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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

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)

sample994.0ms (4.9%)

Memory

-1.2MiB live, 595.7MiB allocated

Samples

706.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 394.0ms

ival-hypot: 384.0ms (97.5% of total)

ival-true: 6.0ms (1.5% of total)

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

Bogosity

explain137.0ms (0.7%)

Memory

-3.8MiB live, 71.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
133	-	-	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	-	`y`
0	-	-	`(*.f64 y y)`
0	-	-	`(*.f64 x x)`
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	117	0
↳	`(*.f64 y y)`	overflow	64
↳	`(*.f64 x x)`	overflow	72
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	117
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	16	0
↳	`(*.f64 y y)`	underflow	60
↳	`(*.f64 x x)`	underflow	64
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	16

Confusion

	Predicted +	Predicted -
+	133	0
-	0	123

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	0
-	0	0	123

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

71.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-hypot: 8.0ms (44.1% of total)

ival-mult: 7.0ms (38.6% of total)

ival-add: 2.0ms (11% of total)

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

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

preprocess16.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	35	42
2	77	42
3	145	42
4	206	42
5	219	42
6	221	42
0	6	8
0	10	8
1	11	8
0	11	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 y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	1	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	4	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	11	23
0	11	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

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
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(hypot.f64 y x)
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y

localize29.0ms (0.1%)

Memory

-5.8MiB live, 30.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	30.978688180341347	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

23.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 11.0ms (67% of total)

ival-hypot: 4.0ms (24.4% of total)

ival-add: 1.0ms (6.1% of total)

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

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

series5.0ms (0%)

Memory

11.3MiB live, 11.3MiB allocated

Counts

4 → 27

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* 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)))))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -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))))))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ 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)))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* 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)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -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	@	0	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))

simplify384.0ms (1.9%)

Memory

2.1MiB live, 237.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	429
1	296	429
2	958	427
3	3724	393
4	6463	391
0	8400	354

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 25

Calls

Call 1

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

rewrite187.0ms (0.9%)

Memory

-0.0MiB live, 234.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1800	21
0	8651	15

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

Outputs
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (hypot.f64 y x))
(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
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(-.f64 (/.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))))) (/.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 y #s(literal 8 binary64)) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (-.f64 x y) (+.f64 y x))) (/.f64 (/.f64 (pow.f64 y #s(literal 8 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (-.f64 x y) (+.f64 y x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))) (.f64 (-.f64 x y) (+.f64 y x))) (/.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))) (.f64 (-.f64 x y) (+.f64 y x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 (-.f64 x y) (+.f64 y x)))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (.f64 (-.f64 x y) (+.f64 y x)))))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (-.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (-.f64 y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))
(exp.f64 (.f64 (neg.f64 (log.f64 (fma.f64 y y (.f64 x x)))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (fma.f64 y y (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
(+.f64 (.f64 y y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 y y)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval76.0ms (0.4%)

Memory: -17.3MiB live, 71.4MiB allocated
Compiler: Compiled 7 430 to 981 computations (86.8% saved)

prune6.0ms (0%)

Memory

20.3MiB live, 20.3MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	260	6	266
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	261	6	267

Accuracy

100.0%

Counts

267 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	51.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	51.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
	92.6%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	6.5%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
▶	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 134 to 92 computations (31.3% saved)

simplify77.0ms (0.4%)

Memory

-17.0MiB live, 58.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	94
0	30	82
1	42	82
2	54	82
3	60	82
4	65	82
5	72	82
6	87	82
7	136	82
8	204	82
9	392	82
10	744	82
11	1482	82
12	1670	82
13	1735	82
14	1759	82
15	1771	82
16	1843	82
17	2334	82
0	2334	82

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize53.0ms (0.3%)

Memory

-13.3MiB live, 70.6MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.12890625	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
accuracy	59.855412596087916	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
accuracy	0.0	(fma.f64 y y (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	30.978688180341347	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0.0	(*.f64 y y)
accuracy	0.2961446204916198	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	30.978688180341347	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0.0	(neg.f64 x)
accuracy	62.814339309551904	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0.0	(hypot.f64 y x)

