Metrics for Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

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

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

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

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

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

const: 0.0ms (0% of total)

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

sample859.0ms (7.5%)

Results

585.0ms	7945×	0	valid
20.0ms	148×	1	valid
16.0ms	93×	2	valid
16.0ms	70×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 381.0ms

ival-div: 170.0ms (44.6% of total)

ival-add: 74.0ms (19.4% of total)

ival-sub: 58.0ms (15.2% of total)

ival-fabs: 56.0ms (14.7% of total)

backward-pass: 12.0ms (3.2% of total)

const: 11.0ms (2.9% of total)

Bogosity

preprocess44.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

192×	`accelerator-lowering-fma.f32`
192×	`accelerator-lowering-fma.f64`
112×	`-lowering-.f32`
112×	`-lowering-.f64`
108×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	52	48
2	135	48
3	262	48
4	382	48
5	459	48
6	522	48
7	565	48
8	569	48
9	572	48
10	574	48
0	7	8
1	12	8
2	19	8
3	27	8
4	46	8
5	93	8
6	151	8
7	180	8
8	225	8
9	261	8
10	297	8
11	309	8
12	315	8
13	318	8
14	320	8
0	320	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ x (/ (fabs (- y x)) 2))

Outputs
(+ x (/ (fabs (- y x)) 2))
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Call 2

Inputs
(+ x (/ (fabs (- y x)) 2))
(+ (neg x) (/ (fabs (- y (neg x))) 2))
(+ x (/ (fabs (- (neg y) x)) 2))
(neg (+ (neg x) (/ (fabs (- y (neg x))) 2)))
(neg (+ x (/ (fabs (- (neg y) x)) 2)))
(+ y (/ (fabs (- x y)) 2))

Outputs
(+ x (/ (fabs (- y x)) 2))
(- x (* (fabs (- y x)) -1/2))
(+ (neg x) (/ (fabs (- y (neg x))) 2))
(- (* (fabs (+ x y)) 1/2) x)
(+ x (/ (fabs (- (neg y) x)) 2))
(+ x (* (fabs (+ x y)) 1/2))
(neg (+ (neg x) (/ (fabs (- y (neg x))) 2)))
(+ x (* (fabs (+ x y)) -1/2))
(neg (+ x (/ (fabs (- (neg y) x)) 2)))
(- (* (fabs (+ x y)) -1/2) x)
(+ y (/ (fabs (- x y)) 2))
(- y (* (fabs (- y x)) -1/2))

explain75.0ms (0.7%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(fabs.f64 (-.f64 y x))`
-	-	`y`
-	-	`#s(literal 2 binary64)`
-	-	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
-	-	`(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))`
-	-	`(-.f64 y x)`

Results

39.0ms	494×	0	valid
2.0ms	8×	2	valid
3.0ms	6×	3	valid
1.0ms	4×	1	valid

Compiler

Compiled 64 to 29 computations (54.7% saved)

Precisions

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

ival-div: 7.0ms (35.7% of total)

ival-sub: 4.0ms (20.4% of total)

ival-fabs: 3.0ms (15.3% of total)

ival-add: 3.0ms (15.3% of total)

const: 1.0ms (5.1% of total)

backward-pass: 1.0ms (5.1% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Compiler

Compiled 10 to 7 computations (30% saved)

localize144.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 y x)
✓	cost-diff	0	(fabs.f64 (-.f64 y x))
✓	cost-diff	0	(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 y x)
✓	accuracy	100.0%	(fabs.f64 (-.f64 y x))
✓	accuracy	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Rules

192×	`accelerator-lowering-fma.f32`
192×	`accelerator-lowering-fma.f64`
112×	`-lowering-.f32`
112×	`-lowering-.f64`
64×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	27	24
4	46	24
5	93	24
6	151	24
7	180	24
8	225	24
9	261	24
10	297	24
11	309	24
12	315	24
13	318	24
14	320	24
0	320	23

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ x (/ (fabs (- y x)) 2))
x
(/ (fabs (- y x)) 2)
(fabs (- y x))
(- y x)
y
2

Outputs
(+ x (/ (fabs (- y x)) 2))
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
x
(/ (fabs (- y x)) 2)
(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(- y x)
(-.f64 y x)
y
2
#s(literal 2 binary64)

Results

18.0ms	247×	0	valid
1.0ms	4×	2	valid
1.0ms	3×	3	valid
0.0ms	2×	1	valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-div: 4.0ms (41.1% of total)

ival-sub: 2.0ms (20.5% of total)

ival-fabs: 2.0ms (20.5% of total)

const: 1.0ms (10.3% of total)

backward-pass: 1.0ms (10.3% of total)

ival-add: 1.0ms (10.3% of total)

series7.0ms (0.1%)

Counts

4 → 96

Calls

Call 1

Inputs
#<alt (+ x (/ (fabs (- y x)) 2))>
#<alt (fabs (- y x))>
#<alt (- y x)>
#<alt (/ (fabs (- y x)) 2)>

Outputs
#<alt (* 1/2 (fabs (- y x)))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))>
#<alt (* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))>
#<alt (* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (- y x))))>
#<alt (+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))>
#<alt (+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))>
#<alt (+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))>
#<alt (+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (neg (+ x (* -1 y))))>
#<alt (fabs (neg (+ x (* -1 y))))>
#<alt (fabs (neg (+ x (* -1 y))))>
#<alt (fabs (neg (+ x (* -1 y))))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (- y x))>
#<alt (fabs (+ y (* -1 x)))>
#<alt (fabs (+ y (* -1 x)))>
#<alt (fabs (+ y (* -1 x)))>
#<alt (fabs (+ y (* -1 x)))>
#<alt (* -1 x)>
#<alt (- y x)>
#<alt (- y x)>
#<alt (- y x)>
#<alt y>
#<alt (* y (+ 1 (* -1 (/ x y))))>
#<alt (* y (+ 1 (* -1 (/ x y))))>
#<alt (* y (+ 1 (* -1 (/ x y))))>
#<alt y>
#<alt (* -1 (* y (- (/ x y) 1)))>
#<alt (* -1 (* y (- (/ x y) 1)))>
#<alt (* -1 (* y (- (/ x y) 1)))>
#<alt y>
#<alt (+ y (* -1 x))>
#<alt (+ y (* -1 x))>
#<alt (+ y (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ y x) 1))>
#<alt (* x (- (/ y x) 1))>
#<alt (* x (- (/ y x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ y x)))))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (neg (+ x (* -1 y)))))>
#<alt (* 1/2 (fabs (neg (+ x (* -1 y)))))>
#<alt (* 1/2 (fabs (neg (+ x (* -1 y)))))>
#<alt (* 1/2 (fabs (neg (+ x (* -1 y)))))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (- y x)))>
#<alt (* 1/2 (fabs (+ y (* -1 x))))>
#<alt (* 1/2 (fabs (+ y (* -1 x))))>
#<alt (* 1/2 (fabs (+ y (* -1 x))))>
#<alt (* 1/2 (fabs (+ y (* -1 x))))>

