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

0.3MiB live, 0.3MiB 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)

sample802.0ms (18.3%)

Memory

20.8MiB live, 611.7MiB allocated

Samples

489.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

ival-hypot: 159.0ms (94.2% of total)

ival-true: 7.0ms (4.1% of total)

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

Bogosity

explain196.0ms (4.5%)

Memory

12.7MiB live, 133.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
130	-	2	(-1.329640433085963e-281 -5.04337311100072e-161)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	oflow-rescue	112	0
↳	`(*.f64 y y)`	overflow	66
↳	`(*.f64 x x)`	overflow	60
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	112
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	16	0
↳	`(*.f64 y y)`	underflow	54
↳	`(*.f64 x x)`	underflow	62
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	16

Confusion

	Predicted +	Predicted -
+	128	2
-	0	126

Precision

1.0

Recall

0.9846153846153847

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	2
-	0	0	126

Precision?

1.0

Recall?

0.9846153846153847

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

132.0ms

512×

valid

Compiler

Compiled 81 to 28 computations (65.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-mult: 105.0ms (89.9% of total)

ival-hypot: 9.0ms (7.7% of total)

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

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

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

preprocess369.0ms (8.4%)

Memory

-21.1MiB live, 138.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	56	42
2	135	42
3	368	42
4	1093	42
5	1477	42
6	1876	42
7	3977	42
8	4593	42
9	5063	42
10	5589	42
11	5979	42
12	6431	42
0	6	8
0	10	8
1	23	8
2	71	8
3	246	8
4	874	8
5	1323	8
6	1694	8
7	3601	8
8	4187	8
9	4633	8
10	5175	8
11	6755	8
12	7895	8
0	8003	3

Stop Event

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

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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify116.0ms (2.7%)

Memory

21.7MiB live, 21.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-5120	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	23	23
2	71	23
3	246	23
4	874	23
5	1323	23
6	1694	23
7	3601	23
8	4187	23
9	4633	23
10	5175	23
11	6755	23
12	7895	23
0	8003	17

Stop Event

1×	iter limit
1×	node limit
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

localize40.0ms (0.9%)

Memory

-15.0MiB live, 22.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (.f64 x x) (.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	30.118028706242477	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

35.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 23.0ms (80.2% of total)

ival-hypot: 4.0ms (13.9% of total)

ival-add: 1.0ms (3.5% of total)

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

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

series5.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

4 → 27

Calls

Call 1

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

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

simplify330.0ms (7.6%)

Memory

9.9MiB live, 251.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	441
1	327	441
2	1249	437
3	6500	435
0	8044	400

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 25

Calls

Call 1

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

rewrite124.0ms (2.8%)

Memory

-27.0MiB live, 171.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	41	21
2	371	21
3	6127	21
0	8068	14

Stop Event

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

Counts

4 → 326

Calls

Call 1

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

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

eval86.0ms (2%)

Memory: 14.6MiB live, 91.5MiB allocated
Compiler: Compiled 5 852 to 984 computations (83.2% saved)

prune10.0ms (0.2%)

Memory

-13.0MiB live, 24.9MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	346	5	351
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	347	5	352

Accuracy

100.0%

Counts

352 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	52.9%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	52.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	94.5%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 100 to 70 computations (30% saved)

simplify206.0ms (4.7%)

Memory

15.6MiB live, 147.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 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 (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
cost-diff	-5120	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(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	19	94
0	28	82
1	52	82
2	139	82
3	490	82
4	1807	82
5	3295	82
6	3819	82
7	5776	82
8	6368	82
9	6825	82
10	7305	82
0	8270	82

Stop Event

1×	iter limit
1×	node limit
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 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
(hypot.f64 y x)
(hypot.f64 x y)
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 x y)
(fma.f64 y y (*.f64 x x))
(fma.f64 x x (*.f64 y y))
y
(*.f64 x x)
x
#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

localize50.0ms (1.1%)

