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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample724.0ms (3.9%)

Memory

-13.7MiB live, 718.5MiB allocated

Samples

504.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 349.0ms

ival-hypot: 339.0ms (97.1% of total)

ival-true: 6.0ms (1.7% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain121.0ms (0.6%)

Memory

5.5MiB live, 81.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
127	-	1	(1.3286062797705977e-155 -1.1164764790709874e-281)	`(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	116	0
↳	`(*.f64 y y)`	overflow	59
↳	`(*.f64 x x)`	overflow	69
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	116
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	10	0
↳	`(*.f64 y y)`	underflow	62
↳	`(*.f64 x x)`	underflow	56
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	10

Confusion

	Predicted +	Predicted -
+	126	1
-	0	129

Precision

1.0

Recall

0.9921259842519685

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	126	0	1
-	0	0	129

Precision?

1.0

Recall?

0.9921259842519685

Freqs

test

number	freq
0	130
1	126

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

74.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 50.0ms (81.4% of total)

ival-hypot: 9.0ms (14.7% of total)

ival-add: 2.0ms (3.3% of total)

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

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

preprocess16.0ms (0.1%)

Memory

33.5MiB live, 33.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval5.0ms (0%)

Memory: -34.2MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize24.0ms (0.1%)

Memory

-9.4MiB live, 36.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (.f64 x x) (.f64 y y))
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	29.37375260464032	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

19.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-hypot: 4.0ms (45.5% of total)

ival-mult: 3.0ms (34.1% of total)

ival-add: 1.0ms (11.4% of total)

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

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

series5.0ms (0%)

Memory

12.4MiB live, 12.4MiB 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	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	x	@	0	((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))

simplify204.0ms (1.1%)

Memory

8.0MiB live, 172.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 25

Calls

Call 1

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

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

rewrite240.0ms (1.3%)

Memory

-7.8MiB live, 150.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

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

eval94.0ms (0.5%)

Memory: -11.4MiB live, 26.5MiB allocated
Compiler: Compiled 7 430 to 981 computations (86.8% saved)

prune22.0ms (0.1%)

Memory

31.5MiB live, 31.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	261	5	266
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	262	5	267

Accuracy

100.0%

Counts

267 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	95.5%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	6.2%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
▶	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 120 to 82 computations (31.7% saved)

simplify116.0ms (0.6%)

Memory

-5.0MiB live, 31.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
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 y x)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
cost-diff	0	(*.f64 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	21	114
0	33	99
1	50	99
2	72	99
3	88	99
4	98	99
5	105	99
6	141	99
7	214	99
8	287	99
9	540	99
10	900	99
11	1776	99
12	2674	99
13	3068	99
14	3152	99
15	3161	99
16	3166	99
17	3166	99
18	3242	99
19	3274	99
20	3274	99
21	3346	99
22	3841	99
0	3841	97

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

localize76.0ms (0.4%)

Memory

7.4MiB live, 87.6MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	(*.f64 x x)
accuracy	0.05917993976203699	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	2.8802632993009074	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
accuracy	0.0	(/.f64 y x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.1171875	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
accuracy	60.04940343435151	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
accuracy	0.0	(*.f64 y y)
accuracy	0.0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	29.37375260464032	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0.0	(neg.f64 x)
accuracy	62.85401734836614	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0.0	(hypot.f64 y x)

Samples

65.0ms

256×

valid

Compiler

Compiled 94 to 18 computations (80.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-hypot: 13.0ms (40.1% of total)

ival-div: 7.0ms (21.6% of total)

ival-mult: 7.0ms (21.6% of total)

ival-add: 3.0ms (9.3% of total)

ival-neg: 1.0ms (3.1% of total)

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

exact: 0.0ms (0% of total)

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

series32.0ms (0.2%)

Memory

-9.2MiB live, 25.5MiB allocated

Counts

14 → 38

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

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

Calls

6 calls:

Time	Variable		Point	Expression
21.0ms	x	@	0	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x))
3.0ms	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 (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x))
2.0ms	y	@	-inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x))
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 (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x))
2.0ms	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 (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x))

simplify199.0ms (1.1%)

Memory

21.6MiB live, 247.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	518
1	351	518
2	1098	516
3	4317	474
4	7920	474
0	8036	433

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 36

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

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

rewrite252.0ms (1.3%)

Memory

-40.1MiB live, 220.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	104
0	33	89
1	113	89
2	774	89
0	8562	87