Calls

24 calls:

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

rewrite629.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4906×	`accelerator-lowering-fma.f32`
4906×	`accelerator-lowering-fma.f64`
4404×	`-lowering-.f32`
4404×	`-lowering-.f64`
2206×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	47	21
2	376	21
3	5337	21
0	8337	20

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 239

Calls

Call 1

Inputs
(+ x (/ (fabs (- y x)) 2))
(fabs (- y x))
(- y x)
(/ (fabs (- y x)) 2)

Outputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)
(+.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))) #s(literal -1 binary64)))
(-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)))
(fma.f64 x #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(fma.f64 x (/.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))) (neg.f64 (/.f64 (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))
(fma.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64) x)
(fma.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64) x)
(fma.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64) x)
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))
(fma.f64 #s(literal 1 binary64) x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)) x)
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) x)
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)) #s(literal -1 binary64)) x)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) x)
(fma.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) x)
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 1/2 binary64) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal -4 binary64)))) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))) (neg.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x x)) (/.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/2 binary64)) #s(literal 8 binary64)))) (+.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (/.f64 x (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))) (neg.f64 (/.f64 (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))
(fma.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)) #s(literal -1/2 binary64) x)
(fma.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1 binary64)) #s(literal -1/2 binary64) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 x y))))) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 x y))) x)
(neg.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/2 binary64)) #s(literal 8 binary64))) (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/2 binary64)) #s(literal 8 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/2 binary64)) #s(literal 8 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))))
(/.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal -4 binary64))) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))))
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(neg.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))
(neg.f64 (*.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) #s(literal 1 binary64)))
(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (fabs.f64 (-.f64 y x))))
(/.f64 (fabs.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (.f64 #s(literal 2 binary64) (fabs.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 x y))))))
(/.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))) (*.f64 #s(literal 2 binary64) (fabs.f64 (+.f64 x y))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))) (fabs.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 x y)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 (.f64 x x) (*.f64 y y)))) (fabs.f64 (+.f64 x y)))
(/.f64 (.f64 (fabs.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) #s(literal 1/2 binary64)) (fabs.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 x y)))))
(/.f64 (.f64 (fabs.f64 (-.f64 (.f64 x x) (*.f64 y y))) #s(literal 1/2 binary64)) (fabs.f64 (+.f64 x y)))
(pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 x y))))))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 (.f64 x x) (*.f64 y y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 x y))))

simplify293.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

3132×	`/-lowering-/.f32`
3132×	`/-lowering-/.f64`
2520×	`accelerator-lowering-fma.f32`
2520×	`accelerator-lowering-fma.f64`
2222×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	479
1	115	479
2	264	479
3	773	479
4	2419	479
5	3218	479
6	4243	479
7	5101	479
8	5674	479
9	6162	479
10	7847	479
0	8336	458

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
x
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(* -1 x)
(- y x)
(- y x)
(- y x)
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))

Outputs
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
x
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (- y x))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ x (* -1 y))))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ x (* -1 y))))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ x (* -1 y))))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ x (* -1 y))))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(fabs (+ y (* -1 x)))
(fabs.f64 (-.f64 y x))
(fabs (+ y (* -1 x)))
(fabs.f64 (-.f64 y x))
(fabs (+ y (* -1 x)))
(fabs.f64 (-.f64 y x))
(fabs (+ y (* -1 x)))
(fabs.f64 (-.f64 y x))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
y
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y x)
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y x)
(* y (+ 1 (* -1 (/ x y))))
(-.f64 y x)
y
(* -1 (* y (- (/ x y) 1)))
(-.f64 y x)
(* -1 (* y (- (/ x y) 1)))
(-.f64 y x)
(* -1 (* y (- (/ x y) 1)))
(-.f64 y x)
y
(+ y (* -1 x))
(-.f64 y x)
(+ y (* -1 x))
(-.f64 y x)
(+ y (* -1 x))
(-.f64 y x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (/ y x) 1))
(-.f64 y x)
(* x (- (/ y x) 1))
(-.f64 y x)
(* x (- (/ y x) 1))
(-.f64 y x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 y x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 y x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(-.f64 y x)
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (+ y (* -1 x))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (+ y (* -1 x))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (+ y (* -1 x))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(* 1/2 (fabs (+ y (* -1 x))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))

eval58.0ms (0.5%)

Compiler: Compiled 7795 to 2470 computations (68.3% saved)

prune68.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	326	9	335
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	326	10	336

Accuracy

100.0%

Counts

336 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)
▶	52.8%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
	25.2%	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 16 binary64))) (.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))) (+.f64 (.f64 x x) (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
▶	51.9%	(+.f64 x (/.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))) (+.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))))) #s(literal 2 binary64)))
	54.2%	(+.f64 x (/.f64 (fabs.f64 (/.f64 (-.f64 (.f64 y y) (.f64 x x)) (+.f64 x y))) #s(literal 2 binary64)))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
	56.8%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
▶	99.7%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))
▶	11.9%	x

Compiler

Compiled 416 to 207 computations (50.2% saved)

localize986.0ms (8.7%)

Algorithm

1×	egg-herbie

Localize:

Found 32 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	2048	(/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))) (+.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))))
✓	cost-diff	2048	(fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))) (+.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))))
✓	cost-diff	2048	(/.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))) (+.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))))) #s(literal 2 binary64))
✓	cost-diff	2048	(+.f64 x (/.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))) (+.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))))) #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 (-.f64 y x) (-.f64 y x))
✓	cost-diff	0	(/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))
✓	cost-diff	0	(-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))
✓	cost-diff	0	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	cost-diff	0	(/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))
✓	cost-diff	0	(-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
✓	cost-diff	0	(fabs.f64 (-.f64 y x))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))))
✓	cost-diff	128	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))
✓	accuracy	97.2%	(-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))))
✓	accuracy	73.5%	(/.f64 (*.f64 y y) (+.f64 x y))
✓	accuracy	70.6%	(/.f64 (*.f64 x x) (+.f64 x y))
✓	accuracy	54.8%	(/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))) (+.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))))
✓	accuracy	100.0%	(*.f64 (-.f64 y x) (-.f64 y x))
✓	accuracy	99.9%	(-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)
✓	accuracy	74.5%	(-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))
✓	accuracy	55.1%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	accuracy	100.0%	(fabs.f64 (-.f64 y x))
✓	accuracy	99.9%	(-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))))
✓	accuracy	100.0%	(fabs.f64 (-.f64 y x))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))
✓	accuracy	99.9%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))))

Rules

12014×	`accelerator-lowering-fma.f32`
12014×	`accelerator-lowering-fma.f64`
3838×	`-lowering-.f32`
3838×	`-lowering-.f64`
2606×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	426
1	86	426
2	213	426
3	624	298
4	2085	282
5	6485	282
0	8026	274

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

Results

156.0ms	226×	0	valid
14.0ms	12×	1	valid
22.0ms	12×	2	valid
19.0ms	6×	3	valid

Compiler

Compiled 464 to 74 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 107.0ms

ival-div: 49.0ms (46% of total)

ival-sub: 20.0ms (18.8% of total)

backward-pass: 13.0ms (12.2% of total)

ival-mult: 11.0ms (10.3% of total)

ival-add: 6.0ms (5.6% of total)

ival-fabs: 4.0ms (3.8% of total)

const: 3.0ms (2.8% of total)

series138.0ms (1.2%)

Counts

20 → 480

Calls

Call 1

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

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

Calls

120 calls:

Time	Variable		Point	Expression
40.0ms	y	@	inf	(/ (- (* (/ (* y y) (+ x y)) (/ (* y y) (+ x y))) (* (/ (* x x) (+ x y)) (/ (* x x) (+ x y)))) (+ (/ (* y y) (+ x y)) (/ (* x x) (+ x y))))
7.0ms	y	@	0	(/ (- (* (/ (* y y) (+ x y)) (/ (* y y) (+ x y))) (* (/ (* x x) (+ x y)) (/ (* x x) (+ x y)))) (+ (/ (* y y) (+ x y)) (/ (* x x) (+ x y))))
4.0ms	x	@	0	(/ (- (* (/ (* y y) (+ x y)) (/ (* y y) (+ x y))) (* (/ (* x x) (+ x y)) (/ (* x x) (+ x y)))) (+ (/ (* y y) (+ x y)) (/ (* x x) (+ x y))))
2.0ms	y	@	0	(/ (- (/ (* (- y x) (- y x)) 4) (* x x)) (- (/ (fabs (- y x)) 2) x))
1.0ms	y	@	-inf	(/ (* y y) (+ x y))

rewrite1.1s (10%)

Algorithm

1×	batch-egg-rewrite

Rules

4722×	`/-lowering-/.f32`
4722×	`/-lowering-/.f64`
3050×	`-lowering-.f32`
3050×	`-lowering-.f64`
2864×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	181
1	270	143
2	2833	143
0	8833	137

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1532

Calls

Call 1

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

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

simplify938.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

10836×	`accelerator-lowering-fma.f32`
10836×	`accelerator-lowering-fma.f64`
5432×	`-lowering-.f32`
5432×	`-lowering-.f64`
4354×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	868	8184
1	2739	7760
0	8682	7380

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

Inputs
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
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(* y (+ 1 (* -1 (/ x y))))
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y
(* -1 (* y (- (/ x y) 1)))
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y
(+ y (* -1 x))
(+ y (* x (- (/ x y) 1)))
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(/ (pow y 2) x)
(/ (+ (* -1 (/ (pow y 3) x)) (pow y 2)) x)
(/ (- (+ (/ (pow y 4) (pow x 2)) (pow y 2)) (/ (pow y 3) x)) x)
(/ (- (+ (* -1 (/ (pow y 5) (pow x 3))) (pow y 2)) (+ (* -1 (/ (pow y 4) (pow x 2))) (/ (pow y 3) x))) x)
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(* -1 (/ (+ (* -1 (pow y 2)) (/ (pow y 3) x)) x))
(* -1 (/ (+ (* -1 (/ (- (/ (pow y 4) x) (pow y 3)) x)) (* -1 (pow y 2))) x))
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(* -1 (pow x 2))
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(* -1/2 (fabs (- y x)))
(* -1/2 (fabs (- y x)))
(* -1/2 (fabs (- y x)))
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(* -1/2 (fabs (- y x)))
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(* -1/2 (fabs (neg (+ x (* -1 y)))))
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(* -1/2 (fabs (+ y (* -1 x))))
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x
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x
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(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
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(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
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(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
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(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
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(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y)))))))
(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y)))))))
(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y)))))))
(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
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(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
(* 1/2 (fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y))))))
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(fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y))))))
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Outputs
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(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- x (* -1 y)) 2)) (/ (pow x 4) (pow (- x (* -1 y)) 2))) (+ (/ (pow x 2) (- x (* -1 y))) (/ (pow y 2) (- x (* -1 y))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (+ x y) 2)) (/ (pow x 4) (pow (+ x y) 2))) (+ (/ (pow x 2) (+ x y)) (/ (pow y 2) (+ x y)))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- y (* -1 x)) 2)) (/ (pow x 4) (pow (- y (* -1 x)) 2))) (+ (/ (pow x 2) (- y (* -1 x))) (/ (pow y 2) (- y (* -1 x))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- y (* -1 x)) 2)) (/ (pow x 4) (pow (- y (* -1 x)) 2))) (+ (/ (pow x 2) (- y (* -1 x))) (/ (pow y 2) (- y (* -1 x))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- y (* -1 x)) 2)) (/ (pow x 4) (pow (- y (* -1 x)) 2))) (+ (/ (pow x 2) (- y (* -1 x))) (/ (pow y 2) (- y (* -1 x))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))
(fabs (/ (- (/ (pow y 4) (pow (- y (* -1 x)) 2)) (/ (pow x 4) (pow (- y (* -1 x)) 2))) (+ (/ (pow x 2) (- y (* -1 x))) (/ (pow y 2) (- y (* -1 x))))))
(fabs.f64 (/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (+.f64 y x)))) (+.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 y y) (+.f64 y x)))))

eval705.0ms (6.2%)