Memory

-26.4MiB live, 47.0MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0	(*.f64 x x)
accuracy	0.37886888894080134	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	3.4684300729485984	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	30.118028706242477	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0	(*.f64 y y)
accuracy	0.3421827969506583	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	30.118028706242477	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(neg.f64 x)
accuracy	62.822005870477625	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0	(hypot.f64 y x)

Samples

36.0ms

256×

valid

Compiler

Compiled 186 to 34 computations (81.7% saved)

Precisions

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

ival-hypot: 14.0ms (55.4% of total)

ival-mult: 5.0ms (19.8% of total)

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

ival-div: 2.0ms (7.9% 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)

series7.0ms (0.2%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

12 → 32

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
1.0ms	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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
1.0ms	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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
1.0ms	y	@	0	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))

simplify161.0ms (3.7%)

Memory

25.9MiB live, 220.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	478
1	355	478
2	1339	461
3	7033	461
0	8123	422

Stop Event

1×	iter limit
1×	node limit

Counts

32 → 30

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)
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))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (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))))))))
(+ 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 (pow x 2)) (pow y 2)) y)
(/ 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))))
(* -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))))))))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))

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

rewrite107.0ms (2.4%)

Memory

-11.1MiB live, 146.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	82
0	28	70
1	98	70
2	832	68
0	9648	68

Stop Event

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

Counts

12 → 489

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

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

eval64.0ms (1.5%)

Memory: -7.8MiB live, 112.4MiB allocated
Compiler: Compiled 11 274 to 1 349 computations (88% saved)

prune11.0ms (0.3%)

Memory

-8.1MiB live, 31.0MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	474	3	477
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	476	6	482

Accuracy

100.0%

Counts

482 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	52.9%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	52.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
▶	4.6%	#s(approx (sqrt (+ (* x x) (* y y))) (/.f64 (*.f64 x x) x))
▶	4.9%	#s(approx (sqrt (+ (* x x) (* y y))) x)

Compiler

Compiled 63 to 43 computations (31.7% saved)

simplify110.0ms (2.5%)

Memory

8.0MiB live, 131.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 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 (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (/.f64 (*.f64 x x) x))
cost-diff	1024	(/.f64 (*.f64 x x) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	70
0	21	62
1	42	62
2	119	62
3	396	62
4	1828	62
5	5151	62
6	7120	62
0	8216	47

Stop Event

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

Calls

Call 1

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

localize31.0ms (0.7%)

Memory

7.2MiB live, 45.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.2265625	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.37886888894080134	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
accuracy	0	(*.f64 x x)
accuracy	27.241252264556216	(/.f64 (*.f64 x x) x)
accuracy	60.83388763055708	#s(approx (sqrt (+ (* x x) (* y y))) (/.f64 (*.f64 x x) x))
accuracy	60.83388763055708	#s(approx (sqrt (+ (* x x) (* y y))) x)

Samples

23.0ms

256×

valid

Compiler

Compiled 126 to 27 computations (78.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-hypot: 5.0ms (35.7% of total)

ival-mult: 4.0ms (28.5% of total)

ival-div: 3.0ms (21.4% of total)

ival-add: 1.0ms (7.1% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

8 → 29

Calls

Call 1

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

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)))))
x
(pow x 2)
(* 1/2 (/ x y))
(* 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 (* 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)))))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ 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)))))))
(* -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))))))))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (/ (* x x) x) (sqrt (+ (* x x) (* y y))) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (/ (* x x) x) (sqrt (+ (* x x) (* y y))) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (/ (* x x) x) (sqrt (+ (* x x) (* y y))) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (/ (* x x) x) (sqrt (+ (* x x) (* y y))) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	y	@	-inf	((sqrt (+ (* x x) (* y y))) (/ (* x x) x) (sqrt (+ (* x x) (* y y))) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))

simplify220.0ms (5%)

Memory

6.8MiB live, 158.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	447
1	338	447
2	1285	432
3	6383	430
0	8135	396

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 27

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)))))
x
(pow x 2)
(* 1/2 (/ x y))
(* 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 (* 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)))))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ 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)))))))
(* -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))))))))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))

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

rewrite200.0ms (4.6%)

