB live, 689.6MiB allocated

Samples

553.0ms	8 256×	0	valid
25.0ms	502×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 416.0ms

ival-add: 321.0ms (77.2% of total)

ival-sqrt: 85.0ms (20.4% of total)

ival-true: 7.0ms (1.7% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

explain174.0ms (3.4%)

Memory

-22.0MiB live, 54.5MiB 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

18.0ms

512×

valid

Compiler

Compiled 53 to 28 computations (47.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-sqrt: 4.0ms (54.3% of total)

ival-add: 3.0ms (40.8% of total)

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

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

preprocess16.0ms (0.3%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

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

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

simplify2.0ms (0%)

Memory

3.4MiB live, 3.4MiB 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))

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

localize16.0ms (0.3%)

Memory

-22.3MiB live, 20.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.0078125	(sqrt.f64 (+.f64 x y))

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 10 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sqrt: 2.0ms (55.5% of total)

ival-add: 1.0ms (27.8% of total)

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

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

series6.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB 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
1.0ms	y	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	y	@	inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	inf	((sqrt (+ x y)) (+ x y))
0.0ms	y	@	0	((sqrt (+ x y)) (+ x y))

simplify292.0ms (5.6%)

Memory

26.2MiB live, 179.4MiB allocated

Algorithm

1×	egg-herbie

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)

rewrite184.0ms (3.6%)

Memory

9.1MiB live, 162.8MiB allocated

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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eval35.0ms (0.7%)

Memory: -10.4MiB live, 61.7MiB allocated
Compiler: Compiled 5 681 to 881 computations (84.5% saved)

prune5.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB 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
▶	99.2%	(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
▶	46.9%	(.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	98.1%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 30 to 26 computations (13.3% saved)

simplify253.0ms (4.9%)

Memory

2.4MiB live, 207.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 y x)
cost-diff	0	(pow.f64 (+.f64 y x) #s(literal 1/4 binary64))
cost-diff	12288	(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
cost-diff	320	(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	85
0	33	85
1	43	80
2	56	79
3	69	79
4	90	79
5	179	79
6	489	79
7	933	79
8	1522	79
9	2354	79
10	3162	79
11	3628	79
12	3732	79
13	3778	79
14	3796	79
15	6058	79
16	6762	79
17	7406	79
18	7987	79
19	7995	79
20	7995	79
0	8257	79

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

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

localize145.0ms (2.8%)

Memory

-25.4MiB live, 101.4MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 (+.f64 y x) #s(literal 1/4 binary64))
accuracy	0	(+.f64 y x)
accuracy	0.5019913086106522	(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy	0.13671875	(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))
accuracy	0.32421875	(.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
accuracy	5.179687500000001	(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y))
accuracy	32.55895534243023	(sqrt.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)))
accuracy	0	(sqrt.f64 y)
accuracy	1.191367696427492	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Samples

132.0ms

256×

valid

Compiler

Compiled 168 to 40 computations (76.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-sqrt: 78.0ms (66.2% of total)

ival-add: 21.0ms (17.8% of total)

ival-mult: 6.0ms (5.1% of total)

ival-pow: 5.0ms (4.2% of total)

ival-pow2: 3.0ms (2.5% of total)

ival-div: 2.0ms (1.7% of total)

ival-sub: 1.0ms (0.8% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.6%)

Memory

5.4MiB live, 43.1MiB allocated

Counts

10 → 216

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	((sqrt (+ x y)) (sqrt y) (+ (* -1 (* x x)) (* y y)) (* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (* x x) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x) (sqrt (/ -1 (- x y))))
5.0ms	x	@	inf	((sqrt (+ x y)) (sqrt y) (+ (* -1 (* x x)) (* y y)) (* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (* x x) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x) (sqrt (/ -1 (- x y))))
4.0ms	y	@	inf	((sqrt (+ x y)) (sqrt y) (+ (* -1 (* x x)) (* y y)) (* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (* x x) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x) (sqrt (/ -1 (- x y))))
4.0ms	y	@	-inf	((sqrt (+ x y)) (sqrt y) (+ (* -1 (* x x)) (* y y)) (* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (* x x) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x) (sqrt (/ -1 (- x y))))
4.0ms	y	@	0	((sqrt (+ x y)) (sqrt y) (+ (* -1 (* x x)) (* y y)) (* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (* x x) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x) (sqrt (/ -1 (- x y))))

simplify308.0ms (6%)

