Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A

analyze18.0ms (0.4%)

Memory

-11.8MiB live, 24.6MiB 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
25%	25%	74.9%	0.1%	0%	0%	0%	3
28.6%	25%	62.4%	0.1%	0%	12.5%	0%	4
46.2%	37.5%	43.7%	0.1%	0%	18.7%	0%	5
52.2%	37.5%	34.3%	0.1%	0%	28.1%	0%	6
65.1%	43.7%	23.4%	0.1%	0%	32.8%	0%	7
70.9%	43.7%	18%	0.1%	0%	38.2%	0%	8
79.5%	46.8%	12.1%	0.1%	0%	41%	0%	9
83.6%	46.8%	9.2%	0.1%	0%	43.9%	0%	10
88.7%	48.4%	6.1%	0.1%	0%	45.4%	0%	11
91.3%	48.4%	4.6%	0.1%	0%	46.9%	0%	12

Compiler

Compiled 6 to 6 computations (0% saved)

sample817.0ms (19.9%)

Memory

20.1MiB live, 894.4MiB allocated

Samples

576.0ms	8 256×	0	valid
17.0ms	515×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-add: 173.0ms (68.9% of total)

ival-sqrt: 69.0ms (27.5% of total)

ival-true: 6.0ms (2.4% of total)

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

Bogosity

preprocess15.0ms (0.4%)

Memory

18.4MiB live, 18.4MiB allocated

Algorithm

2×	egg-herbie

Rules

44×	`sub-neg`
32×	`associate--r+`
24×	`neg-mul-1`
22×	`cancel-sign-sub-inv`
22×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	27	26
2	42	26
3	64	26
4	123	26
5	162	26
6	201	26
7	212	26
8	214	26
0	4	4
1	5	4
0	5	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ x y))

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

Call 2

Inputs
(sqrt (+ x y))
(sqrt (+ (neg x) y))
(sqrt (+ x (neg y)))
(neg (sqrt (+ (neg x) y)))
(neg (sqrt (+ x (neg y))))
(sqrt (+ y x))

Outputs
(sqrt (+ x y))
(sqrt (+ (neg x) y))
(sqrt (- y x))
(sqrt (+ x (neg y)))
(sqrt (- x y))
(neg (sqrt (+ (neg x) y)))
(neg (sqrt (- y x)))
(neg (sqrt (+ x (neg y))))
(neg (sqrt (- x y)))
(sqrt (+ y x))
(sqrt (+ x y))

Symmetry

(sort x y)

explain49.0ms (1.2%)

Memory

-14.6MiB live, 74.7MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(sqrt.f64 (+.f64 x y))`
-	-	`y`
-	-	`(+.f64 x y)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

19.0ms

512×

valid

Compiler

Compiled 34 to 20 computations (41.2% saved)

Precisions

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

ival-add: 4.0ms (49.4% of total)

ival-sqrt: 4.0ms (49.4% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`
2×	`sqrt-lowering-sqrt.f32`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
1	5	9
0	5	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ x y))
(+ x y)
x
y

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

localize15.0ms (0.4%)

Memory

-13.3MiB live, 25.0MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

10.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

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

ival-sqrt: 4.0ms (76.4% of total)

ival-add: 1.0ms (19.1% of total)

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

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

series5.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (sqrt (+ x y))>
#<alt (+ x y)>

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

Calls

12 calls:

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

rewrite417.0ms (10.1%)

Memory

-1.3MiB live, 586.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 128×	`accelerator-lowering-fma.f32`
5 128×	`accelerator-lowering-fma.f64`
4 292×	`/-lowering-/.f32`
4 292×	`/-lowering-/.f64`
3 378×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	20	7
2	143	7
3	1362	7
0	8302	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 226

Calls

Call 1

Inputs
(sqrt (+ x y))
(+ x y)

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

simplify976.0ms (23.7%)

Memory

-5.5MiB live, 1 162.3MiB allocated

Algorithm

1×	egg-herbie

Rules

28 536×	`accelerator-lowering-fma.f32`
28 536×	`accelerator-lowering-fma.f64`
5 638×	`-lowering-.f32`
5 638×	`-lowering-.f64`
2 832×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1425	582
3	4619	570
0	8274	534

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval114.0ms (2.8%)

Memory: -16.7MiB live, 72.1MiB allocated
Compiler: Compiled 7 918 to 856 computations (89.2% saved)

prune33.0ms (0.8%)

Memory

8.8MiB live, 87.2MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	272	3	275

Accuracy

100.0%

Counts

275 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	98.4%	(sqrt.f64 y)

Compiler

Compiled 20 to 14 computations (30% saved)

simplify4.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

4×	`sqrt-lowering-sqrt.f64`
4×	`+-lowering-+.f64`
4×	`/-lowering-/.f32`
4×	`/-lowering-/.f64`
4×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	11	28
0	11	28