Memory

-25.0MiB live, 93.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	21	61
1	84	59
2	670	57
0	9071	42

Stop Event

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

Counts

8 → 216

Calls

Call 1

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

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

eval26.0ms (0.6%)

Memory: 36.6MiB live, 36.6MiB allocated
Compiler: Compiled 6 505 to 824 computations (87.3% saved)

prune46.0ms (1.1%)

Memory

-21.0MiB live, 16.8MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	240	6	246

Accuracy

100.0%

Counts

246 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	52.9%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	52.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	4.6%	#s(approx (sqrt (+ (* x x) (* y y))) (/.f64 (*.f64 x x) x))
✓	4.9%	#s(approx (sqrt (+ (* x x) (* y y))) x)

Compiler

Compiled 162 to 70 computations (56.8% saved)

regimes20.0ms (0.5%)

Memory

23.4MiB live, 23.4MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

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

regimes55.0ms (1.3%)

Memory

-7.6MiB live, 37.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

40.0ms	(*.f64 y y)
3.0ms	y
3.0ms	x
3.0ms	(+.f64 (.f64 x x) (.f64 y y))
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`y`
99.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.4%	1	`(*.f64 x x)`
99.4%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes43.0ms (1%)

Memory

-11.3MiB live, 24.9MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

6 calls:

31.0ms	(*.f64 x x)
2.0ms	x
2.0ms	y
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
52.9%	1	`x`
52.9%	1	`y`
52.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
52.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
52.9%	1	`(*.f64 x x)`
52.9%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes57.0ms (1.3%)

Memory

-9.5MiB live, 27.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

6 calls:

46.0ms	(*.f64 x x)
2.0ms	x
2.0ms	y
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
52.4%	1	`x`
52.4%	1	`(*.f64 x x)`
52.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
52.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
52.4%	1	`(*.f64 y y)`
52.4%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes9.0ms (0.2%)

Memory

17.4MiB live, 17.4MiB allocated

Accuracy

Total -2.0b remaining (-3.3%)

Threshold costs -2b (-3.3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

6 calls:

2.0ms	y
1.0ms	x
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
4.9%	1	`x`
4.9%	1	`(*.f64 x x)`
4.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
4.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
4.9%	1	`(*.f64 y y)`
4.9%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify34.0ms (0.8%)

Memory

5.3MiB live, 44.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	49
1	20	49

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness666.0ms (15.2%)

Memory

-32.9MiB live, 221.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	441
1	327	441
2	1249	437
3	6500	435
0	8044	400
0	6	21
0	10	21
1	41	21
2	371	21
3	6127	21
0	8068	14
0	19	82
0	28	70
1	98	70
2	832	68
0	9648	68

Stop Event

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

Compiler

Compiled 117 to 66 computations (43.6% saved)

preprocess164.0ms (3.8%)

Memory

-1.0MiB live, 118.9MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 170 to 94 computations (44.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample802.0ms (18.3%)

explain196.0ms (4.5%)

preprocess369.0ms (8.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify116.0ms (2.7%)

localize40.0ms (0.9%)

series5.0ms (0.1%)

simplify330.0ms (7.6%)

rewrite124.0ms (2.8%)

eval86.0ms (2%)

prune10.0ms (0.2%)

simplify206.0ms (4.7%)

localize50.0ms (1.1%)

series7.0ms (0.2%)

simplify161.0ms (3.7%)

rewrite107.0ms (2.4%)

eval64.0ms (1.5%)

prune11.0ms (0.3%)

simplify110.0ms (2.5%)

localize31.0ms (0.7%)

series8.0ms (0.2%)

simplify220.0ms (5%)

rewrite200.0ms (4.6%)

eval26.0ms (0.6%)

prune46.0ms (1.1%)

regimes20.0ms (0.5%)

regimes55.0ms (1.3%)

regimes43.0ms (1%)

regimes57.0ms (1.3%)

regimes9.0ms (0.2%)

simplify34.0ms (0.8%)

soundness666.0ms (15.2%)

preprocess164.0ms (3.8%)

end0.0ms (0%)

Profiling