Compiler: Compiled 99264 to 28294 computations (71.5% saved)

prune482.0ms (4.2%)

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	2410	12	2422
Fresh	2	2	4
Picked	2	3	5
Done	0	1	1
Total	2414	18	2432

Accuracy

100.0%

Counts

2432 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)
	25.7%	(/.f64 (/.f64 (-.f64 (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 16 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
	6.8%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
	25.8%	(/.f64 (-.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
▶	76.2%	(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
✓	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
	11.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
	72.7%	(+.f64 (.f64 y (+.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) x)) (/.f64 (.f64 y #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) x)))) (/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) x)))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
▶	87.2%	(+.f64 x (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
	90.4%	(+.f64 x (/.f64 (fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) #s(literal 2 binary64)))
	52.8%	(+.f64 x (/.f64 (fabs.f64 (neg.f64 x)) #s(literal 2 binary64)))
▶	56.8%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
✓	99.7%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))
	99.0%	(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
	76.1%	(*.f64 (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
▶	11.8%	(*.f64 x #s(literal 3/4 binary64))
✓	11.9%	x

Compiler

Compiled 597 to 381 computations (36.2% saved)

localize767.0ms (6.7%)

Algorithm

1×	egg-herbie

Localize:

Found 32 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64)))
✓	cost-diff	0	(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64))
✓	cost-diff	12800	(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	cost-diff	13056	(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
✓	cost-diff	256	(*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	cost-diff	256	(fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))
✓	cost-diff	256	(/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64))
✓	cost-diff	256	(+.f64 x (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
✓	cost-diff	0	(fabs.f64 y)
✓	cost-diff	0	(/.f64 (fabs.f64 y) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 3/4 binary64))
✓	cost-diff	0	(fabs.f64 (-.f64 y x))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))
✓	cost-diff	0	(pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64))
✓	cost-diff	25984	(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)
✓	accuracy	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64)))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
✓	accuracy	99.6%	(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64))
✓	accuracy	99.4%	(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (/.f64 x y))
✓	accuracy	100.0%	(fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))
✓	accuracy	99.9%	(+.f64 x (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
✓	accuracy	92.7%	(*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	accuracy	100.0%	(/.f64 (fabs.f64 y) #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
✓	accuracy	100.0%	(fabs.f64 y)
✓	accuracy	100.0%	(*.f64 x #s(literal 3/4 binary64))
✓	accuracy	100.0%	(fabs.f64 (-.f64 y x))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))
✓	accuracy	99.9%	(pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64))
✓	accuracy	99.5%	(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)

Rules

3664×	`accelerator-lowering-fma.f32`
3664×	`accelerator-lowering-fma.f64`
2600×	`-lowering-.f32`
2600×	`-lowering-.f64`
1258×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	146
1	50	144
2	76	136
3	121	136
4	274	128
5	622	128
6	1139	128
7	2367	128
8	3921	128
9	4855	128
10	5398	128
11	5563	128
12	5743	128
13	6822	128
14	7475	128
15	7554	128
16	7607	128
17	7649	128
18	7667	128
19	7685	128
20	7761	128
21	7969	128
22	7969	128
0	8025	121

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

Results

145.0ms	176×	0	valid
78.0ms	59×	0	invalid
20.0ms	9×	2	valid
13.0ms	8×	1	valid
16.0ms	4×	3	valid

Compiler

Compiled 177 to 88 computations (50.3% saved)

Precisions

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

ival-pow: 70.0ms (41.2% of total)

ival-div: 33.0ms (19.4% of total)

ival-sub: 18.0ms (10.6% of total)

ival-mult: 13.0ms (7.6% of total)

ival-add: 10.0ms (5.9% of total)

ival-fabs: 9.0ms (5.3% of total)

backward-pass: 6.0ms (3.5% of total)

const: 5.0ms (2.9% of total)

<compiled-spec>: 5.0ms (2.9% of total)

series46.0ms (0.4%)

Counts

17 → 372

Calls

Call 1

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

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

Calls

93 calls:

Time	Variable		Point	Expression
6.0ms	y	@	0	(+ (* (pow (/ 2 (fabs (- y x))) -1/2) (pow (/ 2 (fabs (- y x))) -1/2)) x)
3.0ms	y	@	-inf	(pow (pow (+ x (/ (fabs (- x y)) 2)) -1/2) 2)
1.0ms	x	@	0	(pow (+ x (/ (fabs (- x y)) 2)) -1/2)
1.0ms	x	@	-inf	(pow (+ x (/ (fabs (- x y)) 2)) -1/2)
1.0ms	y	@	inf	(pow (pow (+ x (/ (fabs (- x y)) 2)) -1/2) 2)

rewrite767.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4344×	`-lowering-.f32`
4344×	`-lowering-.f64`
4268×	`/-lowering-/.f32`
4268×	`/-lowering-/.f64`
4228×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	125
1	190	119
2	1488	119
0	8499	112

