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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample4.3s (50.2%)

Memory

-322.5MiB live, 944.8MiB allocated

Samples

609.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 249.0ms

ival-hypot: 239.0ms (95.9% of total)

ival-true: 7.0ms (2.8% of total)

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

Bogosity

explain169.0ms (2%)

Memory

-32.7MiB live, 203.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
122	-	2	(1.0735889943679917e-256 8.131038929092841e-159)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	oflow-rescue	103	0
↳	`(*.f64 y y)`	overflow	65
↳	`(*.f64 x x)`	overflow	51
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	103
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	17	0
↳	`(*.f64 y y)`	underflow	61
↳	`(*.f64 x x)`	underflow	78
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	17

Confusion

	Predicted +	Predicted -
+	120	2
-	0	134

Precision

1.0

Recall

0.9836065573770492

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	2
-	0	0	134

Precision?

1.0

Recall?

0.9836065573770492

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

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

ival-mult: 15.0ms (51.3% of total)

ival-hypot: 12.0ms (41% of total)

ival-add: 2.0ms (6.8% of total)

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

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

preprocess26.0ms (0.3%)

Memory

7.2MiB live, 53.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	42	42
2	92	42
3	117	42
4	155	42
0	6	8
0	10	8
1	21	8
2	60	8
3	117	8
4	154	8
0	154	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

series6.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Counts

6 → 27

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

Calls

6 calls:

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

simplify196.0ms (2.3%)

Memory

-17.4MiB live, 268.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	441
1	323	441
2	1251	437
3	6235	435
0	8273	400

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 25

Calls

Call 1

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

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

rewrite139.0ms (1.6%)

Memory

34.4MiB live, 173.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	39	23
2	346	23
3	5889	23
0	8197	17

Stop Event

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

Counts

6 → 262

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

eval53.0ms (0.6%)

Memory: 20.8MiB live, 149.1MiB allocated
Compiler: Compiled 5 609 to 1 077 computations (80.8% saved)

prune116.0ms (1.4%)

Memory

-51.4MiB live, 80.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	326	5	331
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	327	5	332

Accuracy

100.0%

Counts

332 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	95.2%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 100 to 70 computations (30% saved)

simplify0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated

series14.0ms (0.2%)

Memory

-10.7MiB live, 36.1MiB allocated

Counts

15 → 32

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	y	@	0	((sqrt (+ (* y y) (* x x))) y x (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) 1/2)
1.0ms	y	@	-inf	((sqrt (+ (* y y) (* x x))) y x (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) 1/2)
1.0ms	y	@	inf	((sqrt (+ (* y y) (* x x))) y x (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) 1/2)
1.0ms	x	@	inf	((sqrt (+ (* y y) (* x x))) y x (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) 1/2)
1.0ms	x	@	0	((sqrt (+ (* y y) (* x x))) y x (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) 1/2)

simplify235.0ms (2.8%)

Memory

27.3MiB live, 256.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	483
1	349	483
2	1327	466
3	6699	466
0	8417	428

Stop Event

1×	iter limit
1×	node limit

Counts

32 → 30

Calls

Call 1

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

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

rewrite332.0ms (3.9%)

Memory

2.8MiB live, 196.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	85
0	28	73
1	87	73
2	720	73
0	9851	73

Stop Event

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

Counts

15 → 336

Calls

Call 1

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

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

eval285.0ms (3.3%)

Memory: -35.5MiB live, 221.9MiB allocated
Compiler: Compiled 10 003 to 1 389 computations (86.1% saved)

prune39.0ms (0.5%)

Memory

-14.3MiB live, 33.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	482	2	484
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	483	6	489

Accuracy

100.0%

Counts

489 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
▶	3.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))

Compiler

Compiled 76 to 51 computations (32.9% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

series10.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

12 → 30

Calls

Call 1

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

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

Calls

6 calls:

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

simplify326.0ms (3.8%)

Memory

22.6MiB live, 249.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	457
1	332	457
2	1265	442
3	6069	439
0	8290	407

Stop Event

1×	iter limit
1×	node limit

Counts

30 → 28

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

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

rewrite289.0ms (3.4%)

Memory

-25.7MiB live, 166.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	94
0	26	92
1	97	92
2	618	92
0	8946	82

Stop Event

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

Counts

12 → 164

Calls

Call 1

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

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

eval29.0ms (0.3%)

Memory: 40.9MiB live, 40.9MiB allocated
Compiler: Compiled 8 632 to 973 computations (88.7% saved)

prune45.0ms (0.5%)

Memory

-21.4MiB live, 23.5MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	256	7	263

Accuracy

100.0%

Counts

263 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
▶	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
▶	3.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))

Compiler

Compiled 115 to 70 computations (39.1% saved)

simplify0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

series13.0ms (0.2%)

