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)

sample909.0ms (4.7%)

Memory

-28.4MiB live, 754.2MiB allocated

Samples

616.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-hypot: 241.0ms (96.2% of total)

ival-true: 6.0ms (2.4% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain89.0ms (0.5%)

Memory

-23.1MiB live, 133.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
125	-	-	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	-	`y`
0	-	-	`(*.f64 y y)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	oflow-rescue	112	0
↳	`(*.f64 y y)`	overflow	56
↳	`(*.f64 x x)`	overflow	71
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	112
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	13	0
↳	`(*.f64 y y)`	underflow	71
↳	`(*.f64 x x)`	underflow	71
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	13

Confusion

	Predicted +	Predicted -
+	125	0
-	0	131

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	125	0	0
-	0	0	131

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	131
1	125

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms

512×

valid

Compiler

Compiled 81 to 28 computations (65.4% saved)

Precisions

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

ival-hypot: 9.0ms (49.1% of total)

ival-mult: 7.0ms (38.2% of total)

ival-add: 2.0ms (10.9% of total)

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

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

preprocess16.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

3.6MiB live, 3.6MiB 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	11	23
0	11	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (0.2%)

Memory

-23.3MiB live, 52.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (.f64 x x) (.f64 y y))
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	29.115464117306033	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

36.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 23.0ms (81.7% of total)

ival-hypot: 4.0ms (14.2% of total)

ival-add: 1.0ms (3.6% of total)

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

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

series5.0ms (0%)

Memory

7.5MiB live, 7.5MiB 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))))

simplify257.0ms (1.3%)

Memory

-8.7MiB live, 151.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	429
1	296	429
2	951	427
3	3712	393
4	6445	391
0	8382	354

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

rewrite218.0ms (1.1%)

Memory

36.4MiB live, 268.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

Outputs
(.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (.f64 (-.f64 x y) (+.f64 y x))))))
(.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 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)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
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(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) (.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (.f64 y x) #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (sqrt.f64 (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 y x)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(hypot.f64 y x)
(hypot.f64 x y)
(exp.f64 (fma.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/4 binary64) (.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64)))

eval31.0ms (0.2%)

Memory: 18.2MiB live, 89.6MiB allocated
Compiler: Compiled 7 430 to 981 computations (86.8% saved)

prune26.0ms (0.1%)

Memory

-36.2MiB live, 19.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

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

Accuracy

100.0%

Counts

267 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	54.5%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
	94.1%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
▶	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 134 to 92 computations (31.3% saved)

simplify55.0ms (0.3%)

Memory

-7.4MiB live, 31.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 y x)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
cost-diff	-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	20	94
0	30	82
1	42	82
2	54	82
3	60	82
4	65	82
5	72	82
6	87	82
7	136	82
8	204	82
9	392	82
10	744	82
11	1482	82
12	1670	82
13	1735	82
14	1759	82
15	1771	82
16	1843	82
17	2334	82
0	2334	82

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize59.0ms (0.3%)

Memory

0.1MiB live, 74.6MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.08203125	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
accuracy	59.96635441583574	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
accuracy	0.0	(fma.f64 y y (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	29.115464117306033	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0.0	(*.f64 y y)
accuracy	0.2609539862178579	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	29.115464117306033	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0.0	(neg.f64 x)
accuracy	62.79993098474172	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0.0	(hypot.f64 y x)

Samples

46.0ms

256×

valid

Compiler

Compiled 186 to 36 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-div: 16.0ms (45.3% of total)

ival-mult: 8.0ms (22.6% of total)

ival-hypot: 8.0ms (22.6% of total)

ival-add: 3.0ms (8.5% of total)

ival-neg: 1.0ms (2.8% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0%)

Memory

17.5MiB live, 17.5MiB allocated

Counts

13 → 33

Calls

Call 1

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

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

Calls

6 calls:

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

simplify297.0ms (1.5%)

Memory

-29.1MiB live, 187.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

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

rewrite317.0ms (1.6%)

Memory

45.1MiB live, 145.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

13 → 368

Calls

Call 1

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

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

eval60.0ms (0.3%)

Memory: -27.8MiB live, 33.2MiB allocated
Compiler: Compiled 9 401 to 1 209 computations (87.1% saved)

prune4.8s (24.7%)

