Metrics for Data.Octree.Internal:octantDistance from Octree-0.5.4.2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 10 to 5 computations (50% saved)

sample581.0ms (31.3%)

Memory

-9.7MiB live, 862.9MiB allocated; 121ms collecting garbage

Samples

407.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 174.0ms

ival-hypot: 172.0ms (99.1% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

explain94.0ms (5%)

Memory

18.3MiB live, 165.3MiB allocated; 29ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
129	-	3	(6.733807245755619e-157 1.0499538136785611e-234)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	oflow-rescue	119	0
↳	`(*.f64 y y)`	overflow	70
↳	`(*.f64 x x)`	overflow	70
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	119
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	7	0
↳	`(*.f64 y y)`	underflow	52
↳	`(*.f64 x x)`	underflow	50
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	7

Confusion

	Predicted +	Predicted -
+	126	3
-	0	127

Precision

1.0

Recall

0.9767441860465116

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	126	0	3
-	0	0	127

Precision?

1.0

Recall?

0.9767441860465116

Freqs

test

number	freq
0	130
1	126

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

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

ival-hypot: 9.0ms (46.6% of total)

ival-add!: 5.0ms (25.9% of total)

ival-mult!: 5.0ms (25.9% of total)

adjust: 0.0ms (0% of total)

preprocess19.0ms (1%)

Memory

-3.6MiB live, 42.5MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	43	50
2	93	50
3	118	50
4	156	50
0	6	8
0	10	8
1	21	8
2	60	8
3	117	8
4	154	8
0	154	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

(abs y)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.8%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

series9.0ms (0.5%)

Memory

-31.8MiB live, 15.3MiB allocated; 4ms collecting garbage

Counts

6 → 31

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 y))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* 1/2 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ 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)))))))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (pow y 2)))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (+ (pow x 2) (pow y 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (* y y) #s(hole binary64 (pow y 2)))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))))

Calls

6 calls:

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

rewrite216.0ms (11.7%)

Memory

-0.5MiB live, 241.2MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	143	742
0	148	722
1	742	722
0	7664	562

Stop Event

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

Counts

37 → 427

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(+.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 y))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* 1/2 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ 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)))))))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (pow y 2)))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (+ (pow x 2) (pow y 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (* y y) #s(hole binary64 (pow y 2)))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (+ (* x x) (* y y)) #s(hole binary64 (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))))