Memory

23.0MiB live, 23.0MiB allocated

Counts

18 → 49

Calls

Call 1

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

Calls

6 calls:

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

simplify393.0ms (4.6%)

Memory

-29.6MiB live, 255.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	203	862
1	618	827
2	2350	769
0	8547	721

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 47

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

rewrite187.0ms (2.2%)

Memory

41.3MiB live, 413.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	193
0	37	173
1	136	152
2	1135	149
0	9108	133

Stop Event

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

Counts

18 → 1 044

Calls

Call 1

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

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

eval150.0ms (1.8%)

Memory: 18.7MiB live, 484.5MiB allocated
Compiler: Compiled 48 036 to 3 296 computations (93.1% saved)

prune23.0ms (0.3%)

Memory

-30.2MiB live, 76.4MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	843	1	844
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	844	7	851

Accuracy

100.0%

Counts

851 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
✓	3.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))

Compiler

Compiled 316 to 117 computations (63% saved)

regimes22.0ms (0.3%)

Memory

15.2MiB live, 61.8MiB 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) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
(hypot.f64 y x)

Outputs
(hypot.f64 y x)

Calls

6 calls:

5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	y
3.0ms	x
3.0ms	(+.f64 (.f64 x x) (.f64 y y))
3.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes20.0ms (0.2%)

Memory

7.2MiB live, 54.3MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`(*.f64 y y)`
99.8%	1	`(*.f64 x x)`
99.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.8%	1	`x`
99.8%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes41.0ms (0.5%)

Memory

-8.9MiB live, 42.0MiB allocated

Counts

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

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

Calls

6 calls:

28.0ms	x
3.0ms	y
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(*.f64 y y)
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.8%	1	`(*.f64 y y)`
99.8%	1	`(*.f64 x x)`
99.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.8%	1	`x`
99.8%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes38.0ms (0.4%)

Memory

-15.4MiB live, 32.0MiB 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) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))

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

Calls

6 calls:

28.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	x
2.0ms	y
2.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
56.0%	1	`(*.f64 y y)`
56.0%	1	`(*.f64 x x)`
56.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
56.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
56.0%	1	`x`
56.0%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes14.0ms (0.2%)

Memory

-12.4MiB live, 32.4MiB allocated

Counts

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

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

Calls

6 calls:

5.0ms	(*.f64 y y)
2.0ms	x
2.0ms	y
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
55.8%	1	`(*.f64 y y)`
55.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
55.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
55.8%	1	`y`
55.8%	1	`(*.f64 x x)`
55.8%	1	`x`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes6.0ms (0.1%)

Memory

20.9MiB live, 20.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
2.0%	1	`(*.f64 y y)`
2.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
2.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
2.0%	1	`y`
2.0%	1	`(*.f64 x x)`
2.0%	1	`x`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify15.0ms (0.2%)

Memory

-18.6MiB live, 25.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	87
1	45	87
2	86	87
3	143	87
4	180	87

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness920.0ms (10.8%)

Memory

28.8MiB live, 746.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	94
0	26	92
1	97	92
2	618	92
0	8946	82
0	19	85
0	28	73
1	87	73
2	720	73
0	9851	73
0	25	193
0	37	173
1	136	152
2	1135	149
0	9108	133
0	6	23
0	10	23
1	39	23
2	346	23
3	5889	23
0	8197	17
0	104	441
1	323	441
2	1251	437
3	6235	435
0	8273	400

Stop Event

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

Compiler

Compiled 186 to 95 computations (48.9% saved)

preprocess81.0ms (1%)

Memory

-21.6MiB live, 168.7MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 246 to 112 computations (54.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample4.3s (50.2%)

explain169.0ms (2%)

preprocess26.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

series6.0ms (0.1%)

simplify196.0ms (2.3%)

rewrite139.0ms (1.6%)

eval53.0ms (0.6%)

prune116.0ms (1.4%)

simplify0.0ms (0%)

series14.0ms (0.2%)

simplify235.0ms (2.8%)

rewrite332.0ms (3.9%)

eval285.0ms (3.3%)

prune39.0ms (0.5%)

simplify0.0ms (0%)

series10.0ms (0.1%)

simplify326.0ms (3.8%)

rewrite289.0ms (3.4%)

eval29.0ms (0.3%)

prune45.0ms (0.5%)

simplify0.0ms (0%)

series13.0ms (0.2%)

simplify393.0ms (4.6%)

rewrite187.0ms (2.2%)

eval150.0ms (1.8%)

prune23.0ms (0.3%)

regimes22.0ms (0.3%)

regimes20.0ms (0.2%)

regimes41.0ms (0.5%)

regimes38.0ms (0.4%)

regimes14.0ms (0.2%)

regimes6.0ms (0.1%)

simplify15.0ms (0.2%)

soundness920.0ms (10.8%)

preprocess81.0ms (1%)

end0.0ms (0%)

Profiling