Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

analyze18.0ms (0.3%)

Memory

21.0MiB live, 21.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample863.0ms (14.2%)

Memory

-7.5MiB live, 519.5MiB allocated

Samples

578.0ms	8 256×	0	valid
13.0ms	317×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 214.0ms

ival-sqrt: 94.0ms (43.8% of total)

ival-mult: 63.0ms (29.4% of total)

ival-add: 48.0ms (22.4% of total)

ival-true: 6.0ms (2.8% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

preprocess63.0ms (1%)

Memory

-24.3MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Rules

64×	`sub-neg`
34×	`distribute-lft-neg-in`
34×	`associate-+l-`
32×	`associate--r+`
32×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

explain106.0ms (1.8%)

Memory

-6.7MiB live, 32.8MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) y))`	oflow-rescue	76	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	76
↳	`(*.f64 x x)`	overflow	76

Confusion

	Predicted +	Predicted -
+	76	0
-	0	180

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	76	0	0
-	0	0	180

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	180
1	76

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 52 to 24 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (38.8% of total)

ival-sqrt: 4.0ms (38.8% of total)

ival-add: 2.0ms (19.4% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.4%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify5.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`lower-+.f32`
2×	`lift-sqrt.f64`
2×	`lift-+.f64`
2×	`lower-fma.f64`
2×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	9	16
0	9	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.3%)

Memory

17.6MiB live, 17.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	72.4%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

11.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (39.9% of total)

ival-sqrt: 2.0ms (39.9% of total)

ival-add: 1.0ms (19.9% of total)

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

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

series5.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (+.f64 (*.f64 x x) y)>
#<alt (sqrt.f64 (+.f64 (*.f64 x x) y))>
#<alt (*.f64 x x)>

Outputs
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(sqrt (+ (* x x) y))
1.0ms	y	@	inf	(sqrt (+ (* x x) y))
0.0ms	x	@	inf	(sqrt (+ (* x x) y))
0.0ms	x	@	0	(sqrt (+ (* x x) y))
0.0ms	x	@	inf	(+ (* x x) y)

rewrite492.0ms (8.1%)

Memory

-24.0MiB live, 264.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 034×	`lower-fma.f64`
5 034×	`lower-fma.f32`
4 204×	`lower-/.f64`
4 204×	`lower-/.f32`
3 240×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12

Stop Event

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

Counts

3 → 228

Calls

Call 1

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

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

simplify1.0s (16.9%)

Memory

27.6MiB live, 658.3MiB allocated

Algorithm

1×	egg-herbie

Rules

23 136×	`lower-fma.f64`
23 136×	`lower-fma.f32`
5 482×	`lower-*.f64`
5 482×	`lower-*.f32`
2 326×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	635
1	383	620
2	1206	612
3	4042	567
0	8636	515

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 55

Calls

Call 1

Inputs
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
y
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
y
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(neg.f64 (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(neg.f64 (fma.f64 x (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 y (fma.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 y (fma.f64 x (.f64 x (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 y (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval96.0ms (1.6%)

Memory: -4.3MiB live, 69.9MiB allocated
Compiler: Compiled 11 144 to 850 computations (92.4% saved)

prune150.0ms (2.5%)

Memory

5.0MiB live, 120.2MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	276	7	283
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	277	7	284

Accuracy

100.0%

Counts

284 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.5%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
	38.9%	(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 y))
	72.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))
▶	72.4%	(sqrt.f64 (fma.f64 x x y))
▶	36.2%	(sqrt.f64 (*.f64 x x))
▶	38.2%	(sqrt.f64 y)
▶	1.3%	(neg.f64 x)

Compiler

Compiled 108 to 72 computations (33.3% saved)

simplify34.0ms (0.6%)

Memory

16.9MiB live, 56.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	832	(sqrt.f64 (*.f64 x x))
✓	cost-diff	0	(sqrt.f64 y)
✓	cost-diff	0	(neg.f64 x)
✓	cost-diff	0	(fma.f64 x x y)
✓	cost-diff	0	(sqrt.f64 (fma.f64 x x y))