Memory

-24.6MiB live, 15.0MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

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

Accuracy

100.0%

Counts

362 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	54.5%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	94.1%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
✓	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
✓	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 106 to 73 computations (31.1% saved)

simplify9.4s (48.5%)

Memory

28.8MiB live, 62.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 x y))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
cost-diff	448	(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	127
0	39	130
1	70	120
2	159	112
3	376	112
4	764	112
5	1243	112
6	2287	112
7	2739	112
8	3005	112
9	3453	112
10	3702	112
11	3746	112
12	3754	112
13	3774	112
14	3782	112
15	3792	112
16	3822	112
17	3822	112
18	3822	112
0	3822	97

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize94.0ms (0.5%)

Memory

-20.2MiB live, 64.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	(*.f64 x x)
accuracy	0.1383612554236679	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	3.6954449900103583	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.08203125	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x)
accuracy	0.1875	(/.f64 #s(literal 1 binary64) (/.f64 x y))
accuracy	59.96635441583574	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x))
accuracy	0.0	(neg.f64 y)
accuracy	0.08203125	(fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x)
accuracy	0.1484375	(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
accuracy	59.96635441583574	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))

Samples

80.0ms

256×

valid

Compiler

Compiled 227 to 48 computations (78.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 18.0ms (41.9% of total)

ival-mult: 12.0ms (27.9% of total)

ival-hypot: 8.0ms (18.6% of total)

ival-add: 3.0ms (7% of total)

ival-neg: 1.0ms (2.3% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Memory

16.9MiB live, 16.9MiB allocated

Counts

12 → 34

Calls

Call 1

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

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

simplify351.0ms (1.8%)

Memory

-13.2MiB live, 181.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	494
1	329	494
2	1050	492
3	3990	450
4	7449	450
0	8461	412

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 32

Calls

Call 1

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

rewrite303.0ms (1.6%)

Memory

22.5MiB live, 91.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	107
0	39	110
1	153	92
2	1122	92
0	8569	77

Stop Event

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

Counts

12 → 368

Calls

Call 1

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

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

eval69.0ms (0.4%)

Memory: -9.9MiB live, 42.7MiB allocated
Compiler: Compiled 7 686 to 970 computations (87.4% saved)

prune8.0ms (0%)

Memory

12.3MiB live, 12.3MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	281	2	283
Fresh	0	0	0
Picked	3	0	3
Done	1	4	5
Total	285	6	291

Accuracy

100.0%

Counts

291 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	54.5%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.8%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64))))

Compiler

Compiled 79 to 55 computations (30.4% saved)

simplify115.0ms (0.6%)

Memory

-19.2MiB live, 19.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	103
0	32	103
1	59	101
2	140	97
3	327	97
4	729	97
5	1153	97
6	2038	97
7	2420	97
8	2500	97
9	2507	97
10	2521	97
11	2533	97
12	2533	97
13	2533	97
14	2605	97
15	3048	97
0	3048	85

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize110.0ms (0.6%)

Memory

10.2MiB live, 46.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.1383612554236679	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
accuracy	0.15625	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.078125	(*.f64 (/.f64 y x) y)
accuracy	0.19877625772252466	(.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64))
accuracy	0.559930812539792	#s(approx (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64)))
accuracy	59.96635441583574	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64))))

Samples

100.0ms

256×

valid

Compiler

Compiled 171 to 47 computations (72.5% saved)

Precisions

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

ival-hypot: 11.0ms (38.4% of total)

ival-mult: 9.0ms (31.4% of total)

ival-div: 5.0ms (17.4% of total)

ival-add: 2.0ms (7% of total)

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

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

8 → 33

Calls

Call 1

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

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)))))
(* 1/2 (/ (pow y 2) x))
(/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)
(/ (pow y 2) x)
(* 1/2 (/ x y))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(/ (+ (* 1/2 (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) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -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))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* (* (/ y x) y) 1/2) (* (/ y x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* (* (/ y x) y) 1/2) (* (/ y x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* (* (/ y x) y) 1/2) (* (/ y x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	y	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* (* (/ y x) y) 1/2) (* (/ y x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* (* (/ y x) y) 1/2) (* (/ y x) y) (sqrt (+ (* y y) (* x x))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))

simplify379.0ms (2%)

