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)

sample735.0ms (16.1%)

Memory

0.9MiB live, 716.4MiB allocated

Samples

479.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 280.0ms

ival-hypot: 272.0ms (97.1% of total)

ival-true: 5.0ms (1.8% of total)

ival-assert: 2.0ms (0.7% of total)

Bogosity

explain112.0ms (2.5%)

Memory

-12.3MiB live, 146.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
131	-	1	(-8.397758619263641e-162 3.1350869045412482e-260)	`(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	121	0
↳	`(*.f64 y y)`	overflow	71
↳	`(*.f64 x x)`	overflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	121
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	9	0
↳	`(*.f64 y y)`	underflow	56
↳	`(*.f64 x x)`	underflow	53
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	9

Confusion

	Predicted +	Predicted -
+	130	1
-	0	125

Precision

1.0

Recall

0.9923664122137404

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	130	0	1
-	0	0	125

Precision?

1.0

Recall?

0.9923664122137404

Freqs

test

number	freq
0	126
1	130

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

47.0ms

512×

valid

Compiler

Compiled 81 to 28 computations (65.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-hypot: 8.0ms (45.8% of total)

ival-mult: 6.0ms (34.4% of total)

ival-add: 2.0ms (11.5% of total)

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

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

preprocess20.0ms (0.4%)

Memory

-12.4MiB live, 25.3MiB 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

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.4%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	21	23
2	60	23
3	117	23
4	154	23
0	154	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize78.0ms (1.7%)

Memory

-0.7MiB live, 36.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (.f64 x x) (.f64 y y))
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	30.444662169534315	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

73.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-hypot: 62.0ms (93.3% of total)

ival-mult: 4.0ms (6% of total)

ival-add: 1.0ms (1.5% of total)

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

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

series5.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

4 → 27

Calls

Call 1

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

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

Calls

6 calls:

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

simplify146.0ms (3.2%)

Memory

7.6MiB live, 135.9MiB 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)))))

rewrite159.0ms (3.5%)

Memory

3.0MiB live, 123.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	39	21
2	346	21
3	5889	21
0	8197	15

Stop Event

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

Counts

4 → 218

Calls

Call 1

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

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

eval45.0ms (1%)

Memory: -11.2MiB live, 26.8MiB allocated
Compiler: Compiled 4 457 to 759 computations (83% saved)

prune6.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	237	6	243
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	238	6	244

Accuracy

100.0%

Counts

244 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	52.4%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	51.9%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
	89.5%	#s(approx (sqrt (+ (* x x) (* y 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))
▶	93.9%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	1.7%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 152 to 100 computations (34.2% saved)

simplify35.0ms (0.8%)

Memory

-28.7MiB live, 10.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	94
0	28	82
1	46	82
2	117	82
3	270	82
4	487	82
5	653	82
6	666	82
0	666	82

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize53.0ms (1.2%)

Memory

1.6MiB live, 77.2MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	(*.f64 x x)
accuracy	0.14090457777869497	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	3.816634109733847	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
accuracy	0.0	(fma.f64 y y (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	30.444662169534315	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0.0	(*.f64 y y)
accuracy	0.33601793972578275	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	30.444662169534315	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0.0	(neg.f64 x)
accuracy	62.91550292708212	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0.0	(hypot.f64 y x)

Samples

33.0ms

256×

valid

Compiler

Compiled 186 to 34 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 8.0ms (35.9% of total)

ival-hypot: 8.0ms (35.9% of total)

ival-add: 3.0ms (13.5% of total)

ival-div: 2.0ms (9% of total)

ival-neg: 1.0ms (4.5% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

12 → 32

Calls

Call 1

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

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

Calls

6 calls:

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

simplify261.0ms (5.7%)

Memory

23.0MiB live, 182.6MiB 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)))))
(* -1 x)
(pow y 2)
(+ (pow x 2) (pow y 2))
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ 1/2 y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))

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

rewrite222.0ms (4.9%)

Memory

-4.9MiB live, 104.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	82
0	28	70
1	87	70
2	720	70
0	9851	70

Stop Event

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

Counts

12 → 309

Calls

Call 1

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

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

eval202.0ms (4.4%)