Memory

-1.4MiB live, 149.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	595	4246
1	1855	3857
2	7581	3782
0	8107	3573

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 208

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)
(* -1 (pow x 2))
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(* (sqrt x) (pow (sqrt -1) 2))
(+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2)))
(* x (sqrt -1))
(+ (* 1/2 (/ (pow y 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(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)))))))
(pow (* 1 x) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(+ (* y (+ (* -3/32 (* (pow (/ 1 (pow x 7)) 1/4) y)) (* 1/4 (pow (/ 1 (pow x 3)) 1/4)))) (pow (* 1 x) 1/4))
(+ (* y (+ (* 1/4 (pow (/ 1 (pow x 3)) 1/4)) (* y (+ (* -3/32 (pow (/ 1 (pow x 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow x 11)) 1/4) y)))))) (pow (* 1 x) 1/4))
x
(+ x y)
(+ x y)
(+ x y)
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* y (+ (* 3/8 (* (sqrt (/ 1 (pow x 5))) (* y (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* y (+ (* 5/16 (* (sqrt (/ 1 (pow x 7))) (* y (sqrt -1)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(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)
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (sqrt y) (pow (sqrt -1) 2))
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -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))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
y
(* y (+ 1 (* -1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/8 (/ (pow x 4) (pow y 4))))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* -1/16 (/ (pow x 6) (pow y 6)))))))
(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)))))))))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (pow (* 1 y) 1/4)))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 3)) (+ (* 1/384 (pow x 3)) (* 1/12 (pow x 3))))) (pow (* 1 y) 1/4))))
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* (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))))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (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 (* (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)))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 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))))) (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (+ (* -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))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/8 (/ (pow x 4) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* -1/16 (/ (pow x 6) (pow y 6))))))))
(* -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)))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* 1/4 (/ (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) y)) (* -1/4 (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/12 (pow x 3)) (+ (* -1/384 (pow x 3)) (* 1/32 (pow x 3))))) y)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2))))) y)) (* -1/4 (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 y)) (* (pow (sqrt -1) 2) (+ (* -1/4 (* (pow x 2) y)) (pow x 3))))) (* 1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt y)))) (pow y 3))) (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 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))))))))))
(pow y 2)
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(* (sqrt y) (pow (sqrt -1) 2))
(+ (* -1/2 (* x (sqrt (/ 1 y)))) (* (sqrt y) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* (/ x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow y 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (/ x (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 5))))))))) (* (sqrt y) (pow (sqrt -1) 2)))
y
(+ y (* -1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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))))))))))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(+ (* x (+ (* -3/32 (* (pow (/ 1 (pow y 7)) 1/4) x)) (* 1/4 (pow (/ 1 (pow y 3)) 1/4)))) (pow (* 1 y) 1/4))
(+ (* x (+ (* 1/4 (pow (/ 1 (pow y 3)) 1/4)) (* x (+ (* -3/32 (pow (/ 1 (pow y 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow y 11)) 1/4) x)))))) (pow (* 1 y) 1/4))
y
(+ x y)
(+ x y)
(+ x y)
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* -1/2 (* (* x (+ (* 1/4 (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))) (/ 1 (pow y 3)))) (sqrt y))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -1/2 (* (sqrt y) (+ (* 1/4 (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))) (/ 1 (pow y 3))))) (* -1/2 (* (* x (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))) (/ 1 (pow y 3))) (* y (pow (sqrt -1) 2)))) (/ 1 (pow y 4)))) (sqrt y))))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 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))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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))))))
(pow (* 1 x) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (pow (* 1 x) 1/4)))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (+ (* (pow (/ 1 (pow x 11)) 1/4) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))) (pow (* 1 x) 1/4))))
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1 (pow y 3)) (* 1/4 (* x (pow y 2))))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (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)))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (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 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1)))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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)))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* 1/4 (/ (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/12 (pow y 3)) (+ (* -1/384 (pow y 3)) (* 1/32 (pow y 3))))) x)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (* (pow y 2) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (* x (pow y 2))) (pow y 3)))))) (pow x 3))) (+ (* -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 #s(literal 1/2 binary64) y) (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)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(+ (* -1 (pow x 2)) (pow y 2))