Samples

36.0ms

256×

valid

Compiler

Compiled 88 to 16 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-hypot: 8.0ms (31.7% of total)

ival-div: 7.0ms (27.8% of total)

ival-mult: 6.0ms (23.8% of total)

ival-add: 3.0ms (11.9% of total)

ival-neg: 1.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0%)

Memory

24.2MiB live, 24.2MiB allocated

Counts

13 → 33

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* -1 x)
(pow y 2)
(+ (pow x 2) (pow y 2))
(pow x 2)
(* 1/2 (/ (pow y 2) x))
(/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)
(/ y x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* 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)))))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -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))))))))
(* -1 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ 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)))))
(* 1/2 y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* 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)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -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
2.0ms	y	@	inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
2.0ms	y	@	-inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
2.0ms	x	@	0	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
1.0ms	x	@	-inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
1.0ms	x	@	inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))

simplify251.0ms (1.2%)

Memory

1.3MiB live, 200.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	479
1	326	479
2	1027	477
3	4007	435
4	7560	435
0	8303	397

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

rewrite209.0ms (1%)

Memory

-6.8MiB live, 143.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	85
0	30	73
1	87	73
2	562	73
3	7012	73
0	8552	73

Stop Event

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

Counts

13 → 368

Calls

Call 1

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

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

eval74.0ms (0.4%)

Memory: 3.6MiB live, 40.8MiB allocated
Compiler: Compiled 9 401 to 1 209 computations (87.1% saved)

prune8.0ms (0%)

Memory

17.3MiB live, 17.3MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	353	3	356
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	354	8	362

Accuracy

100.0%

Counts

362 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	51.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	51.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	92.6%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
✓	6.5%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
▶	6.5%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
▶	3.3%	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))))
✓	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 125 to 81 computations (35.2% saved)

simplify203.0ms (1%)

Memory

-12.3MiB live, 81.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
cost-diff	3	(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
cost-diff	0	(fma.f64 (/.f64 y x) (*.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))))
cost-diff	2	(.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x))))
cost-diff	19	(.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	228
0	55	219
1	102	219
2	233	216
3	730	210
4	2367	158
5	7298	158
0	8322	143

Stop Event

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

Calls

Call 1

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

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

localize191.0ms (0.9%)

Memory

5.7MiB live, 80.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	(*.f64 x x)
accuracy	0.21466786629304085	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	4.622495535351878	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
accuracy	0.0	(neg.f64 y)
accuracy	0.12890625	(fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x)
accuracy	0.2265625	(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
accuracy	59.855412596087916	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
accuracy	0.1328125	(fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x))
accuracy	0.8786654530644729	(/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x))
accuracy	30.445634372946564	(.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))
accuracy	59.855412596087916	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))))

Samples

174.0ms

256×

valid

Compiler

Compiled 190 to 32 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 160.0ms

ival-div: 76.0ms (47.6% of total)

ival-neg: 53.0ms (33.2% of total)

ival-mult: 16.0ms (10% of total)

ival-hypot: 8.0ms (5% of total)

ival-add: 5.0ms (3.1% of total)

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

exact: 0.0ms (0% of total)

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

series51.0ms (0.3%)

Memory

-9.1MiB live, 33.6MiB allocated

Counts

15 → 63

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	x	@	0	((* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)) (neg y))
6.0ms	y	@	0	((* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)) (neg y))
4.0ms	x	@	-inf	((* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)) (neg y))
4.0ms	y	@	inf	((* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)) (neg y))
3.0ms	x	@	inf	((* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)) (neg y))

simplify336.0ms (1.6%)

Memory

-7.4MiB live, 153.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	280	1288
1	828	1193
2	2825	1115
0	8581	1031

Stop Event

1×	iter limit
1×	node limit

Counts

63 → 61

Calls

Call 1

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

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

rewrite14.2s (69.7%)

