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)

sample668.0ms (29.8%)

Memory

16.5MiB live, 1 099.6MiB allocated; 289ms collecting garbage

Samples

455.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 168.0ms

ival-hypot: 163.0ms (97% of total)

ival-assert: 3.0ms (1.8% of total)

adjust: 2.0ms (1.2% of total)

Bogosity

explain148.0ms (6.6%)

Memory

49.9MiB live, 230.2MiB allocated; 91ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
132	-	2	(3.556163806792005e-236 -1.637048586754833e-155)	`(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	116	0
↳	`(*.f64 y y)`	overflow	70
↳	`(*.f64 x x)`	overflow	62
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	116
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	14	0
↳	`(*.f64 y y)`	underflow	54
↳	`(*.f64 x x)`	underflow	61
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	14

Confusion

	Predicted +	Predicted -
+	130	2
-	0	124

Precision

1.0

Recall

0.9848484848484849

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	130	0	2
-	0	0	124

Precision?

1.0

Recall?

0.9848484848484849

Freqs

test

number	freq
0	126
1	130

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

76.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 38.0ms (76.6% of total)

ival-hypot: 9.0ms (18.1% of total)

ival-add: 2.0ms (4% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess32.0ms (1.4%)

Memory

-5.5MiB live, 39.0MiB allocated; 31ms 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

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

series6.0ms (0.3%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms 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
1.0ms	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	x	@	0	((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	y	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) x (* y y) y)

rewrite275.0ms (12.3%)

Memory

-27.5MiB live, 247.2MiB allocated; 111ms 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)))
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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)))

eval93.0ms (4.1%)

Memory: 26.2MiB live, 81.5MiB allocated; 15ms collecting garbage
Compiler: Compiled 4 246 to 818 computations (80.7% saved)

prune36.0ms (1.6%)

Memory

-15.0MiB live, 30.5MiB allocated; 7ms 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)
▶	52.7%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	6.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 y x) (/.f64 y x)) x))
▶	99.0%	#s(approx (sqrt (+ (* x x) (* y y))) y)

Compiler

Compiled 41 to 27 computations (34.1% saved)

series22.0ms (1%)

Memory

-17.9MiB live, 28.4MiB allocated; 4ms 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
10.0ms	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))))
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))))

rewrite359.0ms (16%)

Memory

15.1MiB live, 318.6MiB allocated; 233ms 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))
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(hypot.f64 (fabs.f64 x) (neg.f64 y))
(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)))

eval104.0ms (4.6%)

Memory: -20.4MiB live, 112.4MiB allocated; 25ms collecting garbage
Compiler: Compiled 7 185 to 1 167 computations (83.8% saved)

prune8.0ms (0.4%)

Memory

37.6MiB live, 37.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Accuracy

100.0%

Counts

551 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	52.7%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	6.5%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
✓	99.0%	#s(approx (sqrt (+ (* x x) (* y y))) y)

Compiler

Compiled 37 to 26 computations (29.7% saved)

series11.0ms (0.5%)

Memory

-38.1MiB live, 17.4MiB allocated; 10ms collecting garbage

Counts

7 → 33

Calls

Call 1

Inputs
#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)
(*.f64 (/.f64 y x) y)
(/.f64 y x)
y
x
#s(literal 1/2 binary64)

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 (+ (* (* (/ 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 (* (/ 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 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 (+ (* 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 (+ (* 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 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 (+ (* (* (/ y x) y) 1/2) 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
4.0ms	y	@	0	((sqrt (+ (* y y) (* x x))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) y x 1/2)
2.0ms	y	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) y x 1/2)
1.0ms	x	@	-inf	((sqrt (+ (* y y) (* x x))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) y x 1/2)
1.0ms	y	@	-inf	((sqrt (+ (* y y) (* x x))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) y x 1/2)
1.0ms	x	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) y x 1/2)

rewrite245.0ms (11%)

Memory

22.9MiB live, 298.0MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	814
0	161	789
1	791	787
0	7945	636