Rules

384×	`lower-fma.f32`
380×	`lower-fma.f64`
268×	`lower-*.f32`
266×	`lower-*.f64`
220×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
0	20	35
1	30	35
2	34	35
3	38	35
4	41	35
5	45	35
6	61	35
7	104	35
8	145	35
9	273	35
10	508	35
11	865	35
12	1200	35
13	1206	35
14	1220	35
15	1232	35
0	1232	35

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize43.0ms (0.7%)

Memory

-11.9MiB live, 110.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	99.9%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	68.5%	(sqrt.f64 (*.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 y)
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(fma.f64 x x y)
✓	accuracy	85.8%	(sqrt.f64 (fma.f64 x x y))

Samples

17.0ms	174×	0	valid
13.0ms	82×	0	invalid

Compiler

Compiled 42 to 14 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-sqrt: 5.0ms (31% of total)

ival-div: 4.0ms (24.8% of total)

ival-add: 3.0ms (18.6% of total)

ival-mult: 3.0ms (18.6% of total)

ival-neg: 1.0ms (6.2% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Memory

-24.0MiB live, 14.7MiB allocated

Counts

8 → 132

Calls

Call 1

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

Outputs
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (* 1/2 (/ y x))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* 1/2 (/ y x))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* 1/2 (/ y x))>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>

Calls

33 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(sqrt y)
0.0ms	y	@	-inf	(sqrt y)
0.0ms	y	@	inf	(+ (* y (/ 1/2 x)) x)
0.0ms	x	@	0	(+ (* y (/ 1/2 x)) x)
0.0ms	x	@	inf	(+ (* y (/ 1/2 x)) x)

rewrite357.0ms (5.9%)

Memory

21.1MiB live, 544.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 960×	`lower-fma.f32`
5 956×	`lower-fma.f64`
3 630×	`lower-*.f32`
3 628×	`lower-*.f64`
1 932×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
0	20	27
1	69	26
2	404	26
3	4626	26
0	8287	26

Stop Event

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

Counts

8 → 357

Calls

Call 1

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

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

simplify478.0ms (7.9%)

Memory

-15.2MiB live, 985.9MiB allocated

Algorithm

1×	egg-herbie

Rules

23 474×	`lower-fma.f64`
23 474×	`lower-fma.f32`
5 372×	`lower-*.f64`
5 372×	`lower-*.f32`
2 410×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	939
1	425	924
2	1313	916
3	4480	824
0	8674	754

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 116

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
x
x
x
x
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(* 1/2 (/ y x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* 1/2 (/ y x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)

Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 x (/.f64 (.f64 y (.f64 y #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (.f64 (.f64 y y) (fma.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 (/.f64 y x) #s(literal -1/2 binary64) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (fma.f64 (/.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (*.f64 (/.f64 y x) #s(literal -1/2 binary64)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(fma.f64 (neg.f64 x) (fma.f64 (.f64 y y) (fma.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (*.f64 (/.f64 y x) #s(literal -1/2 binary64)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (.f64 x #s(literal -1/2 binary64))) (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
y
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
y
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
x
x
x
x
x
x
x
x
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
x
(+ x (* 1/2 (/ y x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(+ x (* 1/2 (/ y x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(+ x (* 1/2 (/ y x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* 1/2 (/ y x))
(*.f64 #s(literal 1/2 binary64) (/.f64 y x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* 1/2 (/ y x))
(*.f64 #s(literal 1/2 binary64) (/.f64 y x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* 1/2 (/ y x))
(*.f64 #s(literal 1/2 binary64) (/.f64 y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)

eval80.0ms (1.3%)

Memory: 26.7MiB live, 143.1MiB allocated
Compiler: Compiled 8 013 to 974 computations (87.8% saved)

prune52.0ms (0.9%)

Memory

-3.6MiB live, 155.6MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	472	1	473
Fresh	0	2	2
Picked	3	2	5
Done	0	0	0
Total	475	5	480

Accuracy

100.0%

Counts

480 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.9%	(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 y))
▶	72.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))
✓	72.4%	(sqrt.f64 (fma.f64 x x y))
✓	38.2%	(sqrt.f64 y)
▶	64.0%	x