Memory

21.9MiB live, 135.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	187
0	55	181
1	210	165
2	1656	132
0	8805	117

Stop Event

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

Counts

15 → 1 626

Calls

Call 1

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

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

eval505.0ms (2.5%)

Memory: -13.8MiB live, 191.8MiB allocated
Compiler: Compiled 52 007 to 4 447 computations (91.4% saved)

prune70.0ms (0.3%)

Memory

-15.2MiB live, 63.1MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1 038	3	1 041
Fresh	0	0	0
Picked	3	0	3
Done	1	4	5
Total	1 042	7	1 049

Accuracy

100.0%

Counts

1 049 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	51.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	51.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.7%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
▶	3.9%	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
▶	50.4%	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x)))
✓	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify287.0ms (1.4%)

Memory

8.3MiB live, 160.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
cost-diff	0	(/.f64 (*.f64 x x) y)
cost-diff	0	(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x))
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x)))
cost-diff	2	(.f64 (.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x)
cost-diff	3	(*.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	199
0	38	200
1	58	200
2	77	200
3	104	200
4	135	200
5	157	178
6	176	178
7	560	178
8	2360	178
9	2600	178
10	2806	178
11	3040	178
12	3362	178
13	3713	178
14	4145	178
15	4692	178
16	4923	178
17	5055	178
18	5171	178
19	5253	178
20	5335	178
21	5934	178
22	6892	178
23	7287	178
24	7433	178
25	7508	178
26	7581	178
27	7697	178
28	7780	178
29	7862	178
30	7944	178
0	8008	162

Stop Event

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

Calls

Call 1

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

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

localize65.0ms (0.3%)

Memory

-12.4MiB live, 110.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.18359375	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.21466786629304085	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
accuracy	0.015625	(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
accuracy	0.21466786629304085	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
accuracy	7.501426045470444	(/.f64 (*.f64 x x) y)
accuracy	61.52834355869554	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
accuracy	0.1015625	(/.f64 (/.f64 y x) x)
accuracy	0.21466786629304085	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x)))
accuracy	14.585081741049656	(.f64 (.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x)
accuracy	16.55058704790987	(*.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x)

Samples

45.0ms

256×

valid

Compiler

Compiled 129 to 20 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 12.0ms (45.8% of total)

ival-div: 6.0ms (22.9% of total)

ival-hypot: 4.0ms (15.3% of total)

ival-add: 3.0ms (11.5% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.1%)

Memory

23.9MiB live, 23.9MiB allocated

Counts

13 → 37

Calls

Call 1

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

Outputs
(/ y x)
(/ (+ y (* 1/2 (/ (pow x 2) y))) x)
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* 1/2 (/ (pow x 2) y))
(/ (pow x 2) y)
(* 1/2 (/ x y))
(/ y (pow x 2))
(* x (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* 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)))))))
(* -1 (* x (- (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y)))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -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))))))))
(/ (+ (* 1/2 x) (/ (pow y 2) x)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ 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)))))
(/ 1/2 y)
(* y (+ (* 1/2 (/ x (pow y 2))) (/ 1 x)))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* 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)))))))
(* -1 (* y (- (* -1/2 (/ x (pow y 2))) (/ 1 x))))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -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
2.0ms	y	@	-inf	((* (+ (/ (/ y x) x) (/ 1/2 y)) x) (* (* (+ (/ (/ y x) x) (/ 1/2 y)) x) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (/ (/ y x) x))
2.0ms	y	@	0	((* (+ (/ (/ y x) x) (/ 1/2 y)) x) (* (* (+ (/ (/ y x) x) (/ 1/2 y)) x) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (/ (/ y x) x))
2.0ms	y	@	inf	((* (+ (/ (/ y x) x) (/ 1/2 y)) x) (* (* (+ (/ (/ y x) x) (/ 1/2 y)) x) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (/ (/ y x) x))
2.0ms	x	@	inf	((* (+ (/ (/ y x) x) (/ 1/2 y)) x) (* (* (+ (/ (/ y x) x) (/ 1/2 y)) x) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (/ (/ y x) x))
2.0ms	x	@	-inf	((* (+ (/ (/ y x) x) (/ 1/2 y)) x) (* (* (+ (/ (/ y x) x) (/ 1/2 y)) x) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (/ (/ y x) x))

simplify199.0ms (1%)