Stop Event

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

Counts

14 → 260

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

Outputs
(.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x)))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 x y) (-.f64 x y)))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (pow.f64 (.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (.f64 x y) #s(literal 2 binary64))))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (.f64 x y) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 y x))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (*.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y)))))
(sqrt.f64 (fma.f64 x x (*.f64 y y)))
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 y)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 y)))
(hypot.f64 (exp.f64 (log.f64 x)) y)
(hypot.f64 x (exp.f64 (log.f64 y)))
(hypot.f64 x y)
(hypot.f64 y (exp.f64 (log.f64 x)))
(hypot.f64 y x)
(exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 y y))) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(.f64 (.f64 (neg.f64 x) x) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (neg.f64 x))) x)
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 (neg.f64 x) x) x)
(/.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (neg.f64 (pow.f64 x #s(literal 3 binary64)))))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 x x) x))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))
(.f64 (pow.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
(exp.f64 (.f64 (log.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #s(literal 1/2 binary64)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y) y))))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x y)))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
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(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 y #s(literal 2 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (+.f64 y (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) y)))))
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(fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 y #s(literal -1 binary64)) x) y)
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(fma.f64 (pow.f64 y #s(literal -1 binary64)) (/.f64 (*.f64 x x) #s(literal 2 binary64)) y)
(fma.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64)) y)
(fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y)
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(fma.f64 #s(literal 1 binary64) y (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(fma.f64 (.f64 (pow.f64 (.f64 y #s(literal 2 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y) y)) (neg.f64 (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y) y))))
(fma.f64 (neg.f64 y) #s(literal -1 binary64) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) (.f64 x x)) y)
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y) y)
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(*.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))
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(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) y))
(*.f64 #s(literal 1/2 binary64) (pow.f64 y #s(literal -1 binary64)))
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(/.f64 #s(literal 1 binary64) (*.f64 y #s(literal 2 binary64)))
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(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) y))
(exp.f64 (.f64 (log.f64 (.f64 y #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
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eval34.0ms (0.2%)

Memory: 4.9MiB live, 80.8MiB allocated
Compiler: Compiled 7 524 to 977 computations (87% saved)

prune26.0ms (0.1%)

Memory

-4.3MiB live, 46.3MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	287	2	289
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	289	5	294

Accuracy

100.0%

Counts

294 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.9%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x y))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
▶	3.4%	#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 69 to 46 computations (33.3% saved)

simplify5.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 x y)
cost-diff	0	(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x y)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) 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	19	97
0	26	97
1	44	95
2	58	95
0	58	85

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize78.0ms (0.4%)

Memory

7.4MiB live, 45.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x y)
accuracy	0.0	(/.f64 x y)
accuracy	0.0078125	(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
accuracy	0.05917993976203699	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x y))
accuracy	0.01171875	(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
accuracy	0.05917993976203699	#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	6.0812574446218886	(/.f64 (*.f64 x x) y)
accuracy	61.76155830370232	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))

Samples

69.0ms

256×

valid

Compiler

Compiled 65 to 16 computations (75.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 7.0ms (36.2% of total)

ival-div: 5.0ms (25.9% of total)

ival-hypot: 5.0ms (25.9% of total)

ival-add: 2.0ms (10.3% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

8 → 29

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

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

Calls

6 calls:

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

simplify4.8s (25.8%)

Memory

3.3MiB live, 75.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	451
1	306	451
2	986	449
3	3693	413
4	7545	413
0	8277	378

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 27

Calls

Call 1

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

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

rewrite9.5s (50.4%)

Memory

-8.5MiB live, 74.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	88
0	26	88
1	101	86
2	701	86
3	7085	86
0	8447	76

Stop Event

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

Counts

8 → 264

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

eval67.0ms (0.4%)

Memory: 13.1MiB live, 49.2MiB allocated
Compiler: Compiled 8 486 to 1 066 computations (87.4% saved)

prune42.0ms (0.2%)

Memory

2.6MiB live, 40.0MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	287	6	293

Accuracy

100.0%

Counts

293 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.9%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x y))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
✓	3.4%	#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))))
▶	3.5%	#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))))

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify4.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
0	18	59
1	31	59
2	46	59
3	48	59
0	48	52

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize212.0ms (1.1%)

Memory

-36.0MiB live, 51.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.05917993976203699	#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))))
accuracy	0.1015625	(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
accuracy	61.76155830370232	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)))