Compiler

Compiled 39 to 26 computations (33.3% saved)

simplify10.0ms (0.2%)

Memory

-19.7MiB live, 17.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) y)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 y))
✓	cost-diff	0	(fma.f64 x x y)
✓	cost-diff	0	(sqrt.f64 (fma.f64 x x y))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y)))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))

Rules

70×	`lower-*.f32`
66×	`lower-*.f64`
30×	`associate-r`
22×	`lower-fma.f32`
20×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
0	26	61
1	39	61
2	61	61
3	75	61
4	76	61
0	76	61

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (0.8%)

Memory

-4.6MiB live, 155.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 y)
✓	accuracy	99.9%	(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 y))
✓	accuracy	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
✓	accuracy	99.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 x x y)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y)))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))
✓	accuracy	85.8%	(sqrt.f64 (fma.f64 x x y))

Samples

24.0ms	174×	0	valid
9.0ms	82×	0	invalid

Compiler

Compiled 72 to 18 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-div: 6.0ms (30.2% of total)

ival-mult: 6.0ms (30.2% of total)

ival-sqrt: 6.0ms (30.2% of total)

ival-add: 2.0ms (10.1% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Memory

33.5MiB live, 33.5MiB allocated

Counts

9 → 180

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y)))>
#<alt (sqrt.f64 (fma.f64 x x y))>
#<alt (fma.f64 x x y)>
#<alt (fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 y))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) y))>
#<alt (/.f64 #s(literal 1 binary64) y)>
#<alt (sqrt.f64 y)>

Outputs
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt (/ 1 y))>
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))>
#<alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))>
#<alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)>
#<alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)>
#<alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x))>
#<alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x))>
#<alt (/ 1 x)>
#<alt (+ (* -1/2 (/ y (pow x 3))) (/ 1 x))>
#<alt (+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))>
#<alt (+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))>
#<alt (sqrt (/ 1 y))>
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))>
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))>
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))>
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))>
#<alt (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))>
#<alt (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))>
#<alt (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (sqrt (/ 1 y))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>

Calls

45 calls:

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

rewrite295.0ms (4.9%)

Memory

-5.0MiB live, 472.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 080×	`lower-fma.f32`
5 076×	`lower-fma.f64`
3 260×	`lower-*.f32`
3 256×	`lower-*.f64`
1 626×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
0	26	50
1	91	44
2	512	44
0	4364	42

Stop Event

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

Counts

9 → 395

Calls

Call 1

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

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

simplify437.0ms (7.2%)

Memory

-3.7MiB live, 1 002.8MiB allocated

Algorithm

1×	egg-herbie

Rules

19 312×	`lower-fma.f64`
19 312×	`lower-fma.f32`
4 950×	`lower-*.f64`
4 950×	`lower-*.f32`
3 760×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	238	2283
1	706	2186
2	2241	2157
3	5198	2121
0	8575	1980

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 173

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))
(/ 1 x)
(/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)
(/ -1 x)
(* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x))
(/ 1 x)
(+ (* -1/2 (/ y (pow x 3))) (/ 1 x))
(+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(* 1/2 (* (pow x 2) (sqrt (/ 1 y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* 1/2 (* (pow x 2) (sqrt (/ 1 y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* 1/2 (* (pow x 2) (sqrt (/ 1 y))))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(sqrt (/ 1 y))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))

Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 x (.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 x (/.f64 (.f64 y (.f64 y #s(literal -1/8 binary64))) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (fma.f64 y (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 (.f64 y (.f64 y y)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 (.f64 y (.f64 y #s(literal -1/8 binary64))) (.f64 (.f64 x x) (.f64 x x))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (fma.f64 (/.f64 (.f64 y y) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(fma.f64 x (fma.f64 (/.f64 (.f64 y (.f64 y y)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (.f64 y y) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64) #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y x))))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 y (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
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(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(/.f64 (fma.f64 (sqrt.f64 y) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (.f64 y (.f64 y y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(/.f64 (fma.f64 (sqrt.f64 y) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (.f64 y (.f64 y y)))) y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/2 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal -1/2 binary64)))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal -1/2 binary64)))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal -1/2 binary64)))
(* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal -1/2 binary64)))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)

eval65.0ms (1.1%)