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 555

Calls

Call 1

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

Outputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)
(exp.f64 (log.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)))
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) x)
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -1/4 binary64)) x)
(fma.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)
(fma.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64) x)
(fma.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64) x)
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)) x)
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -1/8 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/4 binary64)) x)
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 1/2 binary64) x)
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x))) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1/2 binary64)) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/4 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -1/8 binary64)) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1 binary64)) #s(literal -1/2 binary64) x)
(fma.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)
(fma.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) x)
(fma.f64 (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)) x)
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))) (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))) (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(/.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))) (neg.f64 (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))) (neg.f64 (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))) (neg.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) (neg.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)))
(/.f64 (exp.f64 (log.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))))) (exp.f64 (log.f64 (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))))))
(/.f64 (exp.f64 (log.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))))) (exp.f64 (log.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) (.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))) (*.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) (.f64 x x))) (*.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))))) (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))))) (neg.f64 (neg.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)))) (neg.f64 (neg.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))))
(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal -4 binary64))
(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))
(*.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1 binary64))
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(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))))) (neg.f64 (neg.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)))) (neg.f64 (neg.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal -4 binary64))
(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))
(*.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (*.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)))))
(.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))))
(.f64 (-.f64 (.f64 x x) (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
(.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)))
(*.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -3/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) (/.f64 (*.f64 x (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal -2 binary64)))
(neg.f64 (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))))))
(/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (fabs.f64 y) (.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 y) (/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y))) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
(.f64 (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 1/2 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))) #s(literal -1/2 binary64))
(.f64 #s(literal 1/2 binary64) (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))))
(.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y))))) #s(literal -1 binary64)))

simplify603.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

5346×	`accelerator-lowering-fma.f32`
5346×	`accelerator-lowering-fma.f64`
4134×	`-lowering-.f32`
4134×	`-lowering-.f64`
2942×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	287	3226
1	799	2846
2	2069	2762
3	6495	2755
0	8141	2599

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

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

eval283.0ms (2.5%)

Compiler: Compiled 21508 to 10728 computations (50.1% saved)

prune118.0ms (1%)

Pruning

19 alts after pruning (12 fresh and 7 done)

	Pruned	Kept	Total
New	1079	5	1084
Fresh	2	7	9
Picked	2	3	5
Done	0	4	4
Total	1083	19	1102

Accuracy

100.0%

Counts

1102 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(fma.f64 (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)) x)
	25.7%	(/.f64 (/.f64 (-.f64 (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 16 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
	6.8%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
	25.8%	(/.f64 (-.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
	75.8%	(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal 4 binary64)))
✓	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
▶	11.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
▶	66.2%	(+.f64 x (/.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
	63.2%	(+.f64 x (/.f64 (fabs.f64 (.f64 y (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 y x) (.f64 (/.f64 y x) (/.f64 y x)))) #s(literal 1 binary64)) (+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x (neg.f64 y)) #s(literal 1 binary64))))))) #s(literal 2 binary64)))
✓	87.2%	(+.f64 x (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
▶	90.4%	(+.f64 x (/.f64 (fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) #s(literal 2 binary64)))
	52.8%	(+.f64 x (/.f64 (fabs.f64 (neg.f64 x)) #s(literal 2 binary64)))
✓	56.8%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
✓	99.7%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))
	99.0%	(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
✓	11.8%	(*.f64 x #s(literal 3/4 binary64))
▶	48.5%	(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))
✓	11.9%	x

Compiler

Compiled 570 to 359 computations (37% saved)

localize687.0ms (6%)

Algorithm

1×	egg-herbie

Localize:

Found 32 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	256	(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	cost-diff	256	(fabs.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y))))
✓	cost-diff	256	(/.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64))
✓	cost-diff	256	(+.f64 x (/.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
✓	cost-diff	256	(*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))
✓	cost-diff	256	(fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x))))
✓	cost-diff	256	(/.f64 (fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) #s(literal 2 binary64))
✓	cost-diff	256	(+.f64 x (/.f64 (fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) #s(literal 2 binary64)))
✓	cost-diff	0	(fabs.f64 y)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	64	(pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))
✓	cost-diff	128	(*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))
✓	cost-diff	128	(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	6464	(fma.f64 (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)) x)
✓	accuracy	99.9%	(+.f64 x (/.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
✓	accuracy	99.8%	(/.f64 (/.f64 x y) (/.f64 y x))
✓	accuracy	91.9%	(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y)
✓	accuracy	74.9%	(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	accuracy	100.0%	(+.f64 #s(literal -1 binary64) (/.f64 y x))
✓	accuracy	100.0%	(fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x))))
✓	accuracy	99.9%	(+.f64 x (/.f64 (fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) #s(literal 2 binary64)))
✓	accuracy	90.5%	(*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))
✓	accuracy	100.0%	(fabs.f64 y)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))
✓	accuracy	100.0%	(pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))
✓	accuracy	99.8%	(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)) #s(literal -1/2 binary64))
✓	accuracy	99.3%	(fma.f64 (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)) x)

Rules

3658×	`accelerator-lowering-fma.f32`
3658×	`accelerator-lowering-fma.f64`
3114×	`-lowering-.f32`
3114×	`-lowering-.f64`
2440×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	214
1	76	214
2	172	214
3	501	206
4	1428	186
5	2951	186
6	4835	186
0	8273	185

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

Results

202.0ms	235×	0	valid
28.0ms	9×	2	valid
13.0ms	8×	1	valid
17.0ms	4×	3	valid

Compiler

Compiled 249 to 110 computations (55.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 189.0ms

ival-div: 40.0ms (21.2% of total)

ival-add: 40.0ms (21.2% of total)

ival-pow: 36.0ms (19.1% of total)

ival-mult: 27.0ms (14.3% of total)

ival-sub: 14.0ms (7.4% of total)

ival-fabs: 14.0ms (7.4% of total)

backward-pass: 8.0ms (4.2% of total)

const: 5.0ms (2.6% of total)

<compiled-spec>: 5.0ms (2.6% of total)

series59.0ms (0.5%)

Counts

20 → 432

Calls

Call 1

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

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

Calls

108 calls:

Time	Variable		Point	Expression
13.0ms	x	@	inf	(+ x (/ (fabs (/ (* (- 1 (/ (/ x y) (/ y x))) y) (+ 1 (/ x y)))) 2))
1.0ms	x	@	inf	(/ (* (- 1 (/ (/ x y) (/ y x))) y) (+ 1 (/ x y)))
1.0ms	y	@	0	(/ (* (- 1 (/ (/ x y) (/ y x))) y) (+ 1 (/ x y)))
1.0ms	y	@	-inf	(/ (* (- 1 (/ (/ x y) (/ y x))) y) (+ 1 (/ x y)))
1.0ms	x	@	0	(/ (* (- 1 (/ (/ x y) (/ y x))) y) (+ 1 (/ x y)))

rewrite642.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

5362×	`/-lowering-/.f32`
5362×	`/-lowering-/.f64`
4428×	`accelerator-lowering-fma.f32`
4428×	`accelerator-lowering-fma.f64`
3082×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	188
1	228	144
2	2130	140
0	8739	133

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 649

Calls

Call 1

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

Outputs
(+.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(+.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)
(-.f64 (/.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))) (/.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))))
(fma.f64 x #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(fma.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) x)
(fma.f64 (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)
(fma.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64))) x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64))) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64))) x)
(fma.f64 (.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64))) x)
(fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64))) (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/8 binary64)) x)
(fma.f64 (.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)
(fma.f64 (.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64)) x)
(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(fma.f64 (fabs.f64 (pow.f64 x #s(literal 1/2 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/2 binary64))) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (.f64 (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) x)))) (+.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/2 binary64)) (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)))) (-.f64 (.f64 x x) (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/4 binary64)))) (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/4 binary64)))) (+.f64 (.f64 x x) (-.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (.f64 (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) x)))))
(/.f64 (-.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x x)) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/4 binary64))))) (neg.f64 (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/4 binary64))))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (.f64 (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)) x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x x))) (neg.f64 (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64)))) (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/4 binary64)))))) (neg.f64 (neg.f64 (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64)))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x x)))) (neg.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))))) (neg.f64 (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)) (/.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x))) (+.f64 (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x))) (.f64 (/.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 3/4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x (-.f64 x (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))))))))
(.f64 (-.f64 (.f64 (fabs.f64 (-.f64 y x)) (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 1/4 binary64))) x)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1/2 binary64)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1/4 binary64)) (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1/4 binary64))))
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(/.f64 (fabs.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (.f64 y (/.f64 y x)) (.f64 y (/.f64 y x))))) y)) (fabs.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (*.f64 y (/.f64 y x)))) (+.f64 #s(literal 1 binary64) (/.f64 x y)))))
(/.f64 (fabs.f64 (.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 y (/.f64 y x))))) #s(literal 1 binary64))) (fabs.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(/.f64 (fabs.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (/.f64 y x) (/.f64 (/.f64 y x) (/.f64 x y))) (.f64 y (.f64 y y))))) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))) (fabs.f64 (+.f64 #s(literal 1 binary64) (.f64 (/.f64 x (.f64 y (/.f64 y x))) (+.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x))))))))
(/.f64 (fabs.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (.f64 y (/.f64 y x)) (.f64 y (/.f64 y x))))) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y))))) (fabs.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x))))))
(/.f64 (neg.f64 (neg.f64 (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x)))))))) (neg.f64 (neg.f64 (fabs.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y))))))
(pow.f64 (fabs.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x y))) y)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))))
(*.f64 (fabs.f64 y) (fabs.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y))))
(.f64 (fabs.f64 y) (fabs.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 y (/.f64 y x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x y))))))
(.f64 (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 y (/.f64 y x)))))) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)))))
(.f64 (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 y (/.f64 y x)))))) (fabs.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 y x))))))
(.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x))))) (fabs.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))))
(.f64 (fabs.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))) (fabs.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x))))))
(.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)))) (fabs.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 y (/.f64 y x)))))))
(.f64 (fabs.f64 (/.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x))))) (-.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x)))))) (fabs.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y))))
(.f64 (fabs.f64 (/.f64 (.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x (.f64 y (/.f64 y x))))) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y)))))) (fabs.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) (/.f64 y x)))))

simplify337.0ms (3%)

Algorithm

1×	egg-herbie

Rules

4736×	`accelerator-lowering-fma.f32`
4736×	`accelerator-lowering-fma.f64`
3972×	`-lowering-.f32`
3972×	`-lowering-.f64`
1228×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	118	3377
1	290	3365
2	682	2989
3	2223	2989
4	4633	2989
0	8184	2926

