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

analyze28.0ms (0.4%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

Precisions

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

ival-mult: 3.0ms (36.6% of total)

ival-sqrt: 3.0ms (36.6% of total)

ival-add: 2.0ms (24.4% of total)

const: 0.0ms (0% of total)

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

sample752.0ms (9.8%)

Results

545.0ms	8256×	0	valid
20.0ms	383×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 270.0ms

ival-sqrt: 97.0ms (35.9% of total)

ival-mult: 86.0ms (31.8% of total)

ival-add: 76.0ms (28.1% of total)

const: 8.0ms (3% of total)

backward-pass: 3.0ms (1.1% of total)

Bogosity

preprocess33.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

308×	`fnmadd-define`
264×	`fmsub-define`
254×	`fnmsub-define`
228×	`sum3-define`
220×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	42	32
2	87	32
3	184	32
4	387	32
5	612	32
6	946	32
7	1133	32
8	1171	32
9	1183	32
0	5	5
1	8	5
0	8	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(abs x)

explain64.0ms (0.8%)

FPErrors

Click to see full error table

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

Results

42.0ms

512×

valid

Compiler

Compiled 46 to 17 computations (63% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 4.0ms (33.3% of total)

ival-sqrt: 4.0ms (33.3% of total)

ival-add: 3.0ms (24.9% of total)

const: 0.0ms (0% of total)

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

eval0.0ms (0%)

Compiler: Compiled 8 to 5 computations (37.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`
2×	`fma-lowering-fma.f32`
2×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	8	13
0	8	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize28.0ms (0.4%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Results

22.0ms

256×

valid

Compiler

Compiled 19 to 6 computations (68.4% saved)

Precisions

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

ival-mult: 4.0ms (48.9% of total)

ival-add: 2.0ms (24.4% of total)

ival-sqrt: 2.0ms (24.4% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite480.0ms (6.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2820×	`/-lowering-/.f32`
2820×	`/-lowering-/.f64`
2654×	`-lowering-.f32`
2654×	`-lowering-.f64`
1538×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	25	11
2	186	11
3	1828	11
0	8987	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 209

Calls

Call 1

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

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

simplify369.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

4180×	`-lowering-.f32`
4180×	`-lowering-.f64`
1660×	`+-lowering-+.f64`
1660×	`+-lowering-+.f32`
1632×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	590
1	408	509
2	1413	496
3	5183	470
0	8421	470

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+.f64 (sqrt.f64 y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+.f64 (sqrt.f64 y) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(+.f64 (sqrt.f64 y) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (.f64 (.f64 x 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 (*.f64 x x) #s(literal 1/16 binary64))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(+.f64 (+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x)))) (.f64 x (/.f64 (.f64 y (.f64 (*.f64 y #s(literal 1/16 binary64)) y)) (pow.f64 x #s(literal 6 binary64)))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(-.f64 (*.f64 (/.f64 y x) #s(literal -1/2 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(-.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))) (.f64 x (/.f64 (.f64 y (.f64 (*.f64 y #s(literal 1/16 binary64)) y)) (pow.f64 x #s(literal 6 binary64))))))
x
(+ x (* 1/2 (/ y x)))
(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 y (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 y (+.f64 (/.f64 (.f64 y #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) x))))))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (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) (.f64 x x)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 y (+.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) (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -1/8 binary64)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 y (+.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) (.f64 x x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.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 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (-.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) (.f64 x x)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 y (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/8 binary64))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 y (-.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x (.f64 x (.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 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))
y
(+ y (pow x 2))
(+.f64 y (*.f64 x x))
(+ y (pow x 2))
(+.f64 y (*.f64 x x))
(+ y (pow x 2))
(+.f64 y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(+.f64 y (*.f64 x x))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(+.f64 y (*.f64 x x))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(+.f64 y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(+.f64 y (*.f64 x x))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(+.f64 y (*.f64 x x))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(+.f64 y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(+.f64 y (*.f64 x x))
(+ y (pow x 2))
(+.f64 y (*.f64 x x))
(+ y (pow x 2))
(+.f64 y (*.f64 x x))
y
(* y (+ 1 (/ (pow x 2) y)))
(+.f64 y (*.f64 x x))
(* y (+ 1 (/ (pow x 2) y)))
(+.f64 y (*.f64 x x))
(* y (+ 1 (/ (pow x 2) y)))
(+.f64 y (*.f64 x x))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(+.f64 y (*.f64 x x))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(+.f64 y (*.f64 x x))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(+.f64 y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval127.0ms (1.7%)

Compiler: Compiled 9667 to 835 computations (91.4% saved)

prune52.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	265	4	269
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	265	5	270

Accuracy

100.0%

Counts

270 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.8%	(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
▶	67.4%	(+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	34.2%	(sqrt.f64 y)
▶	68.4%	x

Compiler

Compiled 43 to 28 computations (34.9% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
✓	cost-diff	0	(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
✓	cost-diff	0	(/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 x x))) x)
✓	cost-diff	0	(+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	0	(+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	128	(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(sqrt.f64 y)

Rules

196×	`fma-define`
188×	`fma-lowering-fma.f32`
188×	`fma-lowering-fma.f64`
174×	`-lowering-.f32`
174×	`-lowering-.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	91
1	36	86
2	84	82
3	161	82
4	254	80
5	292	80
6	305	80
7	321	80
8	322	80
0	322	80

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(sqrt y)
y
(+ x (* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))))
x
(* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x)))
y
(+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))
(/ (* -1/8 (/ y (* x x))) x)
(* -1/8 (/ y (* x x)))
-1/8
(/ y (* x x))
(* x x)
(/ 1/2 x)
1/2
(+ x (/ (* y 1/2) x))
x
(/ (* y 1/2) x)
(* y 1/2)
y
1/2

Outputs
x
(sqrt y)
(sqrt.f64 y)
y
(+ x (* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))))
(+.f64 x (.f64 (/.f64 y x) (+.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))))
x
(* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x)))
(.f64 (/.f64 y x) (+.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))
y
(+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))
(+.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(/ (* -1/8 (/ y (* x x))) x)
(/.f64 (.f64 y #s(literal -1/8 binary64)) (.f64 x (*.f64 x x)))
(* -1/8 (/ y (* x x)))
(/.f64 (.f64 y #s(literal -1/8 binary64)) (.f64 x x))
-1/8
#s(literal -1/8 binary64)
(/ y (* x x))
(/.f64 (/.f64 y x) x)
(* x x)
(*.f64 x x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(+ x (/ (* y 1/2) x))
(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
x
(/ (* y 1/2) x)
(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* y 1/2)
(*.f64 y #s(literal 1/2 binary64))
y
1/2
#s(literal 1/2 binary64)

localize117.0ms (1.5%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 x x)))
✓	accuracy	99.9%	(/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 x x))) x)
✓	accuracy	95.9%	(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	92.2%	(/.f64 y (*.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 y)