Stop Event

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

Counts

40 → 99

Calls

Call 1

Inputs
#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)
(*.f64 (/.f64 y x) y)
(/.f64 y x)
y
x
#s(literal 1/2 binary64)
#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 (* (/ 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 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 (+ (* 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 (+ (* 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 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 (+ (* (* (/ y x) y) 1/2) 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 (/.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 (/.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) (/.f64 y x)) y 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 (pow.f64 x #s(literal -1 binary64)) (.f64 y 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 (/.f64 y x) y) x)
(fma.f64 y (*.f64 y (/.f64 #s(literal 1/2 binary64) x)) x)
(fma.f64 y (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) 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 (neg.f64 (/.f64 y 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)))
(*.f64 (neg.f64 y) (/.f64 (neg.f64 y) 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 (/.f64 y x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 y (pow.f64 x #s(literal -1 binary64)))
(/.f64 (/.f64 (neg.f64 y) #s(literal -1 binary64)) x)
(/.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 y x)
(neg.f64 (/.f64 y (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 y) x))
y
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 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 (+ (* (* (/ 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 (* (/ y x) y) (*.f64 (/.f64 y x) y))
#s(approx (/ y x) (/.f64 y 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 x) y) 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 x) y) 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 x) y) (/.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 (+ (* (* (/ y x) y) 1/2) x) x)
#s(approx (+ (* (* (/ y x) y) 1/2) x) (.f64 (fma.f64 (/.f64 (.f64 (/.f64 y x) y) 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 x) y) 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 x) y) 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 x) y) (/.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 (+ (* (* (/ y x) y) 1/2) x) (.f64 (neg.f64 x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (/.f64 y x) y) x) #s(literal -1 binary64))))
#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 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 (+ (* (* (/ y x) y) 1/2) x) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) 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 (+ (* (* (/ 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 (+ (* 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 (0.5%)

Memory: 27.4MiB live, 27.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 438 to 372 computations (84.7% saved)

prune8.0ms (0.4%)

Memory

-32.4MiB live, 12.3MiB allocated; 9ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	102	4	106

Accuracy

100.0%

Counts

106 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	52.7%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	6.5%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
✓	99.0%	#s(approx (sqrt (+ (* x x) (* y y))) y)

Compiler

Compiled 103 to 51 computations (50.5% saved)

regimes13.0ms (0.6%)

Memory

32.2MiB live, 32.2MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

2.0ms	y
2.0ms	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)

regimes24.0ms (1.1%)

Memory

-27.2MiB live, 32.1MiB allocated; 27ms collecting garbage

Accuracy

Total -59.4b remaining (-9351.4%)

Threshold costs -59.4b (-9351.4%)

Counts

5 → 1

Calls

Call 1

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

15.0ms	x
2.0ms	y
2.0ms	(*.f64 y y)
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.0%	1	`(*.f64 y y)`
99.0%	1	`(*.f64 x x)`
99.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.0%	1	`x`
99.0%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify14.0ms (0.6%)

Memory

-12.8MiB live, 33.3MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	58	13
3	115	13
4	152	13

Stop Event

1×

saturated

Calls

Call 1

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

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

derivations119.0ms (5.3%)

Memory

21.3MiB live, 65.7MiB allocated; 8ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess41.0ms (1.8%)

Memory

-4.2MiB live, 40.2MiB allocated; 10ms collecting garbage

Remove

(sort x y)

(abs y)

(abs x)

Compiler

Compiled 98 to 72 computations (26.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample668.0ms (29.8%)

explain148.0ms (6.6%)

preprocess32.0ms (1.4%)

eval0.0ms (0%)

prune0.0ms (0%)

series6.0ms (0.3%)

rewrite275.0ms (12.3%)

eval93.0ms (4.1%)

prune36.0ms (1.6%)

series22.0ms (1%)

rewrite359.0ms (16%)

eval104.0ms (4.6%)

prune8.0ms (0.4%)

series11.0ms (0.5%)

rewrite245.0ms (11%)

eval11.0ms (0.5%)

prune8.0ms (0.4%)

regimes13.0ms (0.6%)

regimes24.0ms (1.1%)

simplify14.0ms (0.6%)

derivations119.0ms (5.3%)

preprocess41.0ms (1.8%)

end0.0ms (0%)

Profiling