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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze22.0ms (0.5%)

Memory

-8.0MiB live, 37.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
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)

sample872.0ms (20.5%)

Memory

9.9MiB live, 867.6MiB allocated

Samples

632.0ms	8 256×	0	valid
19.0ms	502×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-sqrt: 76.0ms (54% of total)

ival-add: 55.0ms (39.1% of total)

ival-true: 6.0ms (4.3% of total)

ival-assert: 3.0ms (2.1% of total)

Bogosity

explain46.0ms (1.1%)

Memory

-9.1MiB live, 82.6MiB 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

19.0ms

512×

valid

Compiler

Compiled 35 to 20 computations (42.9% saved)

Precisions

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

ival-sqrt: 4.0ms (50.4% of total)

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

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

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

preprocess16.0ms (0.4%)

Memory

23.0MiB live, 23.0MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB 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 (0.1%)

Memory

3.3MiB live, 3.3MiB 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

localize51.0ms (1.2%)

Memory

-15.1MiB live, 21.2MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.00390625	(sqrt.f64 (+.f64 x y))

Samples

47.0ms

256×

valid

Compiler

Compiled 20 to 10 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-sqrt: 38.0ms (94.1% of total)

ival-add: 2.0ms (5% of total)

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

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

series6.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB 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	y	@	inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	inf	((sqrt (+ x y)) (+ x y))
0.0ms	y	@	0	((sqrt (+ x y)) (+ x y))

simplify218.0ms (5.1%)

Memory

-10.3MiB live, 341.2MiB 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)

rewrite194.0ms (4.6%)

Memory

28.0MiB live, 222.6MiB 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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eval43.0ms (1%)

Memory: -9.3MiB live, 76.0MiB allocated
Compiler: Compiled 5 681 to 881 computations (84.5% saved)

prune5.0ms (0.1%)

Memory

-22.1MiB live, 16.8MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	266	3	269

Accuracy

100.0%

Counts

269 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(.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))
▶	96.8%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify211.0ms (5%)

Memory

9.7MiB live, 164.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score
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: 1 (0.0ms)

Iter	Nodes	Cost
0	15	66
0	25	66
1	34	63
2	44	63
3	57	63
4	78	63
5	167	63
6	473	63
7	914	63
8	1518	63
9	2348	63
10	3156	63
11	3622	63
12	3726	63
13	3772	63
14	3790	63
15	6052	63
16	6757	63
17	7401	63
18	7982	63
19	7990	63
20	7990	63
0	8252	63

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)

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)

localize52.0ms (1.2%)

Memory

6.0MiB live, 44.2MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.15234375	(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))
accuracy	0.2578125	(.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	4.394531250000001	(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y))
accuracy	30.72837467124487	(sqrt.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)))
accuracy	0	(sqrt.f64 y)
accuracy	2.0785205846703634	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Samples

29.0ms

256×

valid

Compiler

Compiled 130 to 30 computations (76.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sqrt: 7.0ms (34.9% of total)

ival-mult: 6.0ms (30% of total)

ival-add: 3.0ms (15% of total)

ival-div: 2.0ms (10% of total)

ival-sub: 1.0ms (5% of total)

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

exact: 0.0ms (0% of total)

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

series84.0ms (2%)

Memory

-32.9MiB live, 76.3MiB allocated

Counts

7 → 144

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	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) (sqrt (/ -1 (- x y))))
3.0ms	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) (sqrt (/ -1 (- x y))))
3.0ms	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) (sqrt (/ -1 (- x y))))
3.0ms	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) (sqrt (/ -1 (- x y))))
2.0ms	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) (sqrt (/ -1 (- x y))))

simplify205.0ms (4.8%)

Memory

35.7MiB live, 153.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	426	2863
1	1357	2574
2	4941	2526
0	8416	2382

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

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

rewrite424.0ms (10%)

Memory

-6.8MiB live, 182.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	51
0	25	50
1	82	46
2	542	36
3	6585	36
0	8325	36

Stop Event

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

Counts

7 → 223

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)
(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))

Outputs
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eval63.0ms (1.5%)

Memory: 7.9MiB live, 80.8MiB allocated
Compiler: Compiled 8 522 to 1 211 computations (85.8% saved)

prune43.0ms (1%)