Results

46.0ms	171×	0	valid
26.0ms	85×	0	invalid

Compiler

Compiled 101 to 17 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-div: 7.0ms (32% of total)

ival-mult: 7.0ms (32% of total)

ival-add: 5.0ms (22.9% of total)

ival-sqrt: 2.0ms (9.2% of total)

const: 1.0ms (4.6% of total)

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

series58.0ms (0.7%)

Counts

10 → 216

Calls

Call 1

Inputs
#<alt (sqrt y)>
#<alt (* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x)))>
#<alt (+ x (* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))))>
#<alt (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))>
#<alt (/ (* -1/8 (/ y (* x x))) x)>
#<alt (+ x (/ (* y 1/2) x))>
#<alt (/ (* y 1/2) x)>
#<alt (* y 1/2)>
#<alt (/ y (* x x))>
#<alt (* -1/8 (/ y (* x x)))>

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 (* 1/2 (/ y x))>
#<alt (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))>
#<alt (* 1/2 (/ y x))>
#<alt (/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)>
#<alt (/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)>
#<alt (/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)>
#<alt (* 1/2 (/ y x))>
#<alt (* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 2) (pow x 2)))) x))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 1)))>
#<alt (* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 1)))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (/ 1/2 x)>
#<alt (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* y (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* y (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* y (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1 (* y (- (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* x y))))))>
#<alt (* -1 (* y (- (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* x y))))))>
#<alt (* -1 (* y (- (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* x y))))))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* -1/8 (/ y (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* -1/8 (/ y (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* -1/8 (/ y (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/8 (/ y (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/8 (/ y (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/8 (/ y (pow x 2))) 1/2) x))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* -1/8 (/ y (pow x 3)))>
#<alt (* 1/2 (/ y x))>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (* 1/2 (/ y x))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* 1/2 (/ y x))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 (/ y x))>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (/ y (pow x 2))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1/8 (/ y (pow x 2)))>

Calls

54 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x)))
1.0ms	y	@	0	(* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x)))
1.0ms	y	@	inf	(* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x)))
1.0ms	y	@	0	(sqrt y)
1.0ms	y	@	inf	(/ (* -1/8 (/ y (* x x))) x)

rewrite490.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4688×	`-lowering-.f32`
4688×	`-lowering-.f64`
3948×	`/-lowering-/.f32`
3948×	`/-lowering-/.f64`
2828×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	77
1	103	68
2	1148	68
0	8814	68

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 633

Calls

Call 1

Inputs
(sqrt y)
(* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x)))
(+ x (* y (+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))))
(+ (/ (* -1/8 (/ y (* x x))) x) (/ 1/2 x))
(/ (* -1/8 (/ y (* x x))) x)
(+ x (/ (* y 1/2) x))
(/ (* y 1/2) x)
(* y 1/2)
(/ y (* x x))
(* -1/8 (/ y (* x x)))

Outputs
(exp.f64 (*.f64 (log.f64 y) #s(literal 1/2 binary64)))
(sqrt.f64 y)
(pow.f64 y #s(literal 1/2 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 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)))
(+.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(+.f64 (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x) (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(-.f64 (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x) (*.f64 #s(literal -1/2 binary64) (/.f64 y x)))
(-.f64 (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x) (/.f64 (*.f64 y #s(literal -1/2 binary64)) x))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x) (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x)) (/.f64 (-.f64 (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 y #s(literal 1/2 binary64))) x)) (/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (/.f64 (-.f64 (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 y #s(literal 1/2 binary64))) x)))
(fma.f64 y (/.f64 (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x) x) (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 #s(literal -1/8 binary64) (.f64 (/.f64 y (.f64 x (*.f64 x x))) y) (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) (.f64 (/.f64 #s(literal 1 binary64) x) y) (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x) x) y (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) y) (/.f64 (.f64 (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 (.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (.f64 (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 #s(literal 1 binary64) (/.f64 y (/.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (.f64 y #s(literal 1/2 binary64)) (/.f64 (.f64 (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x) y) x))
(fma.f64 (.f64 y #s(literal -1/8 binary64)) (/.f64 y (.f64 x (*.f64 x x))) (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (/.f64 #s(literal 1 binary64) x) (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/512 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 y (.f64 y y))) (/.f64 (.f64 y (.f64 y y)) (/.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (+.f64 (.f64 (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x) (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x)) (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 (/.f64 (.f64 (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x) y) x) (/.f64 y (/.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x) (/.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y) x)) (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y))) (/.f64 (-.f64 (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (*.f64 y #s(literal 1/2 binary64))) x))
(/.f64 (.f64 y (+.f64 (.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
(/.f64 (.f64 y (+.f64 (.f64 #s(literal -1/512 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (/.f64 y (.f64 x (.f64 x x))) (/.f64 y (.f64 x (.f64 x x))))) (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64))) (*.f64 x x))))
(/.f64 (.f64 y (/.f64 (-.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) #s(literal 1/4 binary64)) (.f64 x x))) (/.f64 (-.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64)) x))
(/.f64 (.f64 (+.f64 (.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 x #s(literal 1/2 binary64))) y) (*.f64 x x))
(/.f64 (.f64 (+.f64 (.f64 #s(literal -1/512 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) y) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (/.f64 y (.f64 x (.f64 x x))) (/.f64 y (.f64 x (.f64 x x))))) (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64))) (*.f64 x x))))
(/.f64 (.f64 (/.f64 (-.f64 (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) #s(literal 1/4 binary64)) (.f64 x x)) y) (/.f64 (-.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64)) x))
(/.f64 (+.f64 (.f64 y (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 (/.f64 x #s(literal 1/2 binary64)) y)) (.f64 (/.f64 x #s(literal 1/2 binary64)) (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 y x) (.f64 (/.f64 x #s(literal 1/2 binary64)) (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)))) (*.f64 (/.f64 x #s(literal 1/2 binary64)) x))
(/.f64 (+.f64 (.f64 y (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 (/.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal 1 binary64)))) (.f64 (/.f64 x #s(literal 1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 y (-.f64 #s(literal 0 binary64) x)) (.f64 (/.f64 x #s(literal 1/2 binary64)) (.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64))))) (.f64 (/.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (.f64 y x) (.f64 (/.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y))) (*.f64 (/.f64 x #s(literal 1/2 binary64)) x))
(/.f64 (+.f64 (.f64 y (-.f64 #s(literal 0 binary64) x)) (.f64 (/.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64)) y))) (.f64 (/.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (.f64 y (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 (/.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) y))) (.f64 (/.f64 x #s(literal 1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 x y)) (.f64 x (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) x) (.f64 x (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)))) (.f64 x x))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 x (.f64 y #s(literal 1 binary64)))) (.f64 x (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 x (.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64))))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) x) (.f64 x (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y))) (.f64 x x))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 x (.f64 (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64)) y))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 x (.f64 #s(literal 1 binary64) y))) (.f64 x (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal -1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 (-.f64 #s(literal 0 binary64) x) y)) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal -1/2 binary64)) x) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal -1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 y #s(literal 1 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64))))) (*.f64 x x))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal -1/2 binary64)) x) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64)) y))) (*.f64 x x))
(/.f64 (+.f64 (.f64 (.f64 y #s(literal -1/2 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1 binary64) y))) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) y)) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)))) (*.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) x))
(/.f64 (+.f64 (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (.f64 y #s(literal 1 binary64)))) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64))))) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y))) (*.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) x))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (.f64 (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64)) y))) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (.f64 #s(literal 1 binary64) y))) (.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) y)) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (.f64 y (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)))) (*.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) x))
(/.f64 (+.f64 (/.f64 x (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x)) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (.f64 y #s(literal 1 binary64)))) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (/.f64 x (/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (.f64 y (.f64 (/.f64 y (.f64 x x)) #s(literal 1/8 binary64))))) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/8 binary64)) x) x) y))) (*.f64 (/.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) x))
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(.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) x))
(.f64 (.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal 1 binary64) (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 y #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 y #s(literal 2 binary64)))
(*.f64 (/.f64 y x) #s(literal 1/2 binary64))
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) y)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 y (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (*.f64 x x)))
(/.f64 y (*.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 y x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) y))))
(/.f64 (/.f64 y x) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (*.f64 x x) y) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 y x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) y)) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 y x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 y #s(literal 1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (.f64 y #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) y))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 y x))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(pow.f64 (/.f64 (*.f64 x x) y) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) y) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 y x)) #s(literal -1 binary64))
(.f64 y (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 y x))
(*.f64 (/.f64 y x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) y)
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 y (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) y))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 y #s(literal -1/8 binary64))))
(/.f64 (.f64 y #s(literal -1/8 binary64)) (.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 y #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (/.f64 (*.f64 x x) y)))
(/.f64 (neg.f64 (.f64 y #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) y)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 y x)) x)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (*.f64 (/.f64 y x) #s(literal -1/8 binary64)) x)
(/.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x) x)
(/.f64 (neg.f64 (neg.f64 (.f64 y #s(literal -1/8 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) y))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (neg.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 y x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1/8 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (neg.f64 (*.f64 (/.f64 y x) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (/.f64 (*.f64 y #s(literal -1/8 binary64)) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (.f64 x x) (.f64 y #s(literal -1/8 binary64))) #s(literal -1 binary64))
(.f64 y (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64)))
(.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 x x)))
(.f64 (/.f64 y (.f64 x x)) #s(literal -1/8 binary64))
(.f64 (.f64 y #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 y x) (/.f64 #s(literal -1/8 binary64) x))
(.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) (.f64 x x)))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 y x))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) x) (/.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (-.f64 #s(literal 0 binary64) y) x))

