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

analyze18.0ms (0.4%)

Memory

14.2MiB live, 14.2MiB 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)

sample987.0ms (23.5%)

Memory

25.2MiB live, 413.3MiB allocated

Samples

486.0ms	8 256×	0	valid
43.0ms	337×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 250.0ms

ival-add: 99.0ms (39.6% of total)

ival-mult: 81.0ms (32.4% of total)

ival-sqrt: 60.0ms (24% of total)

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

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

Bogosity

preprocess54.0ms (1.3%)

Memory

-28.2MiB live, 7.7MiB 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)

explain80.0ms (1.9%)

Memory

-5.7MiB live, 50.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
94	-	-	`(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	94	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	94
↳	`(*.f64 x x)`	overflow	94

Confusion

	Predicted +	Predicted -
+	94	0
-	0	162

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	94	0	0
-	0	0	162

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	162
1	94

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: 11.0ms

ival-mult: 4.0ms (37.5% of total)

ival-sqrt: 4.0ms (37.5% of total)

ival-add: 2.0ms (18.7% 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

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.8%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify5.0ms (0.1%)

Memory

1.5MiB live, 1.5MiB 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 (0.4%)

Memory

18.3MiB live, 18.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	65.8%	(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 (38.7% of total)

ival-sqrt: 2.0ms (38.7% of total)

ival-add: 1.0ms (19.3% of total)

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

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

series5.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB 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)

rewrite694.0ms (16.5%)

Memory

15.1MiB live, 481.4MiB 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)

simplify507.0ms (12.1%)

Memory

-32.7MiB live, 931.7MiB 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)

eval33.0ms (0.8%)

Memory: 7.9MiB live, 83.5MiB allocated
Compiler: Compiled 11 144 to 850 computations (92.4% saved)

prune78.0ms (1.9%)

Memory

-2.0MiB live, 81.4MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	278	5	283
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	278	6	284

Accuracy

100.0%

Counts

284 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.5%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
▶	65.8%	(sqrt.f64 (fma.f64 x x y))
✓	65.8%	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	33.7%	(sqrt.f64 (*.f64 x x))
▶	34.2%	(sqrt.f64 y)
▶	1.2%	(neg.f64 x)

Compiler

Compiled 66 to 43 computations (34.8% saved)

simplify37.0ms (0.9%)

Memory

-5.0MiB live, 72.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

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	147	35
9	275	35
10	510	35
11	870	35
12	1201	35
13	1207	35
14	1221	35
15	1233	35
0	1233	35

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (1%)

Memory

18.4MiB live, 98.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x y)
✓	accuracy	82.9%	(sqrt.f64 (fma.f64 x x y))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	65.1%	(sqrt.f64 (*.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 y)
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	99.9%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)

Samples

18.0ms	175×	0	valid
10.0ms	81×	0	invalid

Compiler

Compiled 42 to 14 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sqrt: 5.0ms (35.5% of total)

ival-mult: 3.0ms (21.3% of total)

ival-div: 2.0ms (14.2% of total)

ival-add: 2.0ms (14.2% of total)

ival-neg: 1.0ms (7.1% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

8 → 132

Calls

Call 1

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

Outputs
#<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)>
#<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 (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)))>

Calls

33 calls:

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

rewrite316.0ms (7.5%)

Memory

-19.2MiB live, 616.6MiB 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	4611	26
0	8274	26

Stop Event

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

Counts

8 → 357

Calls

Call 1

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

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

simplify480.0ms (11.4%)

Memory

24.8MiB live, 1 143.8MiB 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	871
1	425	856
2	1317	848
3	4473	824
0	8647	754

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 116

Calls

Call 1

Inputs
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)
(* -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)
(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)))

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

eval93.0ms (2.2%)

Memory: -23.4MiB live, 171.1MiB allocated
Compiler: Compiled 8 013 to 967 computations (87.9% saved)

prune61.0ms (1.5%)

Memory

12.9MiB live, 144.5MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	472	1	473
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	474	5	479

Accuracy

100.0%

Counts

479 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.5%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
✓	65.8%	(sqrt.f64 (fma.f64 x x y))
✓	65.8%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	34.2%	(sqrt.f64 y)
▶	68.0%	x

Compiler

Compiled 30 to 19 computations (36.7% saved)

simplify5.0ms (0.1%)

Memory

-30.3MiB live, 9.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated
1×	saturated

Calls

Call 1

Inputs
x

Outputs
x

localize6.0ms (0.2%)

Memory

18.0MiB live, 18.0MiB allocated

Samples

4.0ms

256×

valid

Compiler

Compiled 3 to 4 computations (-33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

series0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite8.0ms (0.2%)