(*.f64 (+.f64 y x) (-.f64 y x))
(+ (* -1 (pow x 2)) (pow y 2))
(*.f64 (+.f64 y x) (-.f64 y x))
(+ (* -1 (pow x 2)) (pow y 2))
(*.f64 (+.f64 y x) (-.f64 y x))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) y (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) y (neg.f64 (sqrt.f64 x)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) y (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) y (neg.f64 (sqrt.f64 x)))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (pow y 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (.f64 y y) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (.f64 y y) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (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))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(fma.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) y) #s(literal 1/4 binary64) (pow.f64 x #s(literal 1/4 binary64)))
(+ (* y (+ (* -3/32 (* (pow (/ 1 (pow x 7)) 1/4) y)) (* 1/4 (pow (/ 1 (pow x 3)) 1/4)))) (pow (* 1 x) 1/4))
(fma.f64 (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) y) #s(literal -3/32 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) y (pow.f64 x #s(literal 1/4 binary64)))
(+ (* y (+ (* 1/4 (pow (/ 1 (pow x 3)) 1/4)) (* y (+ (* -3/32 (pow (/ 1 (pow x 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow x 11)) 1/4) y)))))) (pow (* 1 x) 1/4))
(fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64))) #s(literal 1/4 binary64)) y) #s(literal 7/128 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64))) y (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) y (pow.f64 x #s(literal 1/4 binary64)))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(* (sqrt (/ 1 x)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(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))))
(+ (* y (+ (* 3/8 (* (sqrt (/ 1 (pow x 5))) (* y (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal 3/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* y (+ (* 5/16 (* (sqrt (/ 1 (pow x 7))) (* y (sqrt -1)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 (.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 5/16 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))) y)) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (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)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))))) y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (/.f64 x y))) (*.f64 y y))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (/.f64 x y))) (*.f64 y y))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (/.f64 x y))) (*.f64 y y))
(* (sqrt y) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 y))
(* 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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (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 #s(literal 1/8 binary64) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -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))))) (* (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 -1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) y)
y
(* y (+ 1 (* -1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 y #s(literal -1/2 binary64)) (.f64 (/.f64 x y) (/.f64 x y)) y)
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/8 (/ (pow x 4) (pow y 4))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 (/.f64 x y) x) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) y y)
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* -1/16 (/ (pow x 6) (pow y 6)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 (/.f64 x y) x) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 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)) (+ (* -1/8 (* (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)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (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)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))))) y)
(pow (* 1 y) 1/4)
(pow.f64 y #s(literal 1/4 binary64))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(fma.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64)) x) #s(literal 1/4 binary64) (pow.f64 y #s(literal 1/4 binary64)))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (pow (* 1 y) 1/4)))
(fma.f64 (.f64 #s(literal 1/4 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal -3/32 binary64) (*.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 3)) (+ (* 1/384 (pow x 3)) (* 1/12 (pow x 3))))) (pow (* 1 y) 1/4))))
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(pow x 2)
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(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
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(* -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 (neg.f64 x) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (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 (* 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))))))
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x
(* -1 (* x (- (* -1 (/ y x)) 1)))
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(*.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (/.f64 y x)))
(* (sqrt (/ 1 x)) (sqrt -1))
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(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
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(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (* (pow y 2) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (* x (pow y 2))) (pow y 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 #s(literal -1 binary64))) y (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (.f64 y y) (fma.f64 #s(literal -1/4 binary64) x y)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) y) y) (sqrt.f64 x)))) (pow.f64 x #s(literal 3 binary64)))))