simplify284.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

2808×	`-lowering-.f32`
2808×	`-lowering-.f64`
1340×	`sum4-define`
1218×	`fnmadd-define`
1168×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	1662
1	306	1530
2	859	1488
3	2665	1426
4	6267	1426
0	8114	1426

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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)))
(* 1/2 (/ y x))
(* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))
(* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))
(* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(* 1/2 (/ y x))
(/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)
(/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)
(/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)
(* 1/2 (/ y x))
(* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 2) (pow x 2)))) x))
(* -1/8 (/ (pow y 2) (pow x 3)))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))
(/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 1)))
(* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 1)))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))
(/ 1/2 x)
(+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))
(* -1/8 (/ y (pow x 3)))
(* y (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* y (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* y (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ y (pow x 3)))
(* -1 (* y (- (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* x y))))))
(* -1 (* y (- (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* x y))))))
(* -1 (* y (- (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* x y))))))
(* -1/8 (/ y (pow x 3)))
(/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/2 x)
(/ (+ 1/2 (* -1/8 (/ y (pow x 2)))) x)
(/ (+ 1/2 (* -1/8 (/ y (pow x 2)))) x)
(/ (+ 1/2 (* -1/8 (/ y (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ y (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/8 (/ y (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/8 (/ y (pow x 2))) 1/2) x))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* -1/8 (/ y (pow x 3)))
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
x
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(* 1/2 (/ y x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* 1/2 (/ y x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 (/ y x))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))
(* -1/8 (/ y (pow x 2)))

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)
(* 1/2 (/ y x))
(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(.f64 y (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)) x))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(.f64 y (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)) x))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(.f64 y (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)) x))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(/.f64 (.f64 y (+.f64 (.f64 y #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(/.f64 (.f64 y (+.f64 (.f64 y #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(/.f64 (.f64 y (+.f64 (.f64 y #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(* 1/2 (/ y x))
(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(/ (+ (* -1/8 (/ (pow y 2) (pow x 2))) (* 1/2 y)) x)
(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
(* 1/2 (/ y x))
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(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
(* -1/8 (/ y (pow x 2)))
(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))

eval164.0ms (2.1%)

Compiler: Compiled 23501 to 2763 computations (88.2% saved)

prune124.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	844	5	849
Fresh	0	0	0
Picked	2	2	4
Done	0	1	1
Total	846	8	854

Accuracy

100.0%

Counts

854 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.3%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
▶	3.5%	(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
▶	68.8%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y)))
▶	67.4%	(+.f64 x (.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))))
▶	68.8%	(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	34.2%	(sqrt.f64 y)
✓	68.4%	x

Compiler

Compiled 149 to 94 computations (36.9% saved)

simplify266.0ms (3.5%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓	cost-diff	0	(.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (*.f64 y y))
✓	cost-diff	0	(-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))
✓	cost-diff	0	(/.f64 y x)
✓	cost-diff	0	(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
✓	cost-diff	0	(+.f64 x (.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))))
✓	cost-diff	0	(/.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (/.f64 x #s(literal 1/2 binary64)) y)
✓	cost-diff	0	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y)))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y))
✓	cost-diff	0	(*.f64 y #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
✓	cost-diff	0	(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))

Rules

2668×	`-lowering-.f32`
2668×	`-lowering-.f64`
2312×	`fnmadd-define`
1564×	`/-lowering-/.f32`
1564×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	164
1	76	156
2	192	156
3	409	153
4	946	153
5	2393	153
6	5869	153
0	8461	153

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ x (* (/ 1/2 x) y))
x
(* (/ 1/2 x) y)
(/ 1/2 x)
1/2
y
(/ (* y 1/2) x)
(* y 1/2)
y
1/2
x
(+ x (/ 1 (/ (/ x 1/2) y)))
x
(/ 1 (/ (/ x 1/2) y))
1
(/ (/ x 1/2) y)
(/ x 1/2)
1/2
y
(+ x (* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x)))))
x
(* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x))))
(/ y x)
y
(+ 1/2 (* -1/8 (/ (/ y x) x)))
1/2
(* -1/8 (/ (/ y x) x))
-1/8
(/ (/ y x) x)
(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (/ y (/ x 1/2)) x))
(- (* (/ 1/4 (* x x)) (* y y)) (* x x))
(* (/ 1/4 (* x x)) (* y y))
(/ 1/4 (* x x))
1/4
(* x x)
x
(* y y)
y
(- (/ y (/ x 1/2)) x)
(/ y (/ x 1/2))
(/ x 1/2)
1/2

