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

analyze24.0ms (0.8%)

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 7 to 5 computations (28.6% saved)

Precisions

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

ival-sqrt: 7.0ms (71.5% of total)

ival-add: 2.0ms (20.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample654.0ms (21.5%)

Results

383.0ms	8256×	0	valid
35.0ms	538×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 170.0ms

ival-sqrt: 97.0ms (57.2% of total)

ival-add: 63.0ms (37.1% of total)

const: 7.0ms (4.1% of total)

backward-pass: 3.0ms (1.8% of total)

Bogosity

preprocess25.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

144×	`sum3-define`
144×	`sum5-define`
144×	`sum4-define`
136×	`fmsub-define`
128×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	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)

explain39.0ms (1.3%)

FPErrors

Click to see full error table

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

Results

26.0ms

512×

valid

Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions

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

ival-add: 5.0ms (48.1% of total)

ival-sqrt: 5.0ms (48.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

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)

simplify4.0ms (0.1%)

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

localize19.0ms (0.6%)

Localize:

Found 2 expressions of interest:

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

Results

13.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (49.3% of total)

ival-sqrt: 2.0ms (49.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.2%)

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	y	@	inf	(sqrt (+ x y))
1.0ms	x	@	inf	(sqrt (+ x y))
0.0ms	y	@	0	(sqrt (+ x y))

rewrite442.0ms (14.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2796×	`/-lowering-/.f32`
2796×	`/-lowering-/.f64`
2488×	`-lowering-.f32`
2488×	`-lowering-.f64`
1966×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	20	7
2	157	7
3	1562	7
0	9159	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 216

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

simplify418.0ms (13.7%)

Algorithm

1×	egg-herbie

Rules

4460×	`-lowering-.f32`
4460×	`-lowering-.f64`
2462×	`fma-lowering-fma.f32`
2462×	`fma-lowering-fma.f64`
1876×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	606
1	486	568
2	1689	541
3	6147	539
0	8118	539

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)))))
(+.f64 (sqrt.f64 y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x)))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+.f64 (sqrt.f64 y) (.f64 x (+.f64 (.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 y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(+.f64 (sqrt.f64 y) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x #s(literal 1/16 binary64))))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(.f64 x (+.f64 (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 1/2 binary64)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 y (+.f64 (.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)))))))
(* 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 (+.f64 (+.f64 (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 1/2 binary64)))) (.f64 (.f64 y y) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 y #s(literal 1/16 binary64))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -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 (-.f64 #s(literal 0 binary64) (-.f64 (.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 (+.f64 (-.f64 (.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))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y)) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 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 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 y #s(literal 1/2 binary64))) (+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y)) #s(literal 1/8 binary64)) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) y) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 y #s(literal 1/2 binary64))))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (.f64 y (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 y #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)))))))
(+.f64 (sqrt.f64 x) (.f64 y (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 y (+.f64 (.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))))))))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 y (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x #s(literal -1/8 binary64))))))
(* 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 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x #s(literal -1/8 binary64)))) (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))))))
(* -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 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (-.f64 #s(literal 0 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 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (-.f64 #s(literal 0 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 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))))) (-.f64 #s(literal 0 binary64) y))
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
x
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.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 (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))

eval30.0ms (1%)

Compiler: Compiled 7773 to 906 computations (88.3% saved)

prune41.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	262	3	265

Accuracy

100.0%

Counts

265 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	100.0%	(sqrt.f64 (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))
▶	97.6%	(sqrt.f64 y)

Compiler

Compiled 20 to 14 computations (30% saved)

simplify287.0ms (9.4%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 x y)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 x y))
✓	cost-diff	256	(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	cost-diff	256	(sqrt.f64 (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))
✓	cost-diff	0	(sqrt.f64 y)

Rules

6372×	`-lowering-.f32`
6372×	`-lowering-.f64`
2746×	`cube-prod`
1808×	`/-lowering-/.f32`
1808×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	18	29
2	29	27
3	66	21
4	101	21
5	134	21
6	263	21
7	723	21
8	1925	21
9	2110	21
10	2402	21
11	2691	21
12	2992	21
13	3384	21
14	5339	21
15	6414	21
16	7039	21
17	7149	21
18	7243	21
19	7800	21
0	8833	21

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize54.0ms (1.8%)

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	100.0%	(sqrt.f64 (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))
✓	accuracy	100.0%	(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	accuracy	100.0%	(sqrt.f64 y)

Results

44.0ms

256×

valid

Compiler

Compiled 32 to 9 computations (71.9% saved)

Precisions

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

ival-add: 7.0ms (44.3% of total)

ival-sqrt: 4.0ms (25.3% of total)

ival-div: 2.0ms (12.6% of total)

ival-mult: 2.0ms (12.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series9.0ms (0.3%)

Counts

5 → 108

Calls

Call 1

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

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(sqrt y)
1.0ms	x	@	inf	(* y (+ 1 (/ x y)))
1.0ms	y	@	-inf	(sqrt (* y (+ 1 (/ x y))))
0.0ms	y	@	-inf	(sqrt y)
0.0ms	x	@	-inf	(/ x y)

rewrite193.0ms (6.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1830×	`-lowering-.f32`
1830×	`-lowering-.f64`
1598×	`/-lowering-/.f32`
1598×	`/-lowering-/.f64`
1276×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	43	25
2	323	17
3	5210	17
0	8156	17

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 164

Calls

Call 1

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

simplify394.0ms (13%)

Algorithm

1×	egg-herbie

Rules

3140×	`-lowering-.f32`
3140×	`-lowering-.f64`
2370×	`+-lowering-+.f64`
2370×	`+-lowering-+.f32`
1902×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	771
1	519	709
2	1902	699
3	3873	686
0	8614	686

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

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

eval70.0ms (2.3%)

Compiler: Compiled 4480 to 716 computations (84% saved)

prune24.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Accuracy

100.0%

Counts

275 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	100.0%	(sqrt.f64 (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))
✓	97.6%	(sqrt.f64 y)

Compiler

Compiled 36 to 24 computations (33.3% saved)

regimes8.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

regimes3.0ms (0.1%)

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

2 calls:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify7.0ms (0.2%)

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)

soundness255.0ms (8.4%)

Rules

4460×	`-lowering-.f32`
4460×	`-lowering-.f64`
2462×	`fma-lowering-fma.f32`
2462×	`fma-lowering-fma.f64`
1876×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	606
1	486	568
2	1689	541
3	6147	539
0	8118	539

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 12 to 8 computations (33.3% saved)

preprocess37.0ms (1.2%)

Remove: (sort x y)
Compiler: Compiled 52 to 34 computations (34.6% saved)

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

analyze24.0ms (0.8%)

sample654.0ms (21.5%)

preprocess25.0ms (0.8%)

explain39.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize19.0ms (0.6%)

series5.0ms (0.2%)

rewrite442.0ms (14.5%)

simplify418.0ms (13.7%)

eval30.0ms (1%)

prune41.0ms (1.4%)

simplify287.0ms (9.4%)

localize54.0ms (1.8%)

series9.0ms (0.3%)

rewrite193.0ms (6.3%)

simplify394.0ms (13%)

eval70.0ms (2.3%)

prune24.0ms (0.8%)

regimes8.0ms (0.3%)

regimes3.0ms (0.1%)

simplify7.0ms (0.2%)

soundness255.0ms (8.4%)

preprocess37.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	26
0	4	4
1	5	4
0	5	4

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	26
0	4	4
1	5	4
0	5	4

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	26
0	4	4
1	5	4
0	5	4