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt y)
y
(/ 1 (sqrt (/ 1 (+ x y))))
1
(sqrt (/ 1 (+ x y)))
(/ 1 (+ x y))
(+ x y)
x
y

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

localize29.0ms (0.7%)

Memory

-17.4MiB live, 62.9MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x y))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
✓	accuracy	100.0%	(sqrt.f64 y)

Samples

21.0ms

256×

valid

Compiler

Compiled 30 to 10 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sqrt: 6.0ms (56.3% of total)

ival-div: 3.0ms (28.1% of total)

ival-add: 1.0ms (9.4% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

5 → 108

Calls

Call 1

Inputs
#<alt (sqrt y)>
#<alt (/ 1 (sqrt (/ 1 (+ x y))))>
#<alt (sqrt (/ 1 (+ x y)))>
#<alt (/ 1 (+ x y))>
#<alt (+ x y)>

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

Calls

27 calls:

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

rewrite114.0ms (2.8%)

Memory

2.1MiB live, 197.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 284×	`-lowering-.f32`
1 284×	`-lowering-.f64`
998×	`/-lowering-/.f32`
998×	`/-lowering-/.f64`
876×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	44	19
2	256	19
0	2175	19

Stop Event

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

Counts

5 → 285

Calls

Call 1

Inputs
(sqrt y)
(/ 1 (sqrt (/ 1 (+ x y))))
(sqrt (/ 1 (+ x y)))
(/ 1 (+ x y))
(+ x y)

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

simplify849.0ms (20.7%)

Memory

22.0MiB live, 653.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 404×	`accelerator-lowering-fma.f32`
12 404×	`accelerator-lowering-fma.f64`
4 472×	`+-lowering-+.f64`
4 472×	`+-lowering-+.f32`
4 284×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	339	1630
1	1009	1540
2	3063	1462
3	7057	1456
0	8332	1364

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

Outputs
(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)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.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 x #s(literal -1/8 binary64)))) (sqrt.f64 y))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/16 binary64) (.f64 x (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))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(.f64 x (fma.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
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(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) x))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
y
(* y (+ 1 (/ x y)))
(fma.f64 y (/.f64 x y) y)
(* y (+ 1 (/ x y)))
(fma.f64 y (/.f64 x y) y)
(* y (+ 1 (/ x y)))
(fma.f64 y (/.f64 x y) y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 y (-.f64 #s(literal -1 binary64) (/.f64 x y))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 y (-.f64 #s(literal -1 binary64) (/.f64 x y))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 y (-.f64 #s(literal -1 binary64) (/.f64 x y))))

eval90.0ms (2.2%)

Memory: -15.0MiB live, 101.2MiB allocated
Compiler: Compiled 7 543 to 1 302 computations (82.7% saved)

prune106.0ms (2.6%)

Memory

18.9MiB live, 95.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	393	3	396

Accuracy

100.0%

Counts

396 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.4%	(sqrt.f64 y)

Compiler

Compiled 36 to 23 computations (36.1% saved)

regimes108.0ms (2.6%)

Memory

-27.4MiB live, 10.4MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

102.0ms	(sqrt.f64 (+.f64 x y))
2.0ms	(+.f64 x y)
2.0ms	y
2.0ms	x

Results

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes5.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 y)

Outputs
(sqrt.f64 y)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`y`
98.4%	1	`(sqrt.f64 (+.f64 x y))`
98.4%	1	`(+.f64 x y)`

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify7.0ms (0.2%)

Memory

14.4MiB live, 14.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness264.0ms (6.4%)

Memory

-40.8MiB live, 91.2MiB allocated

Rules

28 536×	`accelerator-lowering-fma.f32`
28 536×	`accelerator-lowering-fma.f64`
5 638×	`-lowering-.f32`
5 638×	`-lowering-.f64`
2 832×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1425	582
3	4619	570
0	8274	534

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 12 to 8 computations (33.3% saved)

preprocess63.0ms (1.5%)

Memory: 15.9MiB live, 51.9MiB allocated
Remove: (sort x y)
Compiler: Compiled 52 to 34 computations (34.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze18.0ms (0.4%)

sample817.0ms (19.9%)

preprocess15.0ms (0.4%)

explain49.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize15.0ms (0.4%)

series5.0ms (0.1%)

rewrite417.0ms (10.1%)

simplify976.0ms (23.7%)

eval114.0ms (2.8%)

prune33.0ms (0.8%)

simplify4.0ms (0.1%)

localize29.0ms (0.7%)

series8.0ms (0.2%)

rewrite114.0ms (2.8%)

simplify849.0ms (20.7%)

eval90.0ms (2.2%)

prune106.0ms (2.6%)

regimes108.0ms (2.6%)

regimes5.0ms (0.1%)

simplify7.0ms (0.2%)

soundness264.0ms (6.4%)

preprocess63.0ms (1.5%)

end0.0ms (0%)

Profiling