Memory: -26.7MiB live, 65.2MiB allocated
Compiler: Compiled 7 646 to 1 010 computations (86.8% saved)

prune9.0ms (0.2%)

Memory

19.7MiB live, 19.7MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	311	3	314
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	313	7	320

Accuracy

100.0%

Counts

320 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	52.4%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	51.9%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	89.5%	#s(approx (sqrt (+ (* y y) (* x x))) (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))
▶	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	1.7%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
▶	3.6%	#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 102 to 66 computations (35.3% saved)

simplify141.0ms (3.1%)

Memory

16.8MiB live, 211.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) (*.f64 x x) #s(literal 1/2 binary64)) y)
cost-diff	0	(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)
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) (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))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
cost-diff	0	(/.f64 (*.f64 x x) y)
cost-diff	0	(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	177
0	43	175
1	85	175
2	247	175
3	942	175
4	4327	175
0	8271	160

Stop Event

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

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

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

localize133.0ms (2.9%)

Memory

-31.0MiB live, 95.7MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) (*.f64 x x) #s(literal 1/2 binary64)) y)
accuracy	0.125	(/.f64 (/.f64 #s(literal -1/8 binary64) y) y)
accuracy	3.8166341074762182	(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)
accuracy	6.539285226430016	(fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) (*.f64 x x) #s(literal 1/2 binary64))
accuracy	0.0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.14090457777869497	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
accuracy	0.2421875	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.0	(*.f64 x x)
accuracy	0.14090457777869497	#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))))
accuracy	7.114031651860749	(/.f64 (*.f64 x x) y)
accuracy	61.68083269348337	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))

Samples

94.0ms

256×

valid

Compiler

Compiled 308 to 53 computations (82.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-hypot: 41.0ms (65.3% of total)

ival-mult: 9.0ms (14.3% of total)

ival-div: 8.0ms (12.7% of total)

ival-add: 4.0ms (6.4% of total)

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

exact: 0.0ms (0% of total)

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

series22.0ms (0.5%)

Memory

3.3MiB live, 37.2MiB allocated

Counts

14 → 48

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

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) (* x x) (/ (/ -1/8 y) y))
4.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) (* x x) (/ (/ -1/8 y) y))
3.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) (* x x) (/ (/ -1/8 y) y))
2.0ms	y	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) (* x x) (/ (/ -1/8 y) y))
2.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) y) (+ (* (/ (/ -1/8 y) y) (* x x)) 1/2) (* x x) (/ (/ -1/8 y) y))

simplify171.0ms (3.8%)

Memory

14.6MiB live, 171.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	699
1	457	699
2	1661	680
0	8496	635

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

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

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

rewrite250.0ms (5.5%)

Memory

14.1MiB live, 214.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	161
0	43	159
1	170	159
2	1239	159
0	8631	144