Outputs
(+ x (* (/ 1/2 x) y))
(+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x y)))
x
(* (/ 1/2 x) y)
(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
y
(/ (* y 1/2) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
(* y 1/2)
(*.f64 #s(literal 1/2 binary64) y)
y
1/2
#s(literal 1/2 binary64)
x
(+ x (/ 1 (/ (/ x 1/2) y)))
(+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x y)))
x
(/ 1 (/ (/ x 1/2) y))
(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
1
#s(literal 1 binary64)
(/ (/ x 1/2) y)
(/.f64 x (*.f64 #s(literal 1/2 binary64) y))
(/ x 1/2)
(/.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
y
(+ x (* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x)))))
(+.f64 x (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x (/.f64 x y)))) (/.f64 x y)))
x
(* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x (/.f64 x y)))) (/.f64 x y))
(/ y x)
(/.f64 y x)
y
(+ 1/2 (* -1/8 (/ (/ y x) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x (/.f64 x y))))
1/2
#s(literal 1/2 binary64)
(* -1/8 (/ (/ y x) x))
(/.f64 #s(literal -1/8 binary64) (*.f64 x (/.f64 x y)))
-1/8
#s(literal -1/8 binary64)
(/ (/ y x) x)
(/.f64 y (*.f64 x x))
(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (/ y (/ x 1/2)) x))
(/.f64 (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) x) x) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))
(- (* (/ 1/4 (* x x)) (* y y)) (* x x))
(-.f64 (/.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) x) x) (*.f64 x x))
(* (/ 1/4 (* x x)) (* y y))
(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) x) x)
(/ 1/4 (* x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
x
(* y y)
(*.f64 y y)
y
(- (/ y (/ x 1/2)) x)
(-.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 x y)) x)
(/ y (/ x 1/2))
(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
(/ x 1/2)
(/.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize196.0ms (2.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 y (/.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓	accuracy	77.3%	(.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (*.f64 y y))
✓	accuracy	51.8%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))
✓	accuracy	100.0%	(*.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))
✓	accuracy	99.9%	(.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x))))
✓	accuracy	99.8%	(/.f64 (/.f64 y x) x)
✓	accuracy	100.0%	(/.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y)))
✓	accuracy	99.6%	(/.f64 (/.f64 x #s(literal 1/2 binary64)) y)
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y))
✓	accuracy	100.0%	(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
✓	accuracy	99.8%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)

Results

118.0ms

256×

valid

Compiler

Compiled 189 to 30 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-div: 18.0ms (46.5% of total)

ival-mult: 12.0ms (31% of total)

ival-add: 5.0ms (12.9% of total)

ival-sub: 2.0ms (5.2% of total)

const: 1.0ms (2.6% of total)

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

series25.0ms (0.3%)

Counts

20 → 432

Calls

Call 1

Inputs
#<alt (+ x (* (/ 1/2 x) y))>
#<alt (* (/ 1/2 x) y)>
#<alt (/ 1/2 x)>
#<alt (/ (* y 1/2) x)>
#<alt (* y 1/2)>
#<alt (/ 1 (/ (/ x 1/2) y))>
#<alt (+ x (/ 1 (/ (/ x 1/2) y)))>
#<alt (/ (/ x 1/2) y)>
#<alt (/ x 1/2)>
#<alt (+ x (* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x)))))>
#<alt (* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x))))>
#<alt (/ y x)>
#<alt (+ 1/2 (* -1/8 (/ (/ y x) x)))>
#<alt (/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (/ y (/ x 1/2)) x))>
#<alt (- (* (/ 1/4 (* x x)) (* y y)) (* x x))>
#<alt (* (/ 1/4 (* x x)) (* y y))>
#<alt (/ 1/4 (* x x))>
#<alt (/ (/ y x) x)>
#<alt (* -1/8 (/ (/ y x) x))>
#<alt (/ y (/ x 1/2))>

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

Calls

108 calls:

Time	Variable		Point	Expression
7.0ms	x	@	0	(/ (/ x 1/2) y)
1.0ms	x	@	0	(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (/ y (/ x 1/2)) x))
1.0ms	y	@	inf	(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (/ y (/ x 1/2)) x))
1.0ms	y	@	0	(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (/ y (/ x 1/2)) x))
1.0ms	x	@	-inf	(/ (/ x 1/2) y)

rewrite420.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2882×	`/-lowering-/.f32`
2882×	`/-lowering-/.f64`
2434×	`fma-lowering-fma.f32`
2434×	`fma-lowering-fma.f64`
2286×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	132
1	204	125
2	1868	125
0	8235	125

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 884

Calls

Call 1

Inputs
(+ x (* (/ 1/2 x) y))
(* (/ 1/2 x) y)
(/ 1/2 x)
(/ (* y 1/2) x)
(* y 1/2)
(/ 1 (/ (/ x 1/2) y))
(+ x (/ 1 (/ (/ x 1/2) y)))
(/ (/ x 1/2) y)
(/ x 1/2)
(+ x (* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x)))))
(* (/ y x) (+ 1/2 (* -1/8 (/ (/ y x) x))))
(/ y x)
(+ 1/2 (* -1/8 (/ (/ y x) x)))
(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (/ y (/ x 1/2)) x))
(- (* (/ 1/4 (* x x)) (* y y)) (* x x))
(* (/ 1/4 (* x x)) (* y y))
(/ 1/4 (* x x))
(/ (/ y x) x)
(* -1/8 (/ (/ y x) x))
(/ y (/ x 1/2))

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

simplify340.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

3066×	`-lowering-.f32`
3066×	`-lowering-.f64`
1570×	`sum3-define`
1212×	`+-lowering-+.f64`
1212×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	3072
1	348	2701
2	969	2648
3	3165	2487
4	6897	2487
0	8154	2487

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

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

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

eval217.0ms (2.8%)

Compiler: Compiled 30436 to 2493 computations (91.8% saved)

prune191.0ms (2.5%)

Pruning

19 alts after pruning (13 fresh and 6 done)

	Pruned	Kept	Total
New	1385	13	1398
Fresh	0	0	0
Picked	2	3	5
Done	0	3	3
Total	1387	19	1406