Memory

18.6MiB live, 18.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify5.0ms (0.1%)

Memory

-28.2MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.5%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
✓	65.8%	(sqrt.f64 (fma.f64 x x y))
✓	65.8%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	34.2%	(sqrt.f64 y)
✓	68.0%	x

Compiler

Compiled 58 to 32 computations (44.8% saved)

regimes16.0ms (0.4%)

Memory

11.3MiB live, 49.5MiB allocated

Counts

7 → 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))

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`x`
83.9%	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)

regimes12.0ms (0.3%)

Memory

2.6MiB live, 44.8MiB allocated

Counts

6 → 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)

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

Calls

4 calls:

4.0ms	(*.f64 x x)
3.0ms	(+.f64 (*.f64 x x) y)
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

Results

Accuracy	Segments	Branch
100.0%	2	`x`
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 23 to 14 computations (39.1% saved)

regimes9.0ms (0.2%)

Memory

-12.4MiB live, 27.3MiB 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:

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

Results

Accuracy	Segments	Branch
90.9%	2	`x`
73.8%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
73.8%	2	`(+.f64 (*.f64 x x) y)`
90.9%	2	`(*.f64 x x)`

Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes8.0ms (0.2%)

Memory

-16.6MiB live, 22.8MiB allocated

Accuracy

Total -42.7b remaining (-208.5%)

Threshold costs -42.7b (-208.5%)

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

Results

Accuracy	Segments	Branch
68.0%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
68.0%	1	`(+.f64 (*.f64 x x) y)`
68.0%	1	`y`
68.0%	1	`x`
68.0%	1	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.3260428599263812e+241	9.242086173206937e+250

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.3260428599263812e+241	9.242086173206937e+250

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2849145567252772e-63	2.6721560163149185e-62

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify6.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	16	35

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 20000000000000001019220591274005456279710505470622733232619203286613548419128326636838181727778134043521316213363512555228359822654904417182365028760483854715262087764856296628876189602931571523608705123012237845488278935519238250121771614208 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 20000000000000001019220591274005456279710505470622733232619203286613548419128326636838181727778134043521316213363512555228359822654904417182365028760483854715262087764856296628876189602931571523608705123012237845488278935519238250121771614208 binary64)) (sqrt.f64 (fma.f64 x x y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 7410693711188237/3705346855594118253554271520278013051304639509300498049262642688253220148477952 binary64)) (sqrt.f64 y) x)
x

Outputs
(if (<=.f64 (.f64 x x) #s(literal 20000000000000001019220591274005456279710505470622733232619203286613548419128326636838181727778134043521316213363512555228359822654904417182365028760483854715262087764856296628876189602931571523608705123012237845488278935519238250121771614208 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 20000000000000001019220591274005456279710505470622733232619203286613548419128326636838181727778134043521316213363512555228359822654904417182365028760483854715262087764856296628876189602931571523608705123012237845488278935519238250121771614208 binary64)) (sqrt.f64 (fma.f64 x x y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 7410693711188237/3705346855594118253554271520278013051304639509300498049262642688253220148477952 binary64)) (sqrt.f64 y) x)
x

soundness517.0ms (12.3%)

Memory

-12.7MiB live, 429.0MiB 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	133	635
1	383	620
2	1206	612
3	4042	567
0	8636	515
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12
0	11	29
0	20	27
1	69	26
2	404	26
3	4611	26
0	8274	26

Stop Event

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

Compiler

Compiled 84 to 46 computations (45.2% saved)

preprocess94.0ms (2.2%)

Memory: 25.5MiB live, 144.4MiB allocated
Compiler: Compiled 182 to 88 computations (51.6% 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 (0.4%)

sample987.0ms (23.5%)

preprocess54.0ms (1.3%)

explain80.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize17.0ms (0.4%)

series5.0ms (0.1%)

rewrite694.0ms (16.5%)

simplify507.0ms (12.1%)

eval33.0ms (0.8%)

prune78.0ms (1.9%)

simplify37.0ms (0.9%)

localize41.0ms (1%)

series6.0ms (0.1%)

rewrite316.0ms (7.5%)

simplify480.0ms (11.4%)

eval93.0ms (2.2%)

prune61.0ms (1.5%)

simplify5.0ms (0.1%)

localize6.0ms (0.2%)

series0.0ms (0%)

rewrite8.0ms (0.2%)

simplify5.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes16.0ms (0.4%)

regimes12.0ms (0.3%)

regimes9.0ms (0.2%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

soundness517.0ms (12.3%)

preprocess94.0ms (2.2%)

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