Stop Event

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

Counts

14 → 255

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y)))
(.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 (.f64 x x) (/.f64 #s(literal 1/2 binary64) y))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) y))
(.f64 x (.f64 (/.f64 x y) #s(literal 1/2 binary64)))
(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(/.f64 (neg.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal 1/2 binary64))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) 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 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x))) (neg.f64 (neg.f64 y)))
(/.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal 1/2 binary64)) (neg.f64 y))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (neg.f64 y))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) x)) (neg.f64 y))
(/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (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) x)
(*.f64 (neg.f64 x) (/.f64 (neg.f64 x) y))
(*.f64 x (/.f64 x y))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 (neg.f64 (neg.f64 y))))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 y))
(/.f64 (*.f64 x x) (neg.f64 (neg.f64 y)))
(/.f64 (*.f64 x x) y)
(neg.f64 (/.f64 (*.f64 (neg.f64 x) x) y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 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 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 y y) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) 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 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (fma.f64 (/.f64 (.f64 y y) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (/.f64 (.f64 y y) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 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 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (/.f64 (.f64 y y) (-.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y))))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) x) #s(literal 3 binary64))) (fma.f64 y y (fma.f64 (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) x) (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) x) (.f64 y (.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x)) x)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 y y (fma.f64 (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x)) (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x)) (.f64 y (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1/2 binary64) y)) #s(literal 3 binary64))) (fma.f64 y y (fma.f64 (.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1/2 binary64) y)) (.f64 y (.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1/2 binary64) y))))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) #s(literal 3 binary64))) (fma.f64 y y (fma.f64 (.f64 (neg.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (.f64 (neg.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (.f64 y (.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (-.f64 (.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 y y) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 y (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 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 #s(literal 1/2 binary64) x) (/.f64 x y)) 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 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (*.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y) (.f64 y y))) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)))
(/.f64 (fma.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (.f64 y y) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 y (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y))))
(/.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 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)))
(/.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 (fma.f64 y y (-.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 y x))))))
(/.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 (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (*.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y))
(/.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))) (fma.f64 y y (-.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 y x)))))
(/.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))) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (*.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 y))) (sqrt.f64 (neg.f64 (neg.f64 y))) (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)))
(fma.f64 (sqrt.f64 (neg.f64 y)) (sqrt.f64 (neg.f64 y)) (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x)) (neg.f64 x) y)
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y)) 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 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y)
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y) y)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x x) y) y)
(fma.f64 x (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) y)
(fma.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) y)
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)))) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 y (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y)))))
(-.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (/.f64 (.f64 y y) (-.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) 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 (.f64 (neg.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)))
(+.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y y (-.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 y x))))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 y x))))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 y x))))) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y y (-.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 y x))))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(+.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))) (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(+.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (/.f64 (.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (-.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 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 #s(literal 1/2 binary64) x) (/.f64 x y)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)) y)
(+.f64 y (.f64 (.f64 #s(literal 1/2 binary64) x) (/.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))
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(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y)) (.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) y) y)))
(+.f64 (/.f64 (.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (.f64 #s(literal 1/2 binary64) x))))) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (*.f64 #s(literal 1/2 binary64) x))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (.f64 #s(literal 1/2 binary64) x))))) (/.f64 (.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (*.f64 #s(literal 1/2 binary64) x))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (.f64 #s(literal 1/2 binary64) x)))) (/.f64 (.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (*.f64 #s(literal 1/2 binary64) x)))))
(+.f64 (/.f64 (.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (.f64 #s(literal 1/2 binary64) x)))) (/.f64 #s(literal 1/8 binary64) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) (*.f64 #s(literal 1/2 binary64) x)))))
(+.f64 (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) x) x))
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.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 (neg.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 #s(literal 1/8 binary64) (*.f64 (neg.f64 y) y))
(/.f64 (/.f64 #s(literal 1/8 binary64) y) (neg.f64 (neg.f64 (neg.f64 y))))
(/.f64 (/.f64 #s(literal 1/8 binary64) y) (neg.f64 y))
(/.f64 (/.f64 #s(literal -1/8 binary64) y) (neg.f64 (neg.f64 y)))
(/.f64 (/.f64 #s(literal -1/8 binary64) y) y)
(/.f64 #s(literal -1/8 binary64) (*.f64 y y))
(neg.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) y) y))

eval60.0ms (1.3%)

Memory: -5.0MiB live, 82.5MiB allocated
Compiler: Compiled 13 601 to 1 456 computations (89.3% saved)

prune39.0ms (0.9%)

Memory

-11.3MiB live, 26.0MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	330	3	333
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	331	9	340

Accuracy

100.0%

Counts

340 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	52.4%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	51.9%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	89.5%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64)) y) (*.f64 x x) y))
✓	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	1.7%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
✓	3.6%	#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))))
▶	3.6%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))))
▶	3.6%	#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 154 to 98 computations (36.4% saved)

simplify144.0ms (3.2%)

Memory

8.8MiB live, 159.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64)) y)
cost-diff	0	(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64)) y) (*.f64 x x) y)
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64)) y) (*.f64 x x) y))
cost-diff	0	(*.f64 (/.f64 x y) x)
cost-diff	0	(.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))))
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
cost-diff	0	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
cost-diff	0	#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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	202
0	45	202
1	88	202
2	261	202
3	1019	202
4	4682	202
0	8022	183

Stop Event

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

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

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

localize100.0ms (2.2%)