Memory: 13.9MiB live, 165.7MiB allocated
Compiler: Compiled 13 018 to 1 483 computations (88.6% saved)

prune66.0ms (1.1%)

Memory

7.3MiB live, 162.3MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	567	1	568
Fresh	0	0	0
Picked	1	2	3
Done	0	2	2
Total	568	5	573

Accuracy

100.0%

Counts

573 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.9%	(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) x (sqrt.f64 y))
✓	72.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))
✓	72.4%	(sqrt.f64 (fma.f64 x x y))
✓	38.2%	(sqrt.f64 y)
✓	64.0%	x

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify8.0ms (0.1%)

Memory

-25.0MiB live, 13.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 y)
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y))
✓	cost-diff	(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) x (sqrt.f64 y))

Rules

42×	`lower-*.f32`
40×	`lower-*.f64`
16×	`lower-fma.f32`
14×	`lower-fma.f64`
12×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
0	12	24
1	19	24
2	28	24
3	38	24
4	40	24
0	40	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize29.0ms (0.5%)

Memory

17.9MiB live, 58.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 y)
✓	accuracy	99.9%	(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) x (sqrt.f64 y))
✓	accuracy	99.7%	(/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y))

Samples

10.0ms	174×	0	valid
5.0ms	82×	0	invalid

Compiler

Compiled 27 to 10 computations (63% saved)

Precisions

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

ival-mult: 3.0ms (39.4% of total)

ival-sqrt: 2.0ms (26.3% of total)

ival-div: 1.0ms (13.1% of total)

ival-add: 1.0ms (13.1% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#<alt (fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) x (sqrt.f64 y))>
#<alt (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y))>
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt (sqrt.f64 y)>

Outputs
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))>
#<alt (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)>
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 (* x (sqrt (/ 1 y))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(/ (* x 1/2) (sqrt y))
1.0ms	y	@	-inf	(+ (* (/ (* x 1/2) (sqrt y)) x) (sqrt y))
0.0ms	x	@	-inf	(* x 1/2)
0.0ms	x	@	0	(+ (* (/ (* x 1/2) (sqrt y)) x) (sqrt y))
0.0ms	x	@	inf	(+ (* (/ (* x 1/2) (sqrt y)) x) (sqrt y))

rewrite255.0ms (4.2%)

Memory

3.5MiB live, 601.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 448×	`lower-fma.f32`
4 446×	`lower-fma.f64`
3 568×	`lower-*.f32`
3 566×	`lower-*.f64`
3 280×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
0	12	21
1	41	21
2	278	21
3	3391	21
0	8425	21

Stop Event

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

Counts

4 → 232

Calls

Call 1

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

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

simplify296.0ms (4.9%)

Memory

-20.2MiB live, 422.0MiB allocated

Algorithm

1×	egg-herbie

Rules

5 348×	`lower-fma.f64`
5 348×	`lower-fma.f32`
3 476×	`lower-*.f64`
3 476×	`lower-*.f32`
3 094×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	564
1	108	564
2	286	564
3	858	564
4	2050	564
5	5264	564
6	7720	564
0	8041	546

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(* 1/2 (* (pow x 2) (sqrt (/ 1 y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* 1/2 (* (pow x 2) (sqrt (/ 1 y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 (pow x 2)) (sqrt y))))
(* 1/2 (* (pow x 2) (sqrt (/ 1 y))))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* (pow x 2) (sqrt y)))) y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 (* x (sqrt (/ 1 y))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))

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

eval36.0ms (0.6%)

Memory: 15.1MiB live, 94.7MiB allocated
Compiler: Compiled 7 939 to 703 computations (91.1% saved)

prune37.0ms (0.6%)

Memory

-14.6MiB live, 101.3MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	344	5	349