Outputs
(.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/4 binary64)))
(pow.f64 (hypot.f64 y x) #s(literal 1 binary64))
(pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 (fabs.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 y)))
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 #s(literal 1 binary64) (fabs.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 (neg.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (fabs.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (exp.f64 (log.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 y))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (fabs.f64 y))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) y)
(hypot.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 (fabs.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 y)))
(hypot.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 #s(literal 1 binary64) (fabs.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (neg.f64 (neg.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (neg.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (exp.f64 (log.f64 y)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (neg.f64 y))
(hypot.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 y))
(hypot.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) y)
(hypot.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (neg.f64 x)))
(hypot.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (fabs.f64 x)))
(hypot.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(hypot.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (neg.f64 (neg.f64 x)))
(hypot.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (exp.f64 (log.f64 x)))
(hypot.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (neg.f64 x))
(hypot.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (fabs.f64 x))
(hypot.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) x)
(hypot.f64 (.f64 (fabs.f64 y) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (neg.f64 x)))
(hypot.f64 (.f64 (fabs.f64 y) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (fabs.f64 x)))
(hypot.f64 (.f64 (fabs.f64 y) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (.f64 (fabs.f64 y) #s(literal 1 binary64)) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(hypot.f64 (*.f64 (fabs.f64 y) #s(literal 1 binary64)) (neg.f64 (neg.f64 x)))
(hypot.f64 (*.f64 (fabs.f64 y) #s(literal 1 binary64)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (*.f64 (fabs.f64 y) #s(literal 1 binary64)) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (*.f64 (fabs.f64 y) #s(literal 1 binary64)) (exp.f64 (log.f64 x)))
(hypot.f64 (*.f64 (fabs.f64 y) #s(literal 1 binary64)) (neg.f64 x))
(hypot.f64 (*.f64 (fabs.f64 y) #s(literal 1 binary64)) (fabs.f64 x))
(hypot.f64 (*.f64 (fabs.f64 y) #s(literal 1 binary64)) x)
(hypot.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 (fabs.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (neg.f64 y)))
(hypot.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (fabs.f64 y)))
(hypot.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 (neg.f64 y)))
(hypot.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (fabs.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (exp.f64 (log.f64 y)))
(hypot.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 y))
(hypot.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (fabs.f64 y))
(hypot.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) y)
(hypot.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 (fabs.f64 y) #s(literal 1 binary64)))
(hypot.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (neg.f64 y)))
(hypot.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (fabs.f64 y)))
(hypot.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (neg.f64 (neg.f64 y)))
(hypot.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (neg.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (fabs.f64 (fabs.f64 y)))
(hypot.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (exp.f64 (log.f64 y)))
(hypot.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (neg.f64 y))
(hypot.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (fabs.f64 y))
(hypot.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) y)
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 y)) (.f64 #s(literal 1 binary64) (neg.f64 x)))
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 y)) (.f64 #s(literal 1 binary64) (fabs.f64 x)))
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 y)) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (.f64 #s(literal 1 binary64) (neg.f64 y)) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 y)) (neg.f64 (neg.f64 x)))
(hypot.f64 (*.f64 #s(literal 1 binary64) (neg.f64 y)) (neg.f64 (fabs.f64 x)))
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(fma.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 y y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 (neg.f64 (neg.f64 y)) y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 y y))
(fma.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x) (.f64 (neg.f64 (neg.f64 y)) y))
(fma.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x) (.f64 y y))
(fma.f64 #s(literal -1 binary64) (.f64 (neg.f64 y) y) (.f64 x x))
(fma.f64 (.f64 y y) #s(literal 1 binary64) (.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 y y) (.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (neg.f64 (neg.f64 y)) y))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 y y))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 y)) y))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 y y))
(fma.f64 y (.f64 #s(literal -1 binary64) (neg.f64 y)) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(fma.f64 x (.f64 #s(literal -1 binary64) (neg.f64 x)) (.f64 (neg.f64 (neg.f64 y)) y))
(fma.f64 x (.f64 #s(literal -1 binary64) (neg.f64 x)) (.f64 y y))
(fma.f64 x x (*.f64 (neg.f64 (neg.f64 y)) y))
(fma.f64 x x (*.f64 y y))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (.f64 (neg.f64 y) y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 x x (.f64 (neg.f64 y) y))))
(-.f64 (.f64 y y) (.f64 (neg.f64 x) x))
(-.f64 (.f64 x x) (.f64 (neg.f64 y) y))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (.f64 y y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 y)) y))
(+.f64 (.f64 x x) (.f64 y y))
(.f64 (.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 x (.f64 #s(literal -1 binary64) (neg.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
(.f64 (.f64 (neg.f64 y) #s(literal -1 binary64)) y)
(.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (*.f64 (neg.f64 y) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 y) #s(literal 1 binary64)) (*.f64 (fabs.f64 y) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 y)) (*.f64 #s(literal 1 binary64) (neg.f64 y)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 y)) (neg.f64 y))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 y)) (*.f64 #s(literal 1 binary64) (fabs.f64 y)))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 y)) (fabs.f64 y))
(*.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 y)))
(*.f64 (neg.f64 (fabs.f64 y)) (neg.f64 (fabs.f64 y)))
(*.f64 (fabs.f64 (fabs.f64 y)) (fabs.f64 (fabs.f64 y)))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(.f64 (.f64 (neg.f64 y) y) #s(literal -1 binary64))
(.f64 (neg.f64 y) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(*.f64 (neg.f64 y) (neg.f64 y))
(.f64 (fabs.f64 y) (.f64 (fabs.f64 y) #s(literal 1 binary64)))
(*.f64 (fabs.f64 y) (fabs.f64 y))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 y) y))
(.f64 (.f64 y y) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 y y))
(.f64 y (.f64 #s(literal -1 binary64) (neg.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (fabs.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(/.f64 (.f64 (.f64 y y) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 y y)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(fabs.f64 (*.f64 y y))
(exp.f64 (fma.f64 (log.f64 y) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 y) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))))
y
#s(approx (sqrt (+ (* x x) (* y y))) y)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (fma.f64 (.f64 x (/.f64 x (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x) y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
#s(approx (+ (* x x) (* y y)) (fma.f64 y y (*.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (+ (* x x) (* y y))) x)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 y x) (/.f64 y x)) x))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) x x))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x x))
#s(approx (+ (* x x) (* y y)) (*.f64 x x))
#s(approx (+ (* x x) (* y y)) (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 y y) x) #s(literal 1/2 binary64) x))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (.f64 y y) x))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 y y) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (.f64 y y) x))
#s(approx (* y y) (*.f64 y y))
#s(approx y y)
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 6 binary64))))) y y))
#s(approx (+ (* x x) (* y y)) (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) (.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 y))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (neg.f64 y) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 6 binary64))))) y y)))