rewrite176.0ms (3.4%)

Memory

7.8MiB live, 161.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	66
0	33	73
1	114	67
2	713	48
0	8746	48

Stop Event

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

Counts

10 → 636

Calls

Call 1

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

Outputs
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval166.0ms (3.2%)

Memory: 1.0MiB live, 229.6MiB allocated
Compiler: Compiled 19 789 to 2 693 computations (86.4% saved)

prune15.0ms (0.3%)

Memory

21.5MiB live, 60.1MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	842	2	844
Fresh	0	0	0
Picked	2	1	3
Done	0	1	1
Total	844	4	848

Accuracy

100.0%

Counts

848 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
▶	47.4%	(.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.1%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 35 to 30 computations (14.3% saved)

simplify357.0ms (6.9%)

Memory

-13.2MiB live, 265.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	124
0	32	121
1	47	118
2	66	118
3	83	118
4	127	118
5	297	118
6	580	118
7	1056	118
8	1737	118
9	2822	118
10	4227	118
11	4957	118
12	5240	118
13	5430	118
14	5526	118
15	5526	118
16	6441	118
17	6593	118
18	6745	118
19	6821	118
20	6821	118
21	7125	118
22	7201	118
23	7277	118
24	7277	118
25	7277	118
26	7277	118
0	9281	118

Stop Event

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

Calls

Call 1

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

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

localize236.0ms (4.6%)

Memory

16.5MiB live, 92.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 #s(literal -1 binary64) (-.f64 x y))
accuracy	0.13671875	(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))
accuracy	0.32421875	(.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
accuracy	0.54296875	(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x)))
accuracy	0.01171875	(/.f64 #s(literal -1 binary64) (-.f64 x y))
accuracy	0.13671875	(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))
accuracy	0.32421875	(.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
accuracy	32.55895534243023	(sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y)))

Samples

221.0ms

256×

valid

Compiler

Compiled 211 to 36 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 210.0ms

ival-mult: 196.0ms (93.5% of total)

ival-sqrt: 7.0ms (3.3% of total)

ival-add: 3.0ms (1.4% of total)

ival-div: 2.0ms (1% of total)

ival-sub: 2.0ms (1% of total)

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

exact: 0.0ms (0% of total)

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

series73.0ms (1.4%)

Memory

-26.9MiB live, 77.6MiB allocated

Counts

10 → 228

Calls

Call 1

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

Outputs
#s(alt (* (sqrt x) (pow (sqrt -1) 2)) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (pow y 2) (* x (sqrt -1)))) (* x (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1))))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (sqrt -1)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1))))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y)) (patch #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y)) (patch #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y)) (patch #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y)) (patch #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (pow (sqrt -1) 2)) (taylor 0 y) (#s(alt (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2))) (taylor 0 y) (#s(alt (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2))) (taylor 0 y) (#s(alt (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2))) (taylor 0 y) (#s(alt (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.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 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.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 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#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 (/ 1 x)) (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 3/8 (* (sqrt (/ 1 (pow x 5))) (* y (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* y (+ (* 5/16 (* (sqrt (/ 1 (pow x 7))) (* y (sqrt -1)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))))))) (* (sqrt (/ 1 x)) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ y (pow x 2))) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
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#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>) () ())) ())
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#s(alt (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
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#s(alt (/ (- (* -1 (/ (pow y 2) (pow x 2))) (+ 1 (/ y x))) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (pow y 3) (pow x 3))) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2))))) x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.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 (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.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 (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.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 (.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1)) (taylor -inf x) (#s(alt #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y)) (patch #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1)) (taylor -inf x) (#s(alt #s(approx (+ (* -1 (* x x)) (* y y)) (.f64 y y)) (patch #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
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#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 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.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 (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) (patch (.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1))))))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.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 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.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 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (patch (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
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#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>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (sqrt -1)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (* (pow y 2) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (* x (pow y 2))) (pow y 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (/ y x)) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 x y)) (patch (/.f64 #s(literal -1 binary64) (-.f64 x y)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
54.0ms	x	@	0	((* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (+ (* -1 (* x x)) (* y y)) (* y y) (* (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (/ -1 (- x y)))) (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (+ x y)) (+ x y) (sqrt (/ -1 (- x y))) (/ -1 (- x y)))
3.0ms	y	@	inf	((* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (+ (* -1 (* x x)) (* y y)) (* y y) (* (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (/ -1 (- x y)))) (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (+ x y)) (+ x y) (sqrt (/ -1 (- x y))) (/ -1 (- x y)))
2.0ms	y	@	-inf	((* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (+ (* -1 (* x x)) (* y y)) (* y y) (* (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (/ -1 (- x y)))) (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (+ x y)) (+ x y) (sqrt (/ -1 (- x y))) (/ -1 (- x y)))
2.0ms	x	@	inf	((* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (+ (* -1 (* x x)) (* y y)) (* y y) (* (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (/ -1 (- x y)))) (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (+ x y)) (+ x y) (sqrt (/ -1 (- x y))) (/ -1 (- x y)))
2.0ms	y	@	0	((* (sqrt (+ (* -1 (* x x)) (* y y))) (sqrt (/ -1 (- x y)))) (sqrt (+ (* -1 (* x x)) (* y y))) (+ (* -1 (* x x)) (* y y)) (* y y) (* (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (/ -1 (- x y)))) (* (sqrt (+ x y)) (sqrt (- y x))) (sqrt (+ x y)) (+ x y) (sqrt (/ -1 (- x y))) (/ -1 (- x y)))