Memory

-5.9MiB live, 189.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	525
1	363	525
2	1155	523
3	4293	479
4	7590	479
0	8415	438

Stop Event

1×	iter limit
1×	node limit

Counts

37 → 35

Calls

Call 1

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

rewrite245.0ms (1.2%)

Memory

-19.6MiB live, 267.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	172
0	38	168
1	140	168
2	1057	168
0	8518	149

Stop Event

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

Counts

13 → 336

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 (/.f64 y x) y)) y) (/.f64 x x))
(.f64 (/.f64 x x) (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 (/.f64 y x) y)) y))
(.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 (/.f64 y x) y)) x) (/.f64 x y))
(.f64 (.f64 (-.f64 (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64))) x) (pow.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1/2 binary64) y)) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64))) x) (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 (/.f64 y x) y)) x) (pow.f64 (.f64 x y) #s(literal -1 binary64)))
(.f64 (.f64 x (-.f64 (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)))) (pow.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1/2 binary64) y)) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 (pow.f64 y #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 3 binary64)))) (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x)) (pow.f64 (/.f64 (/.f64 y x) x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 #s(literal 1/2 binary64) x (.f64 (/.f64 y x) y))) (pow.f64 (.f64 x y) #s(literal -1 binary64)))
(.f64 (/.f64 x y) (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 (/.f64 y x) y)) x))
(*.f64 (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)) x)
(*.f64 x (fma.f64 y (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) y)))
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(exp.f64 (.f64 (log.f64 (.f64 y #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (neg.f64 y) x))
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) x))
(*.f64 (pow.f64 (/.f64 x (neg.f64 y)) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (neg.f64 y) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64)))
(*.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 y x) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)))
(.f64 (.f64 y #s(literal 1 binary64)) (pow.f64 x #s(literal -2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (.f64 x x) y))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 y x))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 y x) x))
(.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) x)))
(*.f64 (/.f64 (neg.f64 y) x) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 y x) x) #s(literal 1 binary64))
(*.f64 (/.f64 y x) (pow.f64 x #s(literal -1 binary64)))
(*.f64 y (pow.f64 x #s(literal -2 binary64)))
(pow.f64 (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 y x) x) #s(literal 1 binary64))
(/.f64 (neg.f64 (.f64 (neg.f64 y) #s(literal 1 binary64))) (neg.f64 (.f64 (neg.f64 x) x)))
(/.f64 (neg.f64 (*.f64 (/.f64 y x) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (.f64 y #s(literal 1 binary64))) (.f64 (neg.f64 x) x))
(/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 x y)))
(/.f64 (neg.f64 (/.f64 (/.f64 y x) x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 y)) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 (*.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(/.f64 (.f64 (neg.f64 y) #s(literal 1 binary64)) (.f64 (neg.f64 x) x))
(/.f64 (.f64 y #s(literal 1 binary64)) (.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) y)))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (/.f64 y x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 x) x) (.f64 (neg.f64 y) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 y #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) y))
(/.f64 (neg.f64 y) (*.f64 (neg.f64 x) x))
(/.f64 (/.f64 (neg.f64 y) x) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 (neg.f64 y) x) (neg.f64 x))
(/.f64 (/.f64 (/.f64 y x) x) #s(literal 1 binary64))
(/.f64 (/.f64 y x) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 y x) x)
(/.f64 y (*.f64 x x))
(neg.f64 (/.f64 (/.f64 (neg.f64 y) x) x))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) x)) (/.f64 y (.f64 (neg.f64 x) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (/.f64 (neg.f64 y) x) x))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) y)) #s(literal -1 binary64)))

eval50.0ms (0.2%)