eval47.0ms (2.6%)

Memory: 18.6MiB live, 112.2MiB allocated; 5ms collecting garbage
Compiler: Compiled 4 246 to 818 computations (80.7% saved)

prune11.0ms (0.6%)

Memory

-22.3MiB live, 25.1MiB allocated; 1ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	427	4	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	428	4	432

Accuracy

100.0%

Counts

432 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	6.6%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 y x) (/.f64 y x)) x))
▶	98.7%	#s(approx (sqrt (+ (* x x) (* y y))) y)

Compiler

Compiled 41 to 27 computations (34.1% saved)

series13.0ms (0.7%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms collecting garbage

Counts

13 → 62

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 y))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* 1/2 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ 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)))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* 1/2 (/ (pow y 2) x))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)))
#s(approx (* x 1/2) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (/ y x) (/ y x)) #s(hole binary64 (/ (pow y 2) (pow x 2))))
#s(approx (/ y x) #s(hole binary64 (/ y x)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 y))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ y (* 1/2 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ 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)))))))
#s(approx (+ (* y y) (* x x)) #s(hole binary64 (pow y 2)))
#s(approx (+ (* y y) (* x x)) #s(hole binary64 (+ (pow x 2) (pow y 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 x))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 x))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (+ (* y y) (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* y y) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx y #s(hole binary64 y))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* (pow y 2) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (+ (* y y) (* x x)) #s(hole binary64 (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 y)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))))

Calls

6 calls:

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

rewrite243.0ms (13.1%)

Memory

-21.1MiB live, 220.9MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	1482
0	208	1262
1	903	1235
0	8682	1162