Memory

1.5MiB live, 193.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	495
1	331	495
2	1052	493
3	3965	451
4	7436	451
0	8442	413

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

rewrite234.0ms (1.2%)

Memory

0.7MiB live, 322.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	94
0	32	94
1	126	88
2	868	88
0	8310	76

Stop Event

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

Counts

8 → 251

Calls

Call 1

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

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

eval41.0ms (0.2%)

Memory: -10.1MiB live, 75.6MiB allocated
Compiler: Compiled 8 636 to 1 055 computations (87.8% saved)

prune13.0ms (0.1%)

Memory

7.0MiB live, 44.6MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	278	6	284

Accuracy

100.0%

Counts

284 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	54.5%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.8%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
✓	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (.f64 (.f64 (/.f64 y x) y) #s(literal 1/2 binary64))))

Compiler

Compiled 256 to 109 computations (57.4% saved)

regimes23.0ms (0.1%)

Memory

5.7MiB live, 44.9MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

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

regimes23.0ms (0.1%)

Memory

-15.5MiB live, 31.1MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

6 calls:

5.0ms	(*.f64 y y)
4.0ms	y
4.0ms	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
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.8%	1	`(*.f64 x x)`
99.8%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes15.0ms (0.1%)

Memory

-14.9MiB live, 24.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
94.1%	1	`x`
94.1%	1	`y`
94.1%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
94.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
94.1%	1	`(*.f64 x x)`
94.1%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes13.0ms (0.1%)

Memory

-10.9MiB live, 28.1MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
54.5%	1	`y`
54.5%	1	`x`
54.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
54.5%	1	`(+.f64 (.f64 x x) (.f64 y y))`
54.5%	1	`(*.f64 x x)`
54.5%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes10.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

6 calls:

2.0ms	y
2.0ms	x
2.0ms	(+.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
54.1%	1	`x`
54.1%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
54.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
54.1%	1	`(*.f64 x x)`
54.1%	1	`(*.f64 y y)`
54.1%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes7.0ms (0%)

Memory

-21.4MiB live, 17.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	x
1.0ms	y
1.0ms	(+.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify68.0ms (0.4%)

Memory

29.3MiB live, 69.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	67
1	30	67
2	33	67
3	35	67
4	39	67
5	43	67
6	59	67
7	158	67
8	3619	67

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness811.0ms (4.2%)

Memory

-8.5MiB live, 538.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1800	21
0	8651	15
0	25	107
0	39	110
1	153	92
2	1122	92
0	8569	77
0	104	429
1	296	429
2	951	427
3	3712	393
4	6445	391
0	8382	354
0	117	479
1	326	479
2	1027	477
3	4007	435
4	7560	435
0	8303	397

Stop Event

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

Compiler

Compiled 143 to 75 computations (47.6% saved)

preprocess76.0ms (0.4%)

Memory

-6.3MiB live, 156.2MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 242 to 138 computations (43% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample909.0ms (4.7%)

explain89.0ms (0.5%)

preprocess16.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize41.0ms (0.2%)

series5.0ms (0%)

simplify257.0ms (1.3%)

rewrite218.0ms (1.1%)

eval31.0ms (0.2%)

prune26.0ms (0.1%)

simplify55.0ms (0.3%)

localize59.0ms (0.3%)

series9.0ms (0%)

simplify297.0ms (1.5%)

rewrite317.0ms (1.6%)

eval60.0ms (0.3%)

prune4.8s (24.7%)

simplify9.4s (48.5%)

localize94.0ms (0.5%)

series10.0ms (0.1%)

simplify351.0ms (1.8%)

rewrite303.0ms (1.6%)

eval69.0ms (0.4%)

prune8.0ms (0%)

simplify115.0ms (0.6%)

localize110.0ms (0.6%)

series10.0ms (0.1%)

simplify379.0ms (2%)

rewrite234.0ms (1.2%)

eval41.0ms (0.2%)

prune13.0ms (0.1%)

regimes23.0ms (0.1%)

regimes23.0ms (0.1%)

regimes15.0ms (0.1%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes7.0ms (0%)

simplify68.0ms (0.4%)

soundness811.0ms (4.2%)

preprocess76.0ms (0.4%)

end0.0ms (0%)

Profiling