simplify289.0ms (5.6%)

Memory

20.5MiB live, 211.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	760	4942
1	2546	4091
0	9074	3850

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 218

Calls

Call 1

Inputs
(* (sqrt x) (pow (sqrt -1) 2))
(+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2)))
(* x (sqrt -1))
(+ (* 1/2 (/ (pow y 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(* -1 (pow x 2))
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (sqrt x) (pow (sqrt -1) 2))
(+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2)))
(* 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 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 (/ 1 x)) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* y (+ (* 3/8 (* (sqrt (/ 1 (pow x 5))) (* y (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* y (+ (* 5/16 (* (sqrt (/ 1 (pow x 7))) (* y (sqrt -1)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(/ -1 x)
(- (* -1 (/ y (pow x 2))) (/ 1 x))
(- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(* (sqrt y) (pow (sqrt -1) 2))
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -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))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
y
(* y (+ 1 (* -1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/8 (/ (pow x 4) (pow y 4))))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* -1/16 (/ (pow x 6) (pow y 6)))))))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (sqrt y) (pow (sqrt -1) 2))
(* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 (+ x (* -1 x))) x))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 (+ x (* -1 x))) x))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (* x (- (* -1 (+ x (* -1 x))) x)))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (* x (- (pow x 2) (* -1 (* x (- (* -1 (+ x (* -1 x))) x)))))) (* 1/4 (/ (* y (pow (- (* -1 (+ x (* -1 x))) x) 2)) (pow (sqrt -1) 2)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 (+ x (* -1 x))) x))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (* x (- (* -1 (+ x (* -1 x))) x)))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
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)) (+ (* -1/8 (* (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)))
(* (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))))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(/ 1 y)
(/ (+ 1 (/ x y)) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (* -1 (/ x y))) y)
(/ (- (+ 1 (/ (pow x 3) (pow y 3))) (+ (* -1 (/ x y)) (* -1 (/ (pow x 2) (pow y 2))))) y)
(* -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))))) (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (+ (* -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))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/8 (/ (pow x 4) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* -1/16 (/ (pow x 6) (pow y 6))))))))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 (* (sqrt y) (pow (sqrt -1) 4)))
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 4)))))
(* -1 (* y (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 4))))))
(* -1 (* y (+ (* -1/8 (* (pow x 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) 4)))))))
(* -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 (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 (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 y)) (* (pow (sqrt -1) 2) (+ (* -1/4 (* (pow x 2) y)) (pow x 3))))) (* 1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt y)))) (pow y 3))) (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(/ 1 y)
(* -1 (/ (- (* -1 (/ x y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) (* -1 x)) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y)) (* -1 x)) y)) 1) y))
(* (sqrt y) (pow (sqrt -1) 2))
(+ (* -1/2 (* x (sqrt (/ 1 y)))) (* (sqrt y) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* (/ x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow y 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (/ x (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 5))))))))) (* (sqrt y) (pow (sqrt -1) 2)))
y
(+ y (* -1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (- (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(+ (* -1 (pow x 2)) (pow y 2))
(* (sqrt y) (pow (sqrt -1) 2))
(+ (* 1/2 (* (* x (- (* -1 (/ (+ y (* -1 y)) y)) 1)) (sqrt (/ 1 y)))) (* (sqrt y) (pow (sqrt -1) 2)))
(+ (* x (+ (* 1/2 (* (sqrt (/ 1 y)) (- (* -1 (/ (+ y (* -1 y)) y)) 1))) (* 1/2 (* (* x (- (/ 1 y) (+ (* -1 (/ (- (* -1 (/ (+ y (* -1 y)) y)) 1) y)) (* 1/4 (/ (pow (- (* -1 (/ (+ y (* -1 y)) y)) 1) 2) (* y (pow (sqrt -1) 2))))))) (sqrt (/ 1 y)))))) (* (sqrt y) (pow (sqrt -1) 2)))
(+ (* x (+ (* 1/2 (* (sqrt (/ 1 y)) (- (* -1 (/ (+ y (* -1 y)) y)) 1))) (* x (+ (* -1/2 (* (* x (+ (* -1 (/ (- (/ 1 y) (* -1 (/ (- (* -1 (/ (+ y (* -1 y)) y)) 1) y))) y)) (* 1/2 (/ (* (- (* -1 (/ (+ y (* -1 y)) y)) 1) (- (/ 1 y) (+ (* -1 (/ (- (* -1 (/ (+ y (* -1 y)) y)) 1) y)) (* 1/4 (/ (pow (- (* -1 (/ (+ y (* -1 y)) y)) 1) 2) (* y (pow (sqrt -1) 2))))))) (* y (pow (sqrt -1) 2)))))) (sqrt (/ 1 y)))) (* 1/2 (* (sqrt (/ 1 y)) (- (/ 1 y) (+ (* -1 (/ (- (* -1 (/ (+ y (* -1 y)) y)) 1) y)) (* 1/4 (/ (pow (- (* -1 (/ (+ y (* -1 y)) y)) 1) 2) (* y (pow (sqrt -1) 2)))))))))))) (* (sqrt y) (pow (sqrt -1) 2)))
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 (+ (* -1/8 (* 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 (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* -1/2 (* (* x (+ (* 1/4 (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))) (/ 1 (pow y 3)))) (sqrt y))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -1/2 (* (sqrt y) (+ (* 1/4 (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))) (/ 1 (pow y 3))))) (* -1/2 (* (* x (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))) (/ 1 (pow y 3))) (* y (pow (sqrt -1) 2)))) (/ 1 (pow y 4)))) (sqrt y))))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(/ 1 y)
(+ (/ 1 y) (/ x (pow y 2)))
(+ (* x (+ (/ 1 (pow y 2)) (/ x (pow y 3)))) (/ 1 y))
(+ (* x (+ (* x (+ (/ 1 (pow y 3)) (/ x (pow y 4)))) (/ 1 (pow y 2)))) (/ 1 y))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1)))))))
(* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* 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)
(* 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)))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1 (pow y 3)) (* 1/4 (* x (pow y 2))))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(/ -1 x)
(/ (- (* -1 (/ y x)) 1) x)
(/ (- (* -1 (/ (pow y 2) (pow x 2))) (+ 1 (/ y x))) x)
(/ (- (* -1 (/ (pow y 3) (pow x 3))) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 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 (/ (pow y 2) (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow x 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow x 2) (sqrt -1)))))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* (pow x 2) (- (/ (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 (* 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) (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)))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (* (pow y 2) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (* x (pow y 2))) (pow y 3)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(/ -1 x)
(* -1 (/ (+ 1 (/ y x)) x))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) x))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) x))