Memory

-17.4MiB live, 27.1MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	365	3	368

Accuracy

100.0%

Counts

368 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.3%	(.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))
✓	96.8%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify412.0ms (9.7%)

Memory

16.3MiB live, 131.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
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	14	68
0	20	65
1	28	62
2	38	62
3	52	62
4	75	62
5	164	62
6	476	62
7	916	62
8	1530	62
9	2350	62
10	3165	62
11	3631	62
12	3737	62
13	3783	62
14	3801	62
15	6063	62
16	6768	62
17	7412	62
18	7993	62
0	8001	62

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

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

localize99.0ms (2.3%)

Memory

-5.5MiB live, 51.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.15234375	(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))
accuracy	0.2578125	(.f64 (sqrt.f64 #s(approx (+ ( -1 (* x x)) (* y y)) (*.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
accuracy	0.5046446110198298	#s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y))
accuracy	30.72837467124487	(sqrt.f64 #s(approx (+ (* -1 (* x x)) (* y y)) (*.f64 y y)))

Samples

49.0ms

256×

valid

Compiler

Compiled 99 to 24 computations (75.8% saved)

Precisions

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

ival-mult: 6.0ms (38.8% of total)

ival-sqrt: 4.0ms (25.9% of total)

ival-div: 2.0ms (12.9% of total)

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

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

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

exact: 0.0ms (0% of total)

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

series22.0ms (0.5%)

Memory

-26.7MiB live, 10.0MiB allocated

Counts

5 → 108

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	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 (/ -1 (- x y))))
1.0ms	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 (/ -1 (- x y))))
1.0ms	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 (/ -1 (- x y))))
0.0ms	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 (/ -1 (- x y))))
0.0ms	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 (/ -1 (- x y))))

simplify496.0ms (11.7%)

Memory

11.3MiB live, 167.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	2286
1	1123	2014
2	4194	1920
0	8265	1810

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 106

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

rewrite144.0ms (3.4%)

Memory

33.7MiB live, 188.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	57
0	20	53
1	70	49
2	442	47
3	4124	47
0	8824	44

Stop Event

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

Counts

5 → 88

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)
(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)))

Outputs
#<batchref>
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eval90.0ms (2.1%)

Memory: -7.9MiB live, 29.9MiB allocated
Compiler: Compiled 3 800 to 641 computations (83.1% saved)

prune22.0ms (0.5%)

Memory

-23.1MiB live, 16.1MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	194	3	197

Accuracy

100.0%

Counts

197 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.3%	(.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))
✓	96.8%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 54 to 36 computations (33.3% saved)

regimes9.0ms (0.2%)

Memory

23.7MiB live, 23.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(+.f64 x y)
2.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 x 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)

regimes5.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
96.8%	1	`x`
96.8%	1	`y`
96.8%	1	`(sqrt.f64 (+.f64 x y))`
96.8%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify107.0ms (2.5%)

Memory

-43.1MiB live, 42.2MiB 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))

soundness237.0ms (5.6%)

Memory

13.1MiB live, 139.5MiB 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)

preprocess52.0ms (1.2%)

Memory: -11.7MiB live, 65.5MiB allocated
Remove: (sort x y)
Compiler: Compiled 38 to 36 computations (5.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

start0.0ms (0%)

analyze22.0ms (0.5%)

sample872.0ms (20.5%)

explain46.0ms (1.1%)

preprocess16.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify2.0ms (0.1%)

localize51.0ms (1.2%)

series6.0ms (0.1%)

simplify218.0ms (5.1%)

rewrite194.0ms (4.6%)

eval43.0ms (1%)

prune5.0ms (0.1%)

simplify211.0ms (5%)

localize52.0ms (1.2%)

series84.0ms (2%)

simplify205.0ms (4.8%)

rewrite424.0ms (10%)

eval63.0ms (1.5%)

prune43.0ms (1%)

simplify412.0ms (9.7%)

localize99.0ms (2.3%)

series22.0ms (0.5%)

simplify496.0ms (11.7%)

rewrite144.0ms (3.4%)

eval90.0ms (2.1%)

prune22.0ms (0.5%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

simplify107.0ms (2.5%)

soundness237.0ms (5.6%)

preprocess52.0ms (1.2%)

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