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

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 10 to 5 computations (50% saved)

sample982.0ms (3.6%)

Memory

9.2MiB live, 882.5MiB allocated

Samples

741.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 371.0ms

ival-hypot: 361.0ms (97.4% of total)

ival-true: 6.0ms (1.6% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain106.0ms (0.4%)

Memory

-27.0MiB live, 143.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
137	-	4	(-6.0899266242930135e-189 -8.667787038236518e-160)	`(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	115	0
↳	`(*.f64 y y)`	overflow	68
↳	`(*.f64 x x)`	overflow	67
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	115
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	18	0
↳	`(*.f64 y y)`	underflow	61
↳	`(*.f64 x x)`	underflow	65
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	18

Confusion

	Predicted +	Predicted -
+	133	4
-	0	119

Precision

1.0

Recall

0.9708029197080292

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	4
-	0	0	119

Precision?

1.0

Recall?

0.9708029197080292

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

512×

valid

Compiler

Compiled 81 to 28 computations (65.4% saved)

Precisions

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

ival-hypot: 8.0ms (44.6% of total)

ival-mult: 7.0ms (39.1% of total)

ival-add: 2.0ms (11.2% of total)

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

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

preprocess17.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB 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	204	42
5	217	42
6	219	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
(hypot.f64 y x)

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.9%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.1%)

Memory

16.9MiB live, 16.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	31.40418597419603	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

15.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-hypot: 4.0ms (47.2% of total)

ival-mult: 3.0ms (35.4% of total)

ival-add: 1.0ms (11.8% of total)

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

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

series12.0ms (0%)

Memory

-26.2MiB live, 11.9MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf y) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	y	@	-inf	((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms	y	@	0	((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms	y	@	inf	((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms	x	@	inf	((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))
1.0ms	x	@	0	((+ (* x x) (* y y)) (* x x) (* y y) (sqrt (+ (* x x) (* y y))))

simplify183.0ms (0.7%)

Memory

37.1MiB live, 226.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	620
1	296	620
2	953	618
3	3667	584
4	6426	582
0	8051	530

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

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

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

rewrite269.0ms (1%)

Memory

-25.3MiB live, 253.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

Outputs
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eval89.0ms (0.3%)

Memory: 27.6MiB live, 65.1MiB allocated
Compiler: Compiled 8 055 to 991 computations (87.7% saved)

prune10.0ms (0%)

Memory

-7.5MiB live, 28.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	308	5	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	309	5	314

Accuracy

100.0%

Counts

314 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.9%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	50.5%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
▶	99.9%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
▶	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 118 to 80 computations (32.2% saved)

simplify7.0ms (0%)

Memory

15.1MiB live, 15.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	-5120	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
cost-diff	0	(/.f64 x y)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize14.1s (52.3%)

Memory

-27.6MiB live, 94.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	31.40418597419603	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0	(*.f64 y y)
accuracy	0.28806961482087234	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	31.40418597419603	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(*.f64 x x)
accuracy	31.40418597419603	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
accuracy	51.770924600617924	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
accuracy	0	(neg.f64 x)
accuracy	62.821626141198685	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.08034471307362684	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))

Samples

14.1s

256×

valid

Compiler

Compiled 217 to 37 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.8s

ival-hypot: 4.8s (98.9% of total)

ival-mult: 48.0ms (1% of total)

ival-add: 3.0ms (0.1% of total)

ival-div: 2.0ms (0% of total)

ival-neg: 1.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

series9.2s (33.8%)

Memory

-2.4MiB live, 36.7MiB allocated

Counts

14 → 288

Calls

Call 1

Inputs
#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 x y) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 y y) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 y y (*.f64 x x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 y) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (fma.f64 y y (*.f64 x x))) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify228.0ms (0.8%)

Memory

5.3MiB live, 123.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	2908
1	326	2908
2	1025	2898
3	3967	2668
4	7525	2668
0	8271	2436

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 265

Calls

Call 1

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

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

rewrite493.0ms (1.8%)

Memory

19.8MiB live, 139.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	109
0	31	103
1	89	103
2	570	103
3	6802	103
0	8328	91

Stop Event

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

Counts

14 → 340

Calls

Call 1

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

Outputs
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eval227.0ms (0.8%)

Memory: -17.1MiB live, 140.6MiB allocated
Compiler: Compiled 14 792 to 1 295 computations (91.2% saved)

prune104.0ms (0.4%)

Memory

16.3MiB live, 52.9MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	631	0	631
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	631	5	636

Accuracy

100.0%

Counts

636 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.9%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	50.5%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
✓	99.9%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 126 to 63 computations (50% saved)

regimes16.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

regimes80.0ms (0.3%)

Memory

-29.6MiB live, 10.0MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

6 calls:

69.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	y
2.0ms	x
2.0ms	(*.f64 y y)
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
50.9%	1	`x`
50.9%	1	`y`
50.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
50.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
50.9%	1	`(*.f64 x x)`
50.9%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes12.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
50.5%	1	`x`
50.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
50.5%	1	`(+.f64 (.f64 x x) (.f64 y y))`
50.5%	1	`(*.f64 x x)`
50.5%	1	`(*.f64 y y)`
50.5%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes10.0ms (0%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
4.6%	1	`x`
4.6%	1	`(*.f64 x x)`
4.6%	1	`y`
4.6%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
4.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
4.6%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes8.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify124.0ms (0.5%)

Memory

-50.6MiB live, 19.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	59
1	26	59
2	28	59
3	29	59

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness643.0ms (2.4%)

Memory

4.1MiB live, 279.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15
0	104	620
1	296	620
2	953	618
3	3667	584
4	6426	582
0	8051	530

Stop Event

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

Compiler

Compiled 92 to 46 computations (50% saved)

preprocess104.0ms (0.4%)

Memory: 31.2MiB live, 148.8MiB allocated
Compiler: Compiled 274 to 146 computations (46.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102

start0.0ms (0%)

analyze0.0ms (0%)

sample982.0ms (3.6%)

explain106.0ms (0.4%)

preprocess17.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize20.0ms (0.1%)

series12.0ms (0%)

simplify183.0ms (0.7%)

rewrite269.0ms (1%)

eval89.0ms (0.3%)

prune10.0ms (0%)

simplify7.0ms (0%)

localize14.1s (52.3%)

series9.2s (33.8%)

simplify228.0ms (0.8%)

rewrite493.0ms (1.8%)

eval227.0ms (0.8%)

prune104.0ms (0.4%)

regimes16.0ms (0.1%)

regimes80.0ms (0.3%)

regimes12.0ms (0%)

regimes10.0ms (0%)

regimes8.0ms (0%)

simplify124.0ms (0.5%)

soundness643.0ms (2.4%)

preprocess104.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102