Memory

13.3MiB live, 134.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64)) y)
accuracy	0.24643073316701325	(/.f64 #s(literal -1/8 binary64) (*.f64 y y))
accuracy	3.8166341074762182	(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64)) y) (*.f64 x x) y)
accuracy	6.539285226430016	(fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.0	(.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))
accuracy	0.14090457777869497	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))))
accuracy	0.14453125	(*.f64 (/.f64 x y) x)
accuracy	61.68083269348337	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64)))
accuracy	0.14090457777869497	#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)))
accuracy	0.14453125	(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
accuracy	0.2421875	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	61.68083269348337	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))

Samples

78.0ms

256×

valid

Compiler

Compiled 340 to 55 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 33.0ms (64.4% of total)

ival-hypot: 8.0ms (15.6% of total)

ival-div: 6.0ms (11.7% of total)

ival-add: 3.0ms (5.9% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.3%)

Memory

-9.0MiB live, 27.6MiB allocated

Counts

13 → 47

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ 1/2 y) x) x) (* (/ 1/2 y) x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ x y) x) 1/2) (* (/ x y) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) (/ -1/8 (* y 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) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ x y) x) 1/2) (* (/ x y) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) (/ -1/8 (* y 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) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ x y) x) 1/2) (* (/ x y) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) (/ -1/8 (* y 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) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ x y) x) 1/2) (* (/ x y) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) (/ -1/8 (* y y)))
2.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ 1/2 y) x) x) (* (/ 1/2 y) x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ x y) x) 1/2) (* (/ x y) x) (sqrt (+ (* y y) (* x x))) (+ (* (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (* x x)) y) (/ (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) y) (+ (* (/ -1/8 (* y y)) (* x x)) 1/2) (/ -1/8 (* y y)))

simplify185.0ms (4.1%)

Memory

6.9MiB live, 202.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	696
1	457	696
2	1661	677
0	8496	632

Stop Event

1×	iter limit
1×	node limit

Counts

47 → 45

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

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

rewrite252.0ms (5.5%)

Memory

-25.6MiB live, 182.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	180
0	45	180
1	158	180
2	1230	180
0	8466	161

Stop Event

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

Counts

13 → 251

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y)))
(.f64 (fabs.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x))) x)
(.f64 (fabs.f64 (.f64 #s(literal 1/2 binary64) x)) (fabs.f64 (/.f64 x y)))
(.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (.f64 #s(literal 1/2 binary64) x)))
(.f64 (fabs.f64 (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x))
(.f64 (fabs.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 #s(literal 1/2 binary64) x) (/.f64 x y))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y)))
(.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))
(.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 y) x))
(.f64 (.f64 x x) (fabs.f64 (/.f64 #s(literal 1/2 binary64) y)))
(.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) y))
(.f64 x (fabs.f64 (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y))))
(.f64 x (fabs.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64))))
(.f64 x (fabs.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x)))
(.f64 x (.f64 (/.f64 x y) #s(literal 1/2 binary64)))
(.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)))
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(+.f64 (/.f64 #s(literal 1/8 binary64) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) y) (/.f64 #s(literal 1/2 binary64) y)))) (/.f64 (.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (*.f64 x x)) y) (/.f64 #s(literal 1/2 binary64) y)))))
(+.f64 (/.f64 (.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) y) (/.f64 #s(literal 1/2 binary64) y)))) (/.f64 #s(literal 1/8 binary64) (-.f64 (fma.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (*.f64 x x)) y) (/.f64 #s(literal 1/2 binary64) y)))))
(+.f64 (.f64 (/.f64 (.f64 #s(literal -1/8 binary64) x) y) (/.f64 x y)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 #s(literal -1/8 binary64) x) y) (/.f64 x y)))
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) (neg.f64 y))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) y))) (neg.f64 (neg.f64 y)))
(/.f64 (/.f64 #s(literal -1/8 binary64) (neg.f64 y)) (neg.f64 y))
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) y)) (neg.f64 y))
(/.f64 (/.f64 #s(literal -1/8 binary64) y) y)
(/.f64 #s(literal 1/8 binary64) (*.f64 (neg.f64 y) y))
(/.f64 #s(literal -1/8 binary64) (*.f64 y y))
(neg.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 y y)))

eval55.0ms (1.2%)