Stop Event

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

Counts

75 → 791

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* y y) (* x x))) y)
y
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) x))
(*.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)))) x) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1/8 binary64))) x) (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)))) (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64)))) (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))) (-.f64 x (.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) x))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (.f64 (neg.f64 x) x))) (neg.f64 (-.f64 (.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (.f64 x (-.f64 x (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x))))))
(/.f64 (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (.f64 (neg.f64 x) x)) (-.f64 (.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) x))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (pow.f64 (/.f64 y x) #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (.f64 x (-.f64 x (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 (neg.f64 y) x)) (/.f64 (neg.f64 y) x) x)
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (fabs.f64 (/.f64 y x))) (fabs.f64 (/.f64 y x)) x)
(fma.f64 (*.f64 x (pow.f64 (/.f64 y x) #s(literal 2 binary64))) #s(literal 1/2 binary64) x)
(fma.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) x) #s(literal 1/2 binary64) x)
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 y x)) (/.f64 y x) x)
(fma.f64 (/.f64 (neg.f64 y) x) (.f64 (/.f64 (neg.f64 y) x) (.f64 #s(literal 1/2 binary64) x)) x)
(fma.f64 (fabs.f64 (/.f64 y x)) (.f64 (fabs.f64 (/.f64 y x)) (.f64 #s(literal 1/2 binary64) x)) x)
(fma.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x x)
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) x)
(fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) x) x)
(fma.f64 (/.f64 y x) (.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) x)) x)
(fma.f64 #s(literal 1/2 binary64) (*.f64 x (pow.f64 (/.f64 y x) #s(literal 2 binary64))) x)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) x) x)
(fma.f64 x (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) x)))
(-.f64 x (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64))) x))
(-.f64 x (.f64 (neg.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 y x))) (/.f64 y x)))
(-.f64 x (.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) x)) (pow.f64 (/.f64 y x) #s(literal 2 binary64))))
(-.f64 x (.f64 (neg.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (.f64 (neg.f64 x) (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (.f64 x (-.f64 x (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 4 binary64))) (.f64 x (-.f64 x (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x))))))
(+.f64 (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) x)
(+.f64 x (.f64 (.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) x))
(.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (neg.f64 y) x)) (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 y) x)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (neg.f64 y) x)) (/.f64 (neg.f64 y) x))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 y x))) (*.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 y x))))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 y x))) (fabs.f64 (/.f64 y x)))
(*.f64 (/.f64 (neg.f64 y) (fabs.f64 x)) (/.f64 (neg.f64 y) (fabs.f64 x)))
(*.f64 (/.f64 (fabs.f64 y) (neg.f64 x)) (/.f64 (fabs.f64 y) (neg.f64 x)))
(*.f64 (/.f64 (fabs.f64 y) x) (/.f64 (fabs.f64 y) x))
(*.f64 (/.f64 y (fabs.f64 x)) (/.f64 y (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 (/.f64 y x))) (neg.f64 (fabs.f64 (/.f64 y x))))
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(hypot.f64 (fabs.f64 x) (fabs.f64 y))
(hypot.f64 (fabs.f64 x) y)
(hypot.f64 y (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(hypot.f64 y (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(hypot.f64 y (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 y (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(hypot.f64 y (neg.f64 (neg.f64 x)))
(hypot.f64 y (neg.f64 (fabs.f64 x)))
(hypot.f64 y (fabs.f64 (fabs.f64 x)))
(hypot.f64 y (exp.f64 (log.f64 x)))
(hypot.f64 y (neg.f64 x))
(hypot.f64 y (fabs.f64 x))
(hypot.f64 y x)
(hypot.f64 x (*.f64 #s(literal 1 binary64) (neg.f64 y)))
(hypot.f64 x (*.f64 #s(literal 1 binary64) (fabs.f64 y)))
(hypot.f64 x (*.f64 (neg.f64 y) #s(literal 1 binary64)))
(hypot.f64 x (*.f64 (fabs.f64 y) #s(literal 1 binary64)))
(hypot.f64 x (neg.f64 (neg.f64 y)))
(hypot.f64 x (neg.f64 (fabs.f64 y)))
(hypot.f64 x (fabs.f64 (fabs.f64 y)))
(hypot.f64 x (exp.f64 (log.f64 y)))
(hypot.f64 x (neg.f64 y))
(hypot.f64 x (fabs.f64 y))
(hypot.f64 x y)
(exp.f64 (.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* y y) (* x x))) y)
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 y #s(literal 3 binary64))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 (.f64 x 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)))) (fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y)))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64)))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (/.f64 (fma.f64 (.f64 y y) #s(literal 1/2 binary64) (.f64 x x)) x))
#s(approx (* x 1/2) (*.f64 #s(literal 1/2 binary64) x))
#s(approx x x)
#s(approx (* (/ y x) (/ y x)) (pow.f64 (/.f64 y x) #s(literal 2 binary64)))
#s(approx (/ y x) (/.f64 y x))
#s(approx (sqrt (+ (* y y) (* x x))) y)
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 y #s(literal 3 binary64))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 (.f64 x 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)))) (fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y)))
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (* y y) (* x x)) (fma.f64 y y (*.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx (sqrt (+ (* y y) (* x x))) x)
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) x))
#s(approx (sqrt (+ (* y y) (* x x))) (*.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) x))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1/16 binary64) (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) x x))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) x)
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) x))
#s(approx (sqrt (+ (* y y) (* x x))) x)
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) x))
#s(approx (sqrt (+ (* y y) (* x x))) (*.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) x))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1/16 binary64) (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) x x))
#s(approx (+ (* y y) (* x x)) (*.f64 x x))
#s(approx (+ (* y y) (* x x)) (fma.f64 x x (pow.f64 (*.f64 (/.f64 y x) x) #s(literal 2 binary64))))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 x))
#s(approx (sqrt (+ (* y y) (* x x))) (*.f64 (neg.f64 x) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* y y) (* x x))) (*.f64 (neg.f64 x) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 (fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1/16 binary64) (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) x x)))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64))))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 x))
#s(approx (sqrt (+ (* y y) (* x x))) (*.f64 (neg.f64 x) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* y y) (* x x))) (*.f64 (neg.f64 x) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 (fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1/16 binary64) (*.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) x x)))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (/.f64 (.f64 y y) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3 binary64)))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x)))
#s(approx y y)
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (/.f64 (.f64 y y) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3 binary64)))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x)))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64))) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 6 binary64))))) y y))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (.f64 (-.f64 (/.f64 x (.f64 y y)) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 y y)))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64))) y))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 6 binary64))))) y y))
#s(approx (+ (* y y) (* x x)) (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) (.f64 y y)))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 y))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (neg.f64 y) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 6 binary64))))) y y)))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 y))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (neg.f64 y) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 6 binary64))))) y y)))