Memory: 0.9MiB live, 123.1MiB allocated
Compiler: Compiled 12 016 to 1 679 computations (86% saved)

prune12.0ms (0.1%)

Memory

-1.6MiB live, 37.0MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	379	1	380
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	380	7	387

Accuracy

100.0%

Counts

387 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	51.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	51.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.7%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	50.4%	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (+.f64 (/.f64 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x)))
	76.4%	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))
✓	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 379 to 142 computations (62.5% saved)

regimes29.0ms (0.1%)

Memory

24.5MiB live, 62.8MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
5.0ms	y
5.0ms	x
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes30.0ms (0.1%)

Memory

-16.3MiB live, 63.8MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

6 calls:

8.0ms	x
5.0ms	(*.f64 x x)
4.0ms	y
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`y`
99.7%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.7%	1	`(*.f64 x x)`
99.7%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes17.0ms (0.1%)

Memory

12.4MiB live, 51.8MiB allocated

Counts

7 → 2

Calls

Call 1

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

Outputs

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

#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (*.f64 #s(approx (* (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
99.5%	2	`x`
92.6%	1	`y`
92.6%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
92.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.5%	2	`(*.f64 x x)`
92.6%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes16.0ms (0.1%)

Memory

-9.3MiB live, 30.0MiB allocated

Counts

6 → 3

Calls

Call 1

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

Outputs

#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (*.f64 #s(approx (* (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))

(sqrt.f64 (fma.f64 y y (*.f64 x x)))

#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (*.f64 #s(approx (* (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
80.3%	3	`y`
80.3%	3	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
80.3%	3	`(+.f64 (.f64 x x) (.f64 y y))`
80.3%	3	`(*.f64 y y)`
76.4%	1	`x`
76.4%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes8.0ms (0%)

Memory

14.5MiB live, 14.5MiB allocated

Counts

4 → 3

Calls

Call 1

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

Outputs

#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (*.f64 #s(approx (* (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))

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

#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (*.f64 #s(approx (* (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
79.8%	3	`y`
79.8%	3	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
79.8%	3	`(+.f64 (.f64 x x) (.f64 y y))`
79.8%	3	`(*.f64 y y)`

Compiler

Compiled 19 to 16 computations (15.8% saved)

regimes33.0ms (0.2%)

Memory

-23.0MiB live, 15.9MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

6 calls:

26.0ms	x
1.0ms	y
1.0ms	(+.f64 (.f64 x x) (.f64 y y))
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
51.1%	1	`x`
51.1%	1	`(*.f64 x x)`
51.1%	1	`y`
51.1%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
51.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
51.1%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes7.0ms (0%)

Memory

14.8MiB live, 14.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
1.9%	1	`x`
1.9%	1	`(*.f64 x x)`
1.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
1.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
1.9%	1	`(*.f64 y y)`
1.9%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.7568119885339482e+175	2.7457217222756758e+178

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	4.094254565971726e+300	2.5231032867652662e+306
0.0ms	0.0	7.784033696149603e-293

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	4.094254565971726e+300	2.5231032867652662e+306
0.0ms	0.0	7.784033696149603e-293

Compiler

Compiled 11 to 11 computations (0% saved)

simplify56.0ms (0.3%)

Memory

-13.9MiB live, 31.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	47	219
1	66	219
2	87	219
3	107	219
4	123	219
5	134	213
6	141	213
7	350	213
8	2002	213
9	3731	213
10	6865	213