Samples

205.0ms

256×

valid

Compiler

Compiled 35 to 13 computations (62.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 154.0ms

ival-hypot: 106.0ms (68.9% of total)

ival-mult: 43.0ms (28% of total)

ival-div: 3.0ms (2% of total)

ival-add: 1.0ms (0.7% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

5 → 28

Calls

Call 1

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

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

Calls

6 calls:

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

simplify510.0ms (2.7%)

Memory

-5.8MiB live, 189.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	444
1	304	444
2	980	442
3	3685	406
4	7525	406
0	8247	371

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 26

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

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

rewrite342.0ms (1.8%)

Memory

3.7MiB live, 160.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	56
0	18	56
1	73	56
2	479	56
3	5759	56
0	8111	49

Stop Event

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

Counts

5 → 86

Calls

Call 1

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

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

eval12.0ms (0.1%)

Memory: 14.0MiB live, 14.0MiB allocated
Compiler: Compiled 3 040 to 458 computations (84.9% saved)

prune86.0ms (0.5%)

Memory

-18.9MiB live, 20.1MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	109	6	115

Accuracy

100.0%

Counts

115 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	54.1%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.9%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x y))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
✓	3.4%	#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))))
✓	3.5%	#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))))

Compiler

Compiled 232 to 101 computations (56.5% saved)

regimes18.0ms (0.1%)

Memory

18.6MiB live, 18.6MiB allocated

Counts

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

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

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes79.0ms (0.4%)

Memory

-16.2MiB live, 30.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

14.0ms	x
3.0ms	y
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.9%	1	`(*.f64 x x)`
99.9%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes13.0ms (0.1%)

Memory

22.8MiB live, 22.8MiB 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 x y) (.f64 #s(literal 1/2 binary64) x))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
54.1%	1	`x`
54.1%	1	`y`
54.1%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
54.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
54.1%	1	`(*.f64 x x)`
54.1%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes20.0ms (0.1%)

Memory

-21.6MiB live, 14.7MiB 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:

14.0ms	(*.f64 y y)
1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	y
1.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
1.8%	1	`(*.f64 x x)`
1.8%	1	`x`
1.8%	1	`y`
1.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
1.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
1.8%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify69.0ms (0.4%)

Memory

8.3MiB live, 45.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	43
1	23	43
2	26	43
3	28	43
4	32	43
5	36	43
6	52	43
7	151	43
8	3611	43

Stop Event

1×	node limit

Calls

Call 1

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

soundness663.0ms (3.5%)

Memory

-15.6MiB live, 384.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	104
0	33	89
1	113	89
2	774	89
0	8562	87
0	6	21
0	10	21
1	29	21
2	196	21
3	1800	21
0	8651	15
0	104	429
1	296	429
2	958	427
3	3724	393
4	6463	391
0	8400	354

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 85 to 48 computations (43.5% saved)

preprocess37.0ms (0.2%)

Memory

-0.5MiB live, 76.3MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 158 to 90 computations (43% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample724.0ms (3.9%)

explain121.0ms (0.6%)

preprocess16.0ms (0.1%)

eval5.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize24.0ms (0.1%)

series5.0ms (0%)

simplify204.0ms (1.1%)

rewrite240.0ms (1.3%)

eval94.0ms (0.5%)

prune22.0ms (0.1%)

simplify116.0ms (0.6%)

localize76.0ms (0.4%)

series32.0ms (0.2%)

simplify199.0ms (1.1%)

rewrite252.0ms (1.3%)

eval34.0ms (0.2%)

prune26.0ms (0.1%)

simplify5.0ms (0%)

localize78.0ms (0.4%)

series9.0ms (0%)

simplify4.8s (25.8%)

rewrite9.5s (50.4%)

eval67.0ms (0.4%)

prune42.0ms (0.2%)

simplify4.0ms (0%)

localize212.0ms (1.1%)

series6.0ms (0%)

simplify510.0ms (2.7%)

rewrite342.0ms (1.8%)

eval12.0ms (0.1%)

prune86.0ms (0.5%)

regimes18.0ms (0.1%)

regimes79.0ms (0.4%)

regimes13.0ms (0.1%)

regimes20.0ms (0.1%)

simplify69.0ms (0.4%)

soundness663.0ms (3.5%)

preprocess37.0ms (0.2%)

end0.0ms (0%)

Profiling