Accuracy

100.0%

Counts

1406 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.5%	(/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 y y) x)) x) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
	3.5%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y))
	35.3%	(/.f64 (-.f64 (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) x) x) (.f64 y y)) (*.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
	35.3%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y)) x))
▶	35.3%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	37.7%	(/.f64 (-.f64 (.f64 (.f64 y (/.f64 #s(literal 1/4 binary64) (.f64 x x))) y) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
✓	3.5%	(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
▶	35.3%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
	37.7%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) y) x)) (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))))))
	3.5%	(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
▶	68.8%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
▶	68.8%	(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y))))
✓	67.4%	(+.f64 x (.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))))
✓	68.8%	(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
	22.2%	(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (.f64 y (.f64 y y)) (/.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))) (+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)))))
▶	3.5%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	34.2%	(sqrt.f64 y)
✓	68.4%	x

Compiler

Compiled 578 to 343 computations (40.7% saved)

simplify176.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
✓	cost-diff	0	(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
✓	cost-diff	0	(/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
✓	cost-diff	0	(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓	cost-diff	0	(.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (*.f64 y y))
✓	cost-diff	0	(-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) y)
✓	cost-diff	0	(*.f64 x (/.f64 #s(literal 2 binary64) y))
✓	cost-diff	0	(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y)))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) y)
✓	cost-diff	0	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))

Rules

3628×	`-lowering-.f32`
3628×	`-lowering-.f64`
2136×	`/-lowering-/.f32`
2136×	`/-lowering-/.f64`
1518×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	211
1	91	192
2	212	185
3	591	185
4	1853	185
5	4118	185
0	8263	185

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ x (/ 1 (/ (/ 1 y) (/ 1/2 x))))
x
(/ 1 (/ (/ 1 y) (/ 1/2 x)))
1
(/ (/ 1 y) (/ 1/2 x))
(/ 1 y)
y
(/ 1/2 x)
1/2
(* (/ 1/2 x) y)
(/ 1/2 x)
1/2
x
y
(+ x (/ 1 (* x (/ 2 y))))
x
(/ 1 (* x (/ 2 y)))
1
(* x (/ 2 y))
(/ 2 y)
2
y
(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (* (/ 1/2 x) y) x))
(- (* (/ 1/4 (* x x)) (* y y)) (* x x))
(* (/ 1/4 (* x x)) (* y y))
(/ 1/4 (* x x))
1/4
(* x x)
x
(* y y)
y
(- (* (/ 1/2 x) y) x)
(* (/ 1/2 x) y)
(/ 1/2 x)
1/2
(/ 1 (/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x))))
1
(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))
(- (/ (* 1/2 y) x) x)
(/ (* 1/2 y) x)
(* 1/2 y)
1/2
y
x
(- (/ (* y y) (/ (* x x) 1/4)) (* x x))
(/ (* y y) (/ (* x x) 1/4))
(* y y)
(/ (* x x) 1/4)
(* x x)
1/4

Outputs
(+ x (/ 1 (/ (/ 1 y) (/ 1/2 x))))
(+.f64 x (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
x
(/ 1 (/ (/ 1 y) (/ 1/2 x)))
(/.f64 y (/.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(/ (/ 1 y) (/ 1/2 x))
(/.f64 x (/.f64 y #s(literal 2 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
y
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(* (/ 1/2 x) y)
(/.f64 y (/.f64 x #s(literal 1/2 binary64)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x
y
(+ x (/ 1 (* x (/ 2 y))))
(+.f64 x (/.f64 y (/.f64 x #s(literal 1/2 binary64))))
x
(/ 1 (* x (/ 2 y)))
(/.f64 y (/.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(* x (/ 2 y))
(/.f64 x (/.f64 y #s(literal 2 binary64)))
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
2
#s(literal 2 binary64)
y
(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (* (/ 1/2 x) y) x))
(/.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 x (.f64 x #s(literal -4 binary64))))) (+.f64 x (/.f64 (/.f64 y x) #s(literal -2 binary64))))
(- (* (/ 1/4 (* x x)) (* y y)) (* x x))
(-.f64 (/.f64 y (/.f64 (/.f64 (.f64 x x) y) #s(literal 1/4 binary64))) (.f64 x x))
(* (/ 1/4 (* x x)) (* y y))
(/.f64 y (/.f64 (/.f64 (*.f64 x x) y) #s(literal 1/4 binary64)))
(/ 1/4 (* x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
x
(* y y)
(*.f64 y y)
y
(- (* (/ 1/2 x) y) x)
(-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x)
(* (/ 1/2 x) y)
(/.f64 y (/.f64 x #s(literal 1/2 binary64)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(/ 1 (/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x))))
(/.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 x (.f64 x #s(literal -4 binary64))))) (+.f64 x (/.f64 (/.f64 y x) #s(literal -2 binary64))))
1
#s(literal 1 binary64)
(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))
(/.f64 (+.f64 x (/.f64 (/.f64 y x) #s(literal -2 binary64))) (+.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 x (.f64 x #s(literal -4 binary64))))))
(- (/ (* 1/2 y) x) x)
(-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x)
(/ (* 1/2 y) x)
(/.f64 y (/.f64 x #s(literal 1/2 binary64)))
(* 1/2 y)
(/.f64 y #s(literal 2 binary64))
1/2
#s(literal 1/2 binary64)
y
x
(- (/ (* y y) (/ (* x x) 1/4)) (* x x))
(-.f64 (/.f64 y (/.f64 (/.f64 (.f64 x x) y) #s(literal 1/4 binary64))) (.f64 x x))
(/ (* y y) (/ (* x x) 1/4))
(/.f64 y (/.f64 (/.f64 (*.f64 x x) y) #s(literal 1/4 binary64)))
(* y y)
(*.f64 y y)
(/ (* x x) 1/4)
(/.f64 (*.f64 x x) #s(literal 1/4 binary64))
(* x x)
(*.f64 x x)
1/4
#s(literal 1/4 binary64)

localize224.0ms (2.9%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (*.f64 x x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
✓	accuracy	77.0%	(/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))
✓	accuracy	50.4%	(/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)))
✓	accuracy	99.8%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
✓	accuracy	99.5%	(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓	accuracy	77.3%	(.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (*.f64 y y))
✓	accuracy	51.8%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) y)
✓	accuracy	100.0%	(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y))))
✓	accuracy	99.3%	(*.f64 x (/.f64 #s(literal 2 binary64) y))
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y)))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	99.8%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
✓	accuracy	99.6%	(/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))

Results

169.0ms

256×

valid

Compiler

Compiled 249 to 32 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-sub: 25.0ms (40.4% of total)

ival-div: 23.0ms (37.1% of total)

ival-mult: 10.0ms (16.1% of total)

ival-add: 3.0ms (4.8% of total)

const: 1.0ms (1.6% of total)

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

series12.0ms (0.2%)