Memory: 8.4MiB live, 45.9MiB allocated
Compiler: Compiled 9 967 to 1 154 computations (88.4% saved)

prune9.0ms (0.2%)

Memory

22.9MiB live, 22.9MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	0	0
Picked	0	3	3
Done	0	6	6
Total	250	9	259

Accuracy

100.0%

Counts

259 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	52.4%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	51.9%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	89.5%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 x x) #s(literal 1/2 binary64)) y) (*.f64 x x) y))
✓	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	1.7%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
✓	3.6%	#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))))
✓	3.6%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))))
✓	3.6%	#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 385 to 153 computations (60.3% saved)

regimes35.0ms (0.8%)

Memory

1.8MiB live, 39.7MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

15.0ms	(*.f64 y y)
4.0ms	x
4.0ms	y
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes55.0ms (1.2%)

Memory

1.1MiB live, 38.6MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

6 calls:

37.0ms	(*.f64 y y)
4.0ms	x
4.0ms	y
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes32.0ms (0.7%)

Memory

-27.9MiB live, 18.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

20.0ms	(*.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
52.4%	1	`x`
52.4%	1	`y`
52.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
52.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
52.4%	1	`(*.f64 x x)`
52.4%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes13.0ms (0.3%)

Memory

19.2MiB live, 19.2MiB 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 y) x) #s(literal 1/2 binary64))))
#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:

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

Results

Accuracy	Segments	Branch
51.9%	1	`x`
51.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
51.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
51.9%	1	`(*.f64 x x)`
51.9%	1	`(*.f64 y y)`
51.9%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes26.0ms (0.6%)

Memory

-27.0MiB live, 12.1MiB 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:

20.0ms	(+.f64 (.f64 x x) (.f64 y y))
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	y
1.0ms	x
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
1.7%	1	`x`
1.7%	1	`(*.f64 x x)`
1.7%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
1.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
1.7%	1	`(*.f64 y y)`
1.7%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify11.0ms (0.2%)

Memory

11.9MiB live, 11.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	35	50
2	75	50
3	132	50
4	169	50

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness654.0ms (14.3%)

Memory

9.1MiB live, 403.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	39	21
2	346	21
3	5889	21
0	8197	15
0	19	82
0	28	70
1	87	70
2	720	70
0	9851	70
0	104	441
1	323	441
2	1251	437
3	6235	435
0	8273	400

Stop Event

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

Compiler

Compiled 107 to 59 computations (44.9% saved)

preprocess61.0ms (1.3%)

Memory

9.9MiB live, 126.3MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 172 to 96 computations (44.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample735.0ms (16.1%)

explain112.0ms (2.5%)

preprocess20.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize78.0ms (1.7%)

series5.0ms (0.1%)

simplify146.0ms (3.2%)

rewrite159.0ms (3.5%)

eval45.0ms (1%)

prune6.0ms (0.1%)

simplify35.0ms (0.8%)

localize53.0ms (1.2%)

series8.0ms (0.2%)

simplify261.0ms (5.7%)

rewrite222.0ms (4.9%)

eval202.0ms (4.4%)

prune9.0ms (0.2%)

simplify141.0ms (3.1%)

localize133.0ms (2.9%)

series22.0ms (0.5%)

simplify171.0ms (3.8%)

rewrite250.0ms (5.5%)

eval60.0ms (1.3%)

prune39.0ms (0.9%)

simplify144.0ms (3.2%)

localize100.0ms (2.2%)

series14.0ms (0.3%)

simplify185.0ms (4.1%)

rewrite252.0ms (5.5%)

eval55.0ms (1.2%)

prune9.0ms (0.2%)

regimes35.0ms (0.8%)

regimes55.0ms (1.2%)

regimes32.0ms (0.7%)

regimes13.0ms (0.3%)

regimes26.0ms (0.6%)

simplify11.0ms (0.2%)

soundness654.0ms (14.3%)

preprocess61.0ms (1.3%)

end0.0ms (0%)

Profiling