Outputs
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y #s(literal -1 binary64))) (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 (neg.f64 (sqrt.f64 x)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (neg.f64 (sqrt.f64 x)))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (pow y 2) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) y) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (.f64 y y) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (* x (sqrt -1)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (* (pow x 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* x (sqrt -1)))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (.f64 y y) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (.f64 y y) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(+ (* -1 (pow x 2)) (pow y 2))
(fma.f64 (neg.f64 x) x (*.f64 y y))
(+ (* -1 (pow x 2)) (pow y 2))
(fma.f64 (neg.f64 x) x (*.f64 y y))
(+ (* -1 (pow x 2)) (pow y 2))
(fma.f64 (neg.f64 x) x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(+ (* -1/2 (* (sqrt (/ 1 x)) y)) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y #s(literal -1 binary64))) (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 (neg.f64 (sqrt.f64 x)))
(+ (* y (+ (* -1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 4)))))))) (* (sqrt x) (pow (sqrt -1) 2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) y (neg.f64 (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 (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (* 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 y #s(literal 1/2 binary64)) (/.f64 (+.f64 y (.f64 (/.f64 #s(literal 0 binary64) (.f64 x x)) y)) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(+ (* 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 (fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))))) y (/.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) y (sqrt.f64 x))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(* (sqrt (/ 1 x)) (sqrt -1))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 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) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* y (+ (* 3/8 (* (sqrt (/ 1 (pow x 5))) (* y (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 3/8 binary64) (.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* y (+ (* 5/16 (* (sqrt (/ 1 (pow x 7))) (* y (sqrt -1)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 (.f64 #s(literal 5/16 binary64) (.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) y)) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(- (* -1 (/ y (pow x 2))) (/ 1 x))
(fma.f64 (/.f64 y (*.f64 x x)) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) y (/.f64 #s(literal -1 binary64) x))
(- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(fma.f64 (fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) y (/.f64 #s(literal -1 binary64) (*.f64 x x))) y (/.f64 #s(literal -1 binary64) x))
(* (sqrt y) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 y))
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (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 binary64))) y)
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64)))) y)
(* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -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))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64))))) y)
y
(* y (+ 1 (* -1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 y #s(literal -1/2 binary64)) (.f64 (/.f64 x y) (/.f64 x y)) y)
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (* -1/8 (/ (pow x 4) (pow y 4))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) y y)
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) (pow y 2))) (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* -1/16 (/ (pow x 6) (pow y 6)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64))))) y y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (/.f64 x y))) (*.f64 y y))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (/.f64 x y))) (*.f64 y y))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (/.f64 x y))) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* (sqrt y) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 y))
(* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 (+ x (* -1 x))) x))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (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 binary64))) y)
(* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 (+ x (* -1 x))) x))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (* x (- (* -1 (+ x (* -1 x))) x)))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 x) (.f64 (fma.f64 x x (.f64 (neg.f64 x) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64))) y)
(* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* -1 (* x (- (pow x 2) (* -1 (* x (- (* -1 (+ x (* -1 x))) x)))))) (* 1/4 (/ (* y (pow (- (* -1 (+ x (* -1 x))) x) 2)) (pow (sqrt -1) 2)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 (+ x (* -1 x))) x))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (* -1 (* x (- (* -1 (+ x (* -1 x))) x)))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 y #s(literal -1 binary64)) (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 x) (.f64 (fma.f64 x x (.f64 (neg.f64 x) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64)))) y)
y
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))
(+.f64 (/.f64 #s(literal 0 binary64) 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 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) y) (/.f64 #s(literal 0 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 (fma.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) y) (/.f64 #s(literal 0 binary64) y))) y y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
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(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
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(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
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(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
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x
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(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (+ 1 (/ y x)) x))
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(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) x))
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(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) (*.f64 y y)) (neg.f64 x)) y) x)) (neg.f64 x))