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

Inputs
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
x
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (neg (+ x (* -1 y))))))
(* 1/2 (sqrt (fabs (neg (+ x (* -1 y))))))
(* 1/2 (sqrt (fabs (neg (+ x (* -1 y))))))
(* 1/2 (sqrt (fabs (neg (+ x (* -1 y))))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (- y x))))
(* 1/2 (sqrt (fabs (+ y (* -1 x)))))
(* 1/2 (sqrt (fabs (+ y (* -1 x)))))
(* 1/2 (sqrt (fabs (+ y (* -1 x)))))
(* 1/2 (sqrt (fabs (+ y (* -1 x)))))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (neg (+ x (* -1 y)))))
(sqrt (fabs (neg (+ x (* -1 y)))))
(sqrt (fabs (neg (+ x (* -1 y)))))
(sqrt (fabs (neg (+ x (* -1 y)))))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (- y x)))
(sqrt (fabs (+ y (* -1 x))))
(sqrt (fabs (+ y (* -1 x))))
(sqrt (fabs (+ y (* -1 x))))
(sqrt (fabs (+ y (* -1 x))))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (neg (+ x (* -1 y)))))
(/ 2 (fabs (neg (+ x (* -1 y)))))
(/ 2 (fabs (neg (+ x (* -1 y)))))
(/ 2 (fabs (neg (+ x (* -1 y)))))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (- y x)))
(/ 2 (fabs (+ y (* -1 x))))
(/ 2 (fabs (+ y (* -1 x))))
(/ 2 (fabs (+ y (* -1 x))))
(/ 2 (fabs (+ y (* -1 x))))
x
x
x
x
x
x
x
x
x
x
x
x
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(fabs y)
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
(* 1/2 (fabs y))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 x)
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
x
(* x (+ 1 (* 1/2 (/ (fabs (* x (- (/ y x) 1))) x))))
(* x (+ 1 (* 1/2 (/ (fabs (* x (- (/ y x) 1))) x))))
(* x (+ 1 (* 1/2 (/ (fabs (* x (- (/ y x) 1))) x))))
x
(* -1 (* x (- (* -1/2 (/ (fabs (* x (- (/ y x) 1))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (* x (- (/ y x) 1))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (* x (- (/ y x) 1))) x)) 1)))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* x (- (/ y x) 1)))))
(+ x (* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))))
(+ x (* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))))
(+ x (* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))))
(+ x (* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* x (- (/ y x) 1)))
(fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))
(fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))
(fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))
(fabs (* -1 (* x (+ 1 (* -1 (/ y x))))))
-1
(- (/ y x) 1)
(- (/ y x) 1)
(- (/ y x) 1)
(/ y x)
(* y (- (/ 1 x) (/ 1 y)))
(* y (- (/ 1 x) (/ 1 y)))
(* y (- (/ 1 x) (/ 1 y)))
(/ y x)
(* -1 (* y (- (/ 1 y) (/ 1 x))))
(* -1 (* y (- (/ 1 y) (/ 1 x))))
(* -1 (* y (- (/ 1 y) (/ 1 x))))
(/ y x)
(/ (+ y (* -1 x)) x)
(/ (+ y (* -1 x)) x)
(/ (+ y (* -1 x)) x)
-1
(- (/ y x) 1)
(- (/ y x) 1)
(- (/ y x) 1)
-1
(- (/ y x) 1)
(- (/ y x) 1)
(- (/ y x) 1)
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 x)
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
y
(+ y (* -1 (/ (pow x 2) y)))
(+ y (* -1 (/ (pow x 2) y)))
(+ y (* -1 (/ (pow x 2) y)))
(* -1 (/ (pow x 2) y))
(* (pow x 2) (- (/ y (pow x 2)) (/ 1 y)))
(* (pow x 2) (- (/ y (pow x 2)) (/ 1 y)))
(* (pow x 2) (- (/ y (pow x 2)) (/ 1 y)))
(* -1 (/ (pow x 2) y))
(* (pow x 2) (- (/ y (pow x 2)) (/ 1 y)))
(* (pow x 2) (- (/ y (pow x 2)) (/ 1 y)))
(* (pow x 2) (- (/ y (pow x 2)) (/ 1 y)))
(* -1 (/ (pow x 2) y))
(/ (+ (* -1 (pow x 2)) (pow y 2)) y)
(/ (+ (* -1 (pow x 2)) (pow y 2)) y)
(/ (+ (* -1 (pow x 2)) (pow y 2)) y)
y
(* y (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
y
(* -1 (* y (- (/ (pow x 2) (pow y 2)) 1)))
(* -1 (* y (- (/ (pow x 2) (pow y 2)) 1)))
(* -1 (* y (- (/ (pow x 2) (pow y 2)) 1)))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(/ (pow x 2) (pow y 2))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
x
(* x (+ 1 (* 1/2 (/ (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))) x))))
(* x (+ 1 (* 1/2 (/ (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))) x))))
(* x (+ 1 (* 1/2 (/ (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))) x))))
x
(* -1 (* x (- (* -1/2 (/ (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y))))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y))))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y))))) x)) 1)))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(+ x (* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (neg (+ x (* -1 y)))))
(/ 4 (fabs (neg (+ x (* -1 y)))))
(/ 4 (fabs (neg (+ x (* -1 y)))))
(/ 4 (fabs (neg (+ x (* -1 y)))))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (- y x)))
(/ 4 (fabs (+ y (* -1 x))))
(/ 4 (fabs (+ y (* -1 x))))
(/ 4 (fabs (+ y (* -1 x))))
(/ 4 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* x (- (/ y x) 1))))
(* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x)))))))
(* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x)))))))
(* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x)))))))
(* 1/2 (fabs (* -1 (* x (+ 1 (* -1 (/ y x)))))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y))))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y))))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y))))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y))))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(* 1/2 (fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y)))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y)))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y)))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y)))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (- 1 (* -1 (/ x y)))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))
(fabs (/ (* y (- 1 (/ (pow x 2) (pow y 2)))) (+ 1 (/ x y))))

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

eval251.0ms (2.2%)

Compiler: Compiled 22000 to 11743 computations (46.6% saved)

prune137.0ms (1.2%)

Pruning

20 alts after pruning (10 fresh and 10 done)

	Pruned	Kept	Total
New	1075	6	1081
Fresh	3	4	7
Picked	2	3	5
Done	0	7	7
Total	1080	20	1100

Accuracy

100.0%

Counts

1100 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.8%	(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (/.f64 (fabs.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 y #s(literal 1 binary64)))) #s(literal 2 binary64)))
	6.8%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
	25.8%	(/.f64 (-.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
	90.3%	(/.f64 (+.f64 (.f64 (fabs.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (.f64 y #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))
	90.2%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (fabs.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 y #s(literal 1 binary64))))))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
✓	11.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
	87.0%	(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x y))) y))) #s(literal 2 binary64)))
	57.4%	(+.f64 x (/.f64 (fabs.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
✓	87.2%	(+.f64 x (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
✓	90.4%	(+.f64 x (/.f64 (fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) #s(literal 2 binary64)))
	52.8%	(+.f64 x (/.f64 (fabs.f64 (neg.f64 x)) #s(literal 2 binary64)))
✓	56.8%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
✓	99.7%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))
	99.0%	(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
✓	11.8%	(*.f64 x #s(literal 3/4 binary64))
✓	48.5%	(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))
	8.5%	(fabs.f64 x)
✓	11.9%	x

Compiler

Compiled 876 to 503 computations (42.6% saved)

regimes32.0ms (0.3%)