Counts

20 → 432

Calls

Call 1

Inputs
#<alt (/ 1 (/ (/ 1 y) (/ 1/2 x)))>
#<alt (/ (/ 1 y) (/ 1/2 x))>
#<alt (+ x (/ 1 (/ (/ 1 y) (/ 1/2 x))))>
#<alt (/ 1 y)>
#<alt (* (/ 1/2 x) y)>
#<alt (/ 1/2 x)>
#<alt (/ 1 (* x (/ 2 y)))>
#<alt (+ x (/ 1 (* x (/ 2 y))))>
#<alt (* x (/ 2 y))>
#<alt (/ 2 y)>
#<alt (/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (* (/ 1/2 x) y) x))>
#<alt (- (* (/ 1/4 (* x x)) (* y y)) (* x x))>
#<alt (* (/ 1/4 (* x x)) (* y y))>
#<alt (/ 1/4 (* x x))>
#<alt (/ 1 (/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x))))>
#<alt (/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))>
#<alt (- (/ (* 1/2 y) x) x)>
#<alt (/ (* 1/2 y) x)>
#<alt (/ (* y y) (/ (* x x) 1/4))>
#<alt (- (/ (* y y) (/ (* x x) 1/4)) (* x x))>

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

Calls

108 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))
0.0ms	x	@	inf	(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))
0.0ms	y	@	inf	(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))
0.0ms	y	@	0	(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))
0.0ms	x	@	-inf	(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))

rewrite486.0ms (6.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4874×	`-lowering-.f32`
4874×	`-lowering-.f64`
2706×	`/-lowering-/.f32`
2706×	`/-lowering-/.f64`
2628×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	142
1	252	109
2	2034	107
0	10256	107

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1613

Calls

Call 1

Inputs
(/ 1 (/ (/ 1 y) (/ 1/2 x)))
(/ (/ 1 y) (/ 1/2 x))
(+ x (/ 1 (/ (/ 1 y) (/ 1/2 x))))
(/ 1 y)
(* (/ 1/2 x) y)
(/ 1/2 x)
(/ 1 (* x (/ 2 y)))
(+ x (/ 1 (* x (/ 2 y))))
(* x (/ 2 y))
(/ 2 y)
(/ (- (* (/ 1/4 (* x x)) (* y y)) (* x x)) (- (* (/ 1/2 x) y) x))
(- (* (/ 1/4 (* x x)) (* y y)) (* x x))
(* (/ 1/4 (* x x)) (* y y))
(/ 1/4 (* x x))
(/ 1 (/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x))))
(/ (- (/ (* 1/2 y) x) x) (- (/ (* y y) (/ (* x x) 1/4)) (* x x)))
(- (/ (* 1/2 y) x) x)
(/ (* 1/2 y) x)
(/ (* y y) (/ (* x x) 1/4))
(- (/ (* y y) (/ (* x x) 1/4)) (* x x))

Outputs
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(neg.f64 (/.f64 (/.f64 y #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))))
(neg.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))
(/.f64 y (/.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 y #s(literal 2 binary64)) x)
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))))
(/.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 y #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 #s(literal 2 binary64) y)))
(/.f64 (neg.f64 (*.f64 y #s(literal -1/2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) y))
(pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1 binary64))
(pow.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (*.f64 y y))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(*.f64 y (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (/.f64 y x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y)))
(.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) y))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(*.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))))
(.f64 (.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 y #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 y x) #s(literal 1/2 binary64))
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) y)
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) y)
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 y #s(literal 2 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(exp.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x))) #s(literal -1 binary64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 x (/.f64 y #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (/.f64 y x))
(/.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 y #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) y) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(/.f64 (/.f64 x #s(literal 1/2 binary64)) y)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) x) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (/.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) y))
(/.f64 (/.f64 x y) #s(literal 1/2 binary64))
(/.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 y #s(literal 2 binary64)))
(/.f64 (*.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) y))
(/.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 y #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 #s(literal 0 binary64) y))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) y))
(pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))
(*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (/.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 x (/.f64 #s(literal 2 binary64) y))
(*.f64 x (/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) y) x))
(*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 y x) #s(literal -1 binary64)))
(*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64)))
(.f64 #s(literal 2 binary64) (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) x) y) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) y) x)
(*.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 x #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) y) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(*.f64 (/.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) y))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (/.f64 x #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 (/.f64 y x) #s(literal -1 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) y))
(*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) y))
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) y))
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) y))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) y))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)
(+.f64 (/.f64 (.f64 y y) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (neg.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x))))
(+.f64 (/.f64 (.f64 y y) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(+.f64 (/.f64 (.f64 y y) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) x))))
(+.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 y x))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))
(+.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 y x))) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) x))))
(+.f64 (fma.f64 y (/.f64 (/.f64 (/.f64 y x) (/.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) (neg.f64 (.f64 (/.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) x))) (fma.f64 (neg.f64 (/.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x))) x (.f64 (/.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) x)))
(+.f64 (fma.f64 y (/.f64 (/.f64 (/.f64 y x) (/.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) (.f64 x x)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x))) (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) (*.f64 x x))))
(+.f64 (fma.f64 y (/.f64 (/.f64 (/.f64 y x) (/.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)) (neg.f64 (.f64 (+.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 x x) (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))))) (fma.f64 (neg.f64 (+.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64))))) (/.f64 (.f64 x x) (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 x x) (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))))))
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(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64)) (/.f64 y x) (neg.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) y (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) y (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) y (neg.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 y y) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(fma.f64 (/.f64 (.f64 y y) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))
(fma.f64 (/.f64 (.f64 y y) #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (neg.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 y y) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(fma.f64 (/.f64 (.f64 y y) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1/4 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))
(fma.f64 (/.f64 (.f64 y y) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1/4 binary64) (neg.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64))))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (-.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64))))))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (neg.f64 (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (.f64 x (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))))))
(/.f64 (+.f64 (.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)))) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))))) (+.f64 (.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))) (-.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))) (-.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64))))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (-.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64))
(.f64 (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))))))
(.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 y x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y x)) x))
(.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (.f64 y y) (.f64 x x))) #s(literal 1/16 binary64)) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 (.f64 y y) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))))

simplify266.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

3656×	`-lowering-.f32`
3656×	`-lowering-.f64`
2052×	`fma-lowering-fma.f32`
2052×	`fma-lowering-fma.f64`
1616×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	3205
1	570	2823
2	1581	2734
3	4998	2554
0	8384	2554