Stop Event

1×	node limit

Calls

Call 1

Inputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
(if (<=.f64 (.f64 x x) #s(literal 19999999999999998743069049246737528200546615119793746550412501356903849205370206764075153567638181693469097644589800066324224103680915737659228242480356123926769783926845079552 binary64)) #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y)) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))))
(if (<=.f64 (.f64 y y) #s(literal 0 binary64)) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))) (if (<=.f64 (.f64 y y) #s(literal 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800 binary64)) (sqrt.f64 (fma.f64 y y (.f64 x x))) #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))))
(if (<=.f64 (.f64 y y) #s(literal 0 binary64)) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))) (if (<=.f64 (.f64 y y) #s(literal 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800 binary64)) (sqrt.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y))) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Outputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
(if (<=.f64 (.f64 x x) #s(literal 19999999999999998743069049246737528200546615119793746550412501356903849205370206764075153567638181693469097644589800066324224103680915737659228242480356123926769783926845079552 binary64)) #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y)) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))))
(if (<=.f64 (.f64 x x) #s(literal 19999999999999998743069049246737528200546615119793746550412501356903849205370206764075153567638181693469097644589800066324224103680915737659228242480356123926769783926845079552 binary64)) #s(approx (sqrt (+ ( y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y)) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))))
(if (<=.f64 (.f64 y y) #s(literal 0 binary64)) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))) (if (<=.f64 (.f64 y y) #s(literal 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800 binary64)) (sqrt.f64 (fma.f64 y y (.f64 x x))) #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))))
(if (or (<=.f64 (.f64 y y) #s(literal 0 binary64)) (not (<=.f64 (.f64 y y) #s(literal 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800 binary64)))) #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))) (sqrt.f64 (fma.f64 y y (*.f64 x x))))
(if (<=.f64 (.f64 y y) #s(literal 0 binary64)) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))) (if (<=.f64 (.f64 y y) #s(literal 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800 binary64)) (sqrt.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y))) #s(approx (sqrt (+ ( y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x)))))
(if (or (<=.f64 (.f64 y y) #s(literal 0 binary64)) (not (<=.f64 (.f64 y y) #s(literal 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800 binary64)))) #s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 #s(approx ( (+ (/ (/ y x) x) (/ 1/2 y)) x) (/.f64 y x)) x))) (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
#s(approx (sqrt (+ (* y y) (* x x))) (neg.f64 x))

soundness1.2s (5.7%)

Memory

18.1MiB live, 764.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	280	1288
1	828	1193
2	2825	1115
0	8581	1031
0	104	429
1	296	429
2	958	427
3	3724	393
4	6463	391
0	8400	354
0	117	479
1	326	479
2	1027	477
3	4007	435
4	7560	435
0	8303	397
0	131	525
1	363	525
2	1155	523
3	4293	479
4	7590	479
0	8415	438
0	32	187
0	55	181
1	210	165
2	1656	132
0	8805	117
0	6	21
0	10	21
1	29	21
2	196	21
3	1800	21
0	8651	15

Stop Event

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

Compiler

Compiled 356 to 154 computations (56.7% saved)

preprocess78.0ms (0.4%)

Memory

-10.1MiB live, 109.6MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 528 to 168 computations (68.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample994.0ms (4.9%)

explain137.0ms (0.7%)

preprocess16.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize29.0ms (0.1%)

series5.0ms (0%)

simplify384.0ms (1.9%)

rewrite187.0ms (0.9%)

eval76.0ms (0.4%)

prune6.0ms (0%)

simplify77.0ms (0.4%)

localize53.0ms (0.3%)

series9.0ms (0%)

simplify251.0ms (1.2%)

rewrite209.0ms (1%)

eval74.0ms (0.4%)

prune8.0ms (0%)

simplify203.0ms (1%)

localize191.0ms (0.9%)

series51.0ms (0.3%)

simplify336.0ms (1.6%)

rewrite14.2s (69.7%)

eval505.0ms (2.5%)

prune70.0ms (0.3%)

simplify287.0ms (1.4%)

localize65.0ms (0.3%)

series13.0ms (0.1%)

simplify199.0ms (1%)

rewrite245.0ms (1.2%)

eval50.0ms (0.2%)

prune12.0ms (0.1%)

regimes29.0ms (0.1%)

regimes30.0ms (0.1%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes8.0ms (0%)

regimes33.0ms (0.2%)

regimes7.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify56.0ms (0.3%)

soundness1.2s (5.7%)

preprocess78.0ms (0.4%)

end0.0ms (0%)

Profiling