Counts

33 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
(fabs.f64 x)
(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))
(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
(+.f64 x (/.f64 (fabs.f64 (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))))
(+.f64 x (/.f64 (fabs.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 y x)))) #s(literal 2 binary64)))
(+.f64 x (/.f64 (fabs.f64 (*.f64 y (-.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
(+.f64 x (/.f64 (fabs.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))))
(+.f64 x (/.f64 (fabs.f64 (/.f64 (-.f64 (.f64 y y) (.f64 x x)) (+.f64 x y))) #s(literal 2 binary64)))
(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x y))) y))) #s(literal 2 binary64)))
(/.f64 (-.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(/.f64 (+.f64 (.f64 (fabs.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (.f64 y #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))
(+.f64 x (/.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 x y) (/.f64 y x))) y) (+.f64 #s(literal 1 binary64) (/.f64 x y)))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (fabs.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 y #s(literal 1 binary64))))))))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(+.f64 x (/.f64 (fabs.f64 (.f64 y (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 y x) (.f64 (/.f64 y x) (/.f64 y x)))) #s(literal 1 binary64)) (+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x (neg.f64 y)) #s(literal 1 binary64))))))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 16 binary64))) (.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))) (+.f64 (.f64 x x) (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))))
(/.f64 (/.f64 (-.f64 (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 16 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(+.f64 x (/.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y)))) (+.f64 (/.f64 (.f64 y y) (+.f64 x y)) (/.f64 (.f64 x x) (+.f64 x y))))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal 4 binary64)))
(+.f64 (.f64 y (+.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) x)) (/.f64 (.f64 y #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) x)))) (/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) x)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (/.f64 (fabs.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 y #s(literal 1 binary64)))) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -1/2 binary64)) x)
(*.f64 (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 x y)) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(+.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 x y))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))))

Outputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Calls

3 calls:

11.0ms	y
10.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
9.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes20.0ms (0.2%)

Counts

8 → 3

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
(fabs.f64 x)
(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))
(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
(+.f64 x (/.f64 (fabs.f64 (neg.f64 x)) #s(literal 2 binary64)))

Outputs
(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
(+.f64 x (/.f64 (fabs.f64 (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))

Calls

2 calls:

11.0ms	x
8.0ms	y

Results

Accuracy	Segments	Branch
80.8%	5	`x`
78.2%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
(fabs.f64 x)
(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))
(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))

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

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
56.8%	1	`x`
56.8%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
(fabs.f64 x)
(*.f64 #s(literal 1/2 binary64) (fabs.f64 y))

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

Calls

2 calls:

4.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
48.5%	1	`x`
51.0%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Accuracy

Total -5.4b remaining (-9.5%)

Threshold costs -5.4b (-9.5%)

Counts

5 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (neg.f64 x))
(fabs.f64 x)

Outputs
x

Calls

2 calls:

3.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
11.9%	1	`y`
11.9%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch25.0ms (0.2%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	3.2478574278179795e-94	5.26950330497773e-93
12.0ms	-1.3639600404976385e-28	-4.4422651402128956e-32

Results

13.0ms	231×	0	valid
1.0ms	6×	1	valid
0.0ms	2×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 300 to 236 computations (21.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 2.0ms (29.3% of total)

ival-sub: 2.0ms (29.3% of total)

ival-fabs: 1.0ms (14.7% of total)

ival-add: 1.0ms (14.7% of total)

const: 0.0ms (0% of total)

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

soundness1.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 48 to 30 computations (37.5% saved)

preprocess33.0ms (0.3%)

Compiler: Compiled 116 to 74 computations (36.2% saved)

Iter	Nodes	Cost
0	23	56
1	52	48
2	135	48
3	262	48
4	382	48
5	459	48
6	522	48
7	565	48
8	569	48
9	572	48
10	574	48
0	7	8
1	12	8
2	19	8
3	27	8
4	46	8
5	93	8
6	151	8
7	180	8
8	225	8
9	261	8
10	297	8
11	309	8
12	315	8
13	318	8
14	320	8
0	320	7

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	27	24
4	46	24
5	93	24
6	151	24
7	180	24
8	225	24
9	261	24
10	297	24
11	309	24
12	315	24
13	318	24
14	320	24
0	320	23

Iter	Nodes	Cost
0	23	56
1	52	48
2	135	48
3	262	48
4	382	48
5	459	48
6	522	48
7	565	48
8	569	48
9	572	48
10	574	48
0	7	8
1	12	8
2	19	8
3	27	8
4	46	8
5	93	8
6	151	8
7	180	8
8	225	8
9	261	8
10	297	8
11	309	8
12	315	8
13	318	8
14	320	8
0	320	7

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	27	24
4	46	24
5	93	24
6	151	24
7	180	24
8	225	24
9	261	24
10	297	24
11	309	24
12	315	24
13	318	24
14	320	24
0	320	23

analyze0.0ms (0%)

sample859.0ms (7.5%)

preprocess44.0ms (0.4%)

explain75.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

localize144.0ms (1.3%)

series7.0ms (0.1%)

rewrite629.0ms (5.5%)

simplify293.0ms (2.6%)

eval58.0ms (0.5%)

prune68.0ms (0.6%)

localize986.0ms (8.7%)

series138.0ms (1.2%)

rewrite1.1s (10%)

simplify938.0ms (8.2%)

eval705.0ms (6.2%)

prune482.0ms (4.2%)

localize767.0ms (6.7%)

series46.0ms (0.4%)

rewrite767.0ms (6.7%)

simplify603.0ms (5.3%)

eval283.0ms (2.5%)

prune118.0ms (1%)

localize687.0ms (6%)

series59.0ms (0.5%)

rewrite642.0ms (5.6%)

simplify337.0ms (3%)

eval251.0ms (2.2%)

prune137.0ms (1.2%)

regimes32.0ms (0.3%)

regimes20.0ms (0.2%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

bsearch25.0ms (0.2%)

soundness1.0ms (0%)

preprocess33.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	23	56
1	52	48
2	135	48
3	262	48
4	382	48
5	459	48
6	522	48
7	565	48
8	569	48
9	572	48
10	574	48
0	7	8
1	12	8
2	19	8
3	27	8
4	46	8
5	93	8
6	151	8
7	180	8
8	225	8
9	261	8
10	297	8
11	309	8
12	315	8
13	318	8
14	320	8
0	320	7

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	27	24
4	46	24
5	93	24
6	151	24
7	180	24
8	225	24
9	261	24
10	297	24
11	309	24
12	315	24
13	318	24
14	320	24
0	320	23