rewrite248.0ms (4.8%)

Memory

5.6MiB live, 164.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	94
0	32	77
1	105	73
2	680	71
0	8010	71

Stop Event

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

Counts

10 → 530

Calls

Call 1

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

Outputs
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eval264.0ms (5.1%)

Memory: -26.9MiB live, 298.5MiB allocated
Compiler: Compiled 25 504 to 2 976 computations (88.3% saved)

prune18.0ms (0.3%)

Memory

19.0MiB live, 56.6MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	927	1	928
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	928	4	932

Accuracy

100.0%

Counts

932 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
▶	98.3%	(.f64 #s(approx ( (sqrt (+ x y)) (sqrt (- y x))) y) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.1%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 32 to 28 computations (12.5% saved)

simplify9.0ms (0.2%)

Memory

12.5MiB live, 12.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
0	17	46
1	24	46
2	31	46
3	41	46
4	61	46
5	119	46
6	158	46
7	203	46
8	224	46
9	232	46
10	233	46
0	233	46

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize252.0ms (4.9%)

Memory

-25.0MiB live, 57.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 #s(literal -1 binary64) (-.f64 x y))
accuracy	0.13671875	(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))
accuracy	0.32421875	(.f64 #s(approx ( (sqrt (+ x y)) (sqrt (- y x))) y) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
accuracy	0.7091349928388258	#s(approx (* (sqrt (+ x y)) (sqrt (- y x))) y)