Accuracy

100.0%

Counts

349 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	38.9%	(fma.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) x (sqrt.f64 y))
✓	72.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))
✓	72.4%	(sqrt.f64 (fma.f64 x x y))
✓	38.2%	(sqrt.f64 y)
✓	64.0%	x

Compiler

Compiled 96 to 46 computations (52.1% saved)

regimes20.0ms (0.3%)

Memory

2.8MiB live, 46.2MiB allocated

Counts

10 → 2

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	y
4.0ms	x
4.0ms	(+.f64 (*.f64 x x) y)
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
85.6%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes9.0ms (0.1%)

Memory

-17.8MiB live, 21.6MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 y)
x

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
90.2%	2	`x`
75.3%	4	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
75.3%	4	`(+.f64 (*.f64 x x) y)`
90.2%	2	`(*.f64 x x)`

Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes8.0ms (0.1%)

Memory

25.7MiB live, 25.8MiB allocated

Accuracy

Total -40.1b remaining (-173.9%)

Threshold costs -40.1b (-173.9%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(neg.f64 x)

Outputs
x

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
64.0%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
64.0%	1	`(+.f64 (*.f64 x x) y)`
64.0%	1	`y`
64.0%	1	`x`
64.0%	1	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.13906448103013e+225	2.6622477297333783e+234

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.8474102151294094e-91	5.2439051985443305e-73

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify7.0ms (0.1%)

Memory

-24.3MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (*.f64 x x) #s(literal 9999999999999999613300728333138614158656013804472910722260188106898877933626732224819925546638620725877678611585164563028980399740553218842096696042786355031638703687528415058284784747112853848287855356936724432692495112994816 binary64)) (sqrt.f64 (fma.f64 x x y)) x)

(if (<=.f64 (*.f64 x x) #s(literal 4586997231980143/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496 binary64)) (sqrt.f64 y) x)

Outputs

(if (<=.f64 (*.f64 x x) #s(literal 9999999999999999613300728333138614158656013804472910722260188106898877933626732224819925546638620725877678611585164563028980399740553218842096696042786355031638703687528415058284784747112853848287855356936724432692495112994816 binary64)) (sqrt.f64 (fma.f64 x x y)) x)

(if (<=.f64 (*.f64 x x) #s(literal 4586997231980143/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496 binary64)) (sqrt.f64 y) x)

soundness477.0ms (7.8%)

Memory

2.9MiB live, 404.8MiB allocated

Rules

23 136×	`lower-fma.f64`
23 136×	`lower-fma.f32`
5 960×	`lower-fma.f32`
5 956×	`lower-fma.f64`
5 482×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
0	20	27
1	69	26
2	404	26
3	4626	26
0	8287	26
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12
0	133	635
1	383	620
2	1206	612
3	4042	567
0	8636	515

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 62 to 37 computations (40.3% saved)

preprocess64.0ms (1.1%)

Memory: 26.9MiB live, 103.9MiB allocated
Compiler: Compiled 154 to 82 computations (46.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

analyze18.0ms (0.3%)

sample863.0ms (14.2%)

preprocess63.0ms (1%)

explain106.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize17.0ms (0.3%)

series5.0ms (0.1%)

rewrite492.0ms (8.1%)

simplify1.0s (16.9%)

eval96.0ms (1.6%)

prune150.0ms (2.5%)

simplify34.0ms (0.6%)

localize43.0ms (0.7%)

series8.0ms (0.1%)

rewrite357.0ms (5.9%)

simplify478.0ms (7.9%)

eval80.0ms (1.3%)

prune52.0ms (0.9%)

simplify10.0ms (0.2%)

localize51.0ms (0.8%)

series12.0ms (0.2%)

rewrite295.0ms (4.9%)

simplify437.0ms (7.2%)

eval65.0ms (1.1%)

prune66.0ms (1.1%)

simplify8.0ms (0.1%)

localize29.0ms (0.5%)

series3.0ms (0.1%)

rewrite255.0ms (4.2%)

simplify296.0ms (4.9%)

eval36.0ms (0.6%)

prune37.0ms (0.6%)

regimes20.0ms (0.3%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

soundness477.0ms (7.8%)

preprocess64.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5