eval63.0ms (3.4%)

Memory: 27.4MiB live, 119.4MiB allocated; 9ms collecting garbage
Compiler: Compiled 7 185 to 1 167 computations (83.8% saved)

prune11.0ms (0.6%)

Memory

-15.3MiB live, 31.7MiB allocated; 4ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	545	2	547
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	546	5	551

Accuracy

100.0%

Counts

551 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	6.7%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
▶	6.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64))))
✓	98.7%	#s(approx (sqrt (+ (* x x) (* y y))) y)

Compiler

Compiled 67 to 44 computations (34.3% saved)

series8.0ms (0.4%)

Memory

15.2MiB live, 15.2MiB allocated; 0ms collecting garbage

Counts

10 → 63

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 y))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* 1/2 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ 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)))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* 1/2 (/ (pow y 2) x))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)))
#s(approx (* (* (/ y x) y) 1/2) #s(hole binary64 (* 1/2 (/ (pow y 2) x))))
#s(approx (* (/ y x) y) #s(hole binary64 (/ (pow y 2) x)))
#s(approx (/ y x) #s(hole binary64 (/ y x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 y))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ y (* 1/2 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ 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)))))))
#s(approx (+ (* (* (/ y x) y) 1/2) x) #s(hole binary64 (* 1/2 (/ (pow y 2) x))))
#s(approx (+ (* (* (/ y x) y) 1/2) x) #s(hole binary64 (/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 x))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 x))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (+ (* (* (/ y x) y) 1/2) x) #s(hole binary64 x))
#s(approx (+ (* (* (/ y x) y) 1/2) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))))
#s(approx (+ (* (* (/ y x) y) 1/2) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (* (/ y x) y) 1/2) x) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) #s(hole binary64 (* (pow y 2) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (+ (* (* (/ y x) y) 1/2) x) #s(hole binary64 (* (pow y 2) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 y)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))))

Calls

6 calls:

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

rewrite152.0ms (8.2%)

Memory

25.0MiB live, 211.6MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	194	1676
0	201	1576
1	871	1572
0	8389	1261

Stop Event

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

Counts

73 → 155

Calls

Call 1

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

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

eval22.0ms (1.2%)

Memory: -16.4MiB live, 39.1MiB allocated; 6ms collecting garbage
Compiler: Compiled 4 494 to 541 computations (88% saved)

prune8.0ms (0.4%)