Samples

244.0ms

256×

valid

Compiler

Compiled 72 to 22 computations (69.4% saved)

Precisions

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

ival-sqrt: 5.0ms (34.1% of total)

ival-mult: 3.0ms (20.5% of total)

ival-sub: 2.0ms (13.6% of total)

ival-div: 2.0ms (13.6% of total)

ival-add: 2.0ms (13.6% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

4 → 96

Calls

Call 1

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

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

Calls

6 calls:

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

simplify184.0ms (3.6%)

Memory

-11.8MiB live, 179.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	554	2742
1	1855	2050
2	7675	2031
0	8132	1916

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 94

Calls

Call 1

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

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

rewrite171.0ms (3.3%)

Memory

28.0MiB live, 216.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	40
0	17	38
1	66	38
2	447	35
3	7183	35
0	9175	35

Stop Event

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

Counts

4 → 145

Calls

Call 1

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

Outputs
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eval113.0ms (2.2%)

Memory: -30.0MiB live, 74.5MiB allocated
Compiler: Compiled 5 406 to 1 037 computations (80.8% saved)

prune5.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	239	4	243

Accuracy

100.0%

Counts

243 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.f64 (.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
✓	98.3%	(.f64 #s(approx ( (sqrt (+ x y)) (sqrt (- y x))) y) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.1%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 99 to 57 computations (42.4% saved)

regimes38.0ms (0.7%)

Memory

-3.7MiB live, 33.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

29.0ms	(+.f64 x y)
3.0ms	(sqrt.f64 (+.f64 x y))
3.0ms	x
3.0ms	y

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)

regimes8.0ms (0.2%)

Memory

-13.5MiB live, 22.9MiB 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:

4.0ms	(sqrt.f64 (+.f64 x y))
1.0ms	y
1.0ms	(+.f64 x y)
1.0ms	x

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`y`
98.1%	1	`(sqrt.f64 (+.f64 x y))`
98.1%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify27.0ms (0.5%)

Memory

3.3MiB live, 49.1MiB allocated

Algorithm

1×	egg-herbie

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))

soundness179.0ms (3.5%)

Memory

-11.8MiB live, 100.9MiB allocated

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)

preprocess56.0ms (1.1%)

Memory: 34.2MiB live, 114.7MiB 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	13	46
0	17	46
1	24	46
2	31	46
3	41	46
4	61	46
5	119	46
6	158	46
7	203	46
8	224	46
9	232	46
10	233	46
0	233	46

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	13	46
0	17	46
1	24	46
2	31	46
3	41	46
4	61	46
5	119	46
6	158	46
7	203	46
8	224	46
9	232	46
10	233	46
0	233	46

start0.0ms (0%)

analyze23.0ms (0.4%)

sample788.0ms (15.2%)

explain174.0ms (3.4%)

preprocess16.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify2.0ms (0%)

localize16.0ms (0.3%)

series6.0ms (0.1%)

simplify292.0ms (5.6%)

rewrite184.0ms (3.6%)

eval35.0ms (0.7%)

prune5.0ms (0.1%)

simplify253.0ms (4.9%)

localize145.0ms (2.8%)

series31.0ms (0.6%)

simplify308.0ms (6%)

rewrite176.0ms (3.4%)

eval166.0ms (3.2%)

prune15.0ms (0.3%)

simplify357.0ms (6.9%)

localize236.0ms (4.6%)

series73.0ms (1.4%)

simplify289.0ms (5.6%)

rewrite248.0ms (4.8%)

eval264.0ms (5.1%)

prune18.0ms (0.3%)

simplify9.0ms (0.2%)

localize252.0ms (4.9%)

series5.0ms (0.1%)

simplify184.0ms (3.6%)

rewrite171.0ms (3.3%)

eval113.0ms (2.2%)

prune5.0ms (0.1%)

regimes38.0ms (0.7%)

regimes8.0ms (0.2%)

simplify27.0ms (0.5%)

soundness179.0ms (3.5%)

preprocess56.0ms (1.1%)

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

Iter	Nodes	Cost
0	13	46
0	17	46
1	24	46
2	31	46
3	41	46
4	61	46
5	119	46
6	158	46
7	203	46
8	224	46
9	232	46
10	233	46
0	233	46