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

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

Outputs
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
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(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
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(* 2 (/ x y))
(/.f64 (*.f64 x #s(literal 2 binary64)) y)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
x
(+ x (* 1/2 (/ y x)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(+ x (* 1/2 (/ y x)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(+ x (* 1/2 (/ y x)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
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(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
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(/ 1/2 x)
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(/ 1/2 x)
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(* 1/2 (/ y x))
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(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
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(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
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x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
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x
(+ x (* 1/2 (/ y x)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(+ x (* 1/2 (/ y x)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(+ x (* 1/2 (/ y x)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(+.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) y) x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
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(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
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(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/2 binary64)) x) x) (+.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 y (.f64 (*.f64 y y) #s(literal -1/8 binary64))) (pow.f64 x #s(literal 6 binary64)))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 1/2 (/ y (pow x 2))) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) x)) x)
(* -1 (/ (- (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/2 binary64)) x) x) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x x))))) x)
(* -1 (/ (- (+ (* 1/8 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))) (+ 1 (* 1/4 (/ (pow y 2) (pow x 4))))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 y #s(literal -1/2 binary64)) x) x) (+.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 y (.f64 (*.f64 y y) #s(literal -1/8 binary64))) (pow.f64 x #s(literal 6 binary64)))))) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(- (* 1/2 (/ y x)) x)
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(- (* 1/2 (/ y x)) x)
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(- (* 1/2 (/ y x)) x)
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* y (+ (* -1 (/ x y)) (* 1/2 (/ 1 x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* y (+ (* -1 (/ x y)) (* 1/2 (/ 1 x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* y (+ (* -1 (/ x y)) (* 1/2 (/ 1 x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* -1 (* y (- (/ x y) (* 1/2 (/ 1 x)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* -1 (* y (- (/ x y) (* 1/2 (/ 1 x)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* -1 (* y (- (/ x y) (* 1/2 (/ 1 x)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(/ (+ (* -1 (pow x 2)) (* 1/2 y)) x)
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
(/ (+ (* -1 (pow x 2)) (* 1/2 y)) x)
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
(/ (+ (* -1 (pow x 2)) (* 1/2 y)) x)
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 x x)) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 1/2 (/ y (pow x 2))) 1))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* x (- (* 1/2 (/ y (pow x 2))) 1))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* x (- (* 1/2 (/ y (pow x 2))) 1))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ y (pow x 2))))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* -1 (* x (+ 1 (* -1/2 (/ y (pow x 2))))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* -1 (* x (+ 1 (* -1/2 (/ y (pow x 2))))))
(-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) y) x) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(- (* 1/4 (/ (pow y 2) (pow x 2))) (pow x 2))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(- (* 1/4 (/ (pow y 2) (pow x 2))) (pow x 2))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(- (* 1/4 (/ (pow y 2) (pow x 2))) (pow x 2))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* (pow y 2) (+ (* -1 (/ (pow x 2) (pow y 2))) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(* (pow y 2) (+ (* -1 (/ (pow x 2) (pow y 2))) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(* (pow y 2) (+ (* -1 (/ (pow x 2) (pow y 2))) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(* (pow y 2) (+ (* -1 (/ (pow x 2) (pow y 2))) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(* (pow y 2) (+ (* -1 (/ (pow x 2) (pow y 2))) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(* (pow y 2) (+ (* -1 (/ (pow x 2) (pow y 2))) (* 1/4 (/ 1 (pow x 2)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (.f64 x x))
(* 1/4 (/ (pow y 2) (pow x 2)))
(/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))
(/ (+ (* -1 (pow x 4)) (* 1/4 (pow y 2))) (pow x 2))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x))
(/ (+ (* -1 (pow x 4)) (* 1/4 (pow y 2))) (pow x 2))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x))
(/ (+ (* -1 (pow x 4)) (* 1/4 (pow y 2))) (pow x 2))
(/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/4 (/ (pow y 2) (pow x 4))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 2) (- (* 1/4 (/ (pow y 2) (pow x 4))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 2) (- (* 1/4 (/ (pow y 2) (pow x 4))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/4 (/ (pow y 2) (pow x 4))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 2) (- (* 1/4 (/ (pow y 2) (pow x 4))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 2) (- (* 1/4 (/ (pow y 2) (pow x 4))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))

eval290.0ms (3.8%)

Compiler: Compiled 65258 to 2874 computations (95.6% saved)

prune176.0ms (2.3%)

Pruning

32 alts after pruning (24 fresh and 8 done)

	Pruned	Kept	Total
New	2149	21	2170
Fresh	5	3	8
Picked	3	2	5
Done	0	6	6
Total	2157	32	2189

Accuracy

100.0%

Counts

2189 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.3%	(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	2.5%	(/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 y y) x)) x) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
	3.5%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y))
	37.8%	(/.f64 (-.f64 (/.f64 (/.f64 y #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) x)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	37.3%	(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (/.f64 #s(literal 2 binary64) y))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	37.3%	(/.f64 (-.f64 (/.f64 (.f64 (/.f64 y #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 y x))) x) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	37.8%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	37.8%	(/.f64 (-.f64 (.f64 (/.f64 (/.f64 y x) (/.f64 x #s(literal 1/4 binary64))) y) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	35.3%	(/.f64 (-.f64 (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) x) x) (.f64 y y)) (*.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
	37.8%	(/.f64 (-.f64 (.f64 (/.f64 y x) (/.f64 y (/.f64 x #s(literal 1/4 binary64)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
	35.3%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y)) x))
	37.8%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
✓	3.5%	(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
	2.7%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
	35.5%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 y y)) x) (.f64 x x))))
	37.2%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 y (.f64 #s(literal 1/2 binary64) (/.f64 y x)))) (*.f64 x x))))
	37.7%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (*.f64 x x))))
	68.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
	3.5%	(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
	3.5%	(/.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) x))
	33.7%	(-.f64 (/.f64 (.f64 y y) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)))
✓	68.8%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
	68.8%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) y)))))
	68.8%	(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
✓	67.4%	(+.f64 x (.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))))
✓	68.8%	(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
	22.2%	(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))))
	3.5%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1/2 binary64) x))
✓	3.5%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
✓	69.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	34.2%	(sqrt.f64 y)
✓	68.4%	x

Compiler

Compiled 1384 to 547 computations (60.5% saved)

regimes86.0ms (1.1%)

Counts

44 → 2

Calls

Call 1

Inputs
x
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(/.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1/2 binary64) x))
(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y))))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y)))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) y)))))
(+.f64 x (.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))))
(+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 y y) x)) x) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 y (/.f64 #s(literal 1/4 binary64) (.f64 x x))) y) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 y x) (/.f64 y (/.f64 x #s(literal 1/4 binary64)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) x) x) (.f64 y y)) (*.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 y x) (/.f64 x #s(literal 1/4 binary64))) y) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) y) x)) (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 y y)) x) (.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y)) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y)) x))
(/.f64 (-.f64 (/.f64 (.f64 (/.f64 y #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 y x))) x) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (/.f64 (/.f64 y #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) x)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 y (.f64 #s(literal 1/2 binary64) (/.f64 y x)))) (*.f64 x x))))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (/.f64 #s(literal 2 binary64) y))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(-.f64 (/.f64 (.f64 y y) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (*.f64 x x))))
(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (.f64 y (.f64 y y)) (/.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))) (+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))))
(sqrt.f64 y)
(sqrt.f64 (+.f64 (*.f64 x x) y))

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

Calls

5 calls:

27.0ms	y
15.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
14.0ms	x
13.0ms	(*.f64 x x)
12.0ms	(+.f64 (*.f64 x x) y)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
86.2%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes19.0ms (0.2%)

Counts

43 → 2

Calls

Call 1

Inputs
x
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(/.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1/2 binary64) x))
(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y))))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y)))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) y)))))
(+.f64 x (.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))))
(+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 y y) x)) x) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 y (/.f64 #s(literal 1/4 binary64) (.f64 x x))) y) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 y x) (/.f64 y (/.f64 x #s(literal 1/4 binary64)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) x) x) (.f64 y y)) (*.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 y x) (/.f64 x #s(literal 1/4 binary64))) y) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) y) x)) (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 y y)) x) (.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y)) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y)) x))
(/.f64 (-.f64 (/.f64 (.f64 (/.f64 y #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 y x))) x) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (/.f64 (/.f64 y #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) x)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 y (.f64 #s(literal 1/2 binary64) (/.f64 y x)))) (*.f64 x x))))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (/.f64 #s(literal 2 binary64) y))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(-.f64 (/.f64 (.f64 y y) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (*.f64 x x))))
(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (.f64 y (.f64 y y)) (/.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))) (+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))))
(sqrt.f64 y)

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

Calls

1 calls:

14.0ms

Results

Accuracy	Segments	Branch
91.0%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes30.0ms (0.4%)

Counts

42 → 1

Calls

Call 1

Inputs
x
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(/.f64 #s(literal 1/2 binary64) (/.f64 x y))
(/.f64 (*.f64 y #s(literal 1/2 binary64)) x)
(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(+.f64 x (/.f64 (*.f64 y #s(literal 1/2 binary64)) x))
(/.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal -1/2 binary64) x))
(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y))))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 1/2 binary64)) y)))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) y)))))
(+.f64 x (.f64 (/.f64 y x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y x) x)))))
(+.f64 x (.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x))) x) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 y y) x)) x) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 y (/.f64 #s(literal 1/4 binary64) (.f64 x x))) y) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 y x) (/.f64 y (/.f64 x #s(literal 1/4 binary64)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) x) x) (.f64 y y)) (*.f64 x x)) (-.f64 (/.f64 y (/.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 y x) (/.f64 x #s(literal 1/4 binary64))) y) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) y) x)) (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 y y)) x) (.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y)) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 y y)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y)) x))
(/.f64 (-.f64 (/.f64 (.f64 (/.f64 y #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 y x))) x) (.f64 x x)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (/.f64 (/.f64 y #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) x)) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 y (.f64 #s(literal 1/2 binary64) (/.f64 y x)))) (*.f64 x x))))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (/.f64 #s(literal 2 binary64) y))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (/.f64 y x)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))))) (.f64 x x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))
(-.f64 (/.f64 (.f64 y y) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x) (/.f64 (.f64 x x) #s(literal 1/4 binary64)))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) y) x) x) (-.f64 (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 y x)))) (*.f64 x x))))
(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (.f64 y (.f64 y y)) (/.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 y x) (/.f64 y x))) (+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (/.f64 (.f64 y y) (/.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x x) (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))))

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

Calls

2 calls:

14.0ms	y
13.0ms	x

Results

Accuracy	Segments	Branch
68.8%	1	`y`
68.8%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total -41.6b remaining (-205.6%)

Threshold costs -41.6b (-205.6%)

Counts

4 → 1

Calls

Call 1

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

Outputs
x

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
68.4%	1	`y`
68.4%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.286064679246439e+197	2.7748241879703083e+208

Compiler

Compiled 13 to 9 computations (30.8% saved)

bsearch15.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	4.317340974879183e-57	1.5585052176397189e-55

Results

8.0ms	112×	0	valid
2.0ms	29×	0	invalid

Compiler

Compiled 132 to 100 computations (24.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-add: 1.0ms (31% of total)

ival-mult: 1.0ms (31% of total)

ival-sqrt: 1.0ms (31% of total)

const: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	36
1	30	36

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 1000000000000000017535541566019400541537441865177200086145798104936341572305513193378283771523764365204900328030374534281861011105867876227585990799216050325567033999660761493056632508247061001404416 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 x #s(literal 8061239733051379/110427941548649020598956093796432407239217743554726184882600387580788736 binary64)) (sqrt.f64 y) (+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y)))))
(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
x

Outputs
(if (<=.f64 (.f64 x x) #s(literal 1000000000000000017535541566019400541537441865177200086145798104936341572305513193378283771523764365204900328030374534281861011105867876227585990799216050325567033999660761493056632508247061001404416 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 x #s(literal 8061239733051379/110427941548649020598956093796432407239217743554726184882600387580788736 binary64)) (sqrt.f64 y) (+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 #s(literal 2 binary64) y)))))
(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(+.f64 x (*.f64 y (/.f64 #s(literal 1/2 binary64) x)))
x

soundness966.0ms (12.6%)

Rules

4688×	`-lowering-.f32`
4688×	`-lowering-.f64`
4180×	`-lowering-.f32`
4180×	`-lowering-.f64`
3948×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	77
1	103	68
2	1148	68
0	8814	68
0	29	132
1	204	125
2	1868	125
0	8235	125
0	133	590
1	408	509
2	1413	496
3	5183	470
0	8421	470

Stop Event

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

Compiler

Compiled 97 to 63 computations (35.1% saved)

preprocess53.0ms (0.7%)

Compiler: Compiled 214 to 118 computations (44.9% saved)

analyze28.0ms (0.4%)

sample752.0ms (9.8%)

preprocess33.0ms (0.4%)

explain64.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize28.0ms (0.4%)

series5.0ms (0.1%)

rewrite480.0ms (6.3%)

simplify369.0ms (4.8%)

eval127.0ms (1.7%)

prune52.0ms (0.7%)

simplify26.0ms (0.3%)

localize117.0ms (1.5%)

series58.0ms (0.7%)

rewrite490.0ms (6.4%)

simplify284.0ms (3.7%)

eval164.0ms (2.1%)

prune124.0ms (1.6%)

simplify266.0ms (3.5%)

localize196.0ms (2.5%)

series25.0ms (0.3%)

rewrite420.0ms (5.5%)

simplify340.0ms (4.4%)

eval217.0ms (2.8%)

prune191.0ms (2.5%)

simplify176.0ms (2.3%)

localize224.0ms (2.9%)

series12.0ms (0.2%)

rewrite486.0ms (6.3%)

simplify266.0ms (3.5%)

eval290.0ms (3.8%)

prune176.0ms (2.3%)

regimes86.0ms (1.1%)

regimes19.0ms (0.2%)

regimes30.0ms (0.4%)

regimes4.0ms (0.1%)

bsearch1.0ms (0%)

bsearch15.0ms (0.2%)

simplify8.0ms (0.1%)

soundness966.0ms (12.6%)

preprocess53.0ms (0.7%)

end0.0ms (0%)

Profiling