Memory

-32.2MiB live, 14.6MiB allocated; 3ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	0	0
Picked	1	1	2
Done	0	3	3
Total	167	5	172

Accuracy

100.0%

Counts

172 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	6.7%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) y x))
✓	6.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64))))
✓	98.7%	#s(approx (sqrt (+ (* x x) (* y y))) y)

Compiler

Compiled 67 to 44 computations (34.3% saved)

series6.0ms (0.3%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Counts

7 → 33

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 y))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ y (* 1/2 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ 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)))))))
#s(approx (+ (* (* (/ 1/2 x) y) y) x) #s(hole binary64 (* 1/2 (/ (pow y 2) x))))
#s(approx (+ (* (* (/ 1/2 x) y) y) x) #s(hole binary64 (/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)))
#s(approx (* (/ 1/2 x) y) #s(hole binary64 (* 1/2 (/ y x))))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 x))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (+ (* (* (/ 1/2 x) y) y) x) #s(hole binary64 x))
#s(approx (+ (* (* (/ 1/2 x) y) y) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))))
#s(approx (+ (* (* (/ 1/2 x) y) y) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (* (/ 1/2 x) y) y) x) #s(hole binary64 (+ x (* 1/2 (/ (pow y 2) x)))))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (+ (* (* (/ 1/2 x) y) y) x) #s(hole binary64 (* (pow y 2) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 y)))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))))
#s(approx (sqrt (+ (* y y) (* x x))) #s(hole binary64 (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))))

Calls

6 calls:

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

rewrite156.0ms (8.4%)

Memory

-5.7MiB live, 225.5MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	814
0	163	790
1	795	787
0	8077	636

Stop Event

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

Counts

40 → 98

Calls

Call 1

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

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

eval11.0ms (0.6%)

Memory: 27.9MiB live, 27.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 400 to 359 computations (85% saved)

prune5.0ms (0.3%)

Memory

13.6MiB live, 13.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	101	5	106

Accuracy

100.0%

Counts

106 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	6.7%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) y x))
✓	6.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (* x 1/2) (* (/ y x) (/ y x))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64))))
✓	98.7%	#s(approx (sqrt (+ (* x x) (* y y))) y)

Compiler

Compiled 180 to 82 computations (54.4% saved)

regimes17.0ms (0.9%)

Memory

-9.1MiB live, 37.5MiB allocated; 2ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

4.0ms	y
3.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes65.0ms (3.5%)

Memory

-18.3MiB live, 34.1MiB allocated; 70ms collecting garbage

Accuracy

Total -59.2b remaining (-7393.6%)

Threshold costs -59.2b (-7393.6%)

Counts

7 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) y)

Calls

6 calls:

53.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	y
2.0ms	x
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
98.7%	1	`(*.f64 y y)`
98.7%	1	`(*.f64 x x)`
98.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.7%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
98.7%	1	`x`
98.7%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

derivations71.0ms (3.8%)

Memory

-20.8MiB live, 77.9MiB allocated; 8ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess26.0ms (1.4%)

Memory: 10.0MiB live, 56.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 158 to 114 computations (27.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample581.0ms (31.3%)

explain94.0ms (5%)

preprocess19.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

series9.0ms (0.5%)

rewrite216.0ms (11.7%)

eval47.0ms (2.6%)

prune11.0ms (0.6%)

series13.0ms (0.7%)

rewrite243.0ms (13.1%)

eval63.0ms (3.4%)

prune11.0ms (0.6%)

series8.0ms (0.4%)

rewrite152.0ms (8.2%)

eval22.0ms (1.2%)

prune8.0ms (0.4%)

series6.0ms (0.3%)

rewrite156.0ms (8.4%)

eval11.0ms (0.6%)

prune5.0ms (0.3%)

regimes17.0ms (0.9%)

regimes65.0ms (3.5%)

derivations71.0ms (3.8%)

preprocess26.0ms (1.4%)

end0.0ms (0%)

Profiling