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)

sample894.0ms (10.1%)

Results

478.0ms	7944×	0	valid
17.0ms	101×	2	valid
15.0ms	70×	3	valid
15.0ms	141×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 295.0ms

ival-fabs: 96.0ms (32.5% of total)

ival-sub: 68.0ms (23% of total)

ival-div: 65.0ms (22% of total)

ival-add: 47.0ms (15.9% of total)

const: 11.0ms (3.7% of total)

backward-pass: 9.0ms (3% of total)

Bogosity

preprocess92.0ms (1%)

Algorithm

2×	egg-herbie

Rules

552×	`fnmadd-define`
488×	`fnmsub-define`
488×	`fmsub-define`
446×	`fmm-def`
294×	`sum3-define`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	52	48
2	143	48
3	372	48
4	795	44
5	1281	44
6	1538	42
7	1786	42
8	1897	42
9	1934	42
10	1954	42
11	1962	42
0	7	8
1	12	8
2	19	8
3	28	8
4	50	8
5	123	8
6	278	8
7	436	8
8	581	7
9	722	7
10	871	7
11	943	7
12	957	7
13	970	7
14	990	7
15	998	7
0	998	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))
(fma (fabs (- y x)) 1/2 x)
(+ (neg x) (/ (fabs (- y (neg x))) 2))
(fnmsub (fabs (+ x y)) -1/2 x)
(+ x (/ (fabs (- (neg y) x)) 2))
(fma (fabs (+ x y)) 1/2 x)
(neg (+ (neg x) (/ (fabs (- y (neg x))) 2)))
(fma (fabs (+ x y)) -1/2 x)
(neg (+ x (/ (fabs (- (neg y) x)) 2)))
(fnmsub (fabs (+ x y)) 1/2 x)
(+ y (/ (fabs (- x y)) 2))
(fma (fabs (- y x)) 1/2 y)

explain75.0ms (0.8%)

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

44.0ms	498×	0	valid
2.0ms	8×	2	valid
1.0ms	2×	3	valid
1.0ms	4×	1	valid

Compiler

Compiled 64 to 23 computations (64.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-div: 6.0ms (35.1% of total)

ival-sub: 4.0ms (23.4% of total)

ival-fabs: 4.0ms (23.4% of total)

ival-add: 3.0ms (17.5% of total)

const: 1.0ms (5.8% of total)

backward-pass: 1.0ms (5.8% 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)

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 y x)
✓	cost-diff	(fabs.f64 (-.f64 y x))
✓	cost-diff	(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
✓	cost-diff	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Rules

248×	`fnmadd-define`
212×	`fnmsub-define`
212×	`fmsub-define`
202×	`fmm-def`
192×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	28	24
4	50	24
5	123	24
6	278	24
7	436	24
8	581	23
9	722	23
10	871	23
11	943	23
12	957	23
13	970	23
14	990	23
15	998	23
0	998	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)

localize33.0ms (0.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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)))

Results

24.0ms	249×	0	valid
1.0ms	4×	2	valid
0.0ms	2×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 27 to 8 computations (70.4% saved)

Precisions

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

ival-add: 4.0ms (38.1% of total)

ival-div: 2.0ms (19% of total)

ival-sub: 2.0ms (19% of total)

ival-fabs: 2.0ms (19% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0%)

Counts

4 → 96

Calls

Call 1

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

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 (* 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 (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)))))>

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))

rewrite450.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2728×	`-lowering-.f32`
2728×	`-lowering-.f64`
2374×	`/-lowering-/.f32`
2374×	`/-lowering-/.f64`
1952×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	47	20
2	399	20
3	5813	20
0	8172	20

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 196

Calls

Call 1

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

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

simplify142.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1496×	`sum5-define`
1462×	`fmsub-define`
1448×	`fnmsub-define`
1210×	`sum3-define`
1192×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	479
1	117	458
2	293	458
3	903	458
4	3274	458
5	6167	458
0	8066	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))))))
(* 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))))
(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)))))

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

eval51.0ms (0.6%)

Compiler: Compiled 7005 to 800 computations (88.6% saved)

prune43.0ms (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	283	9	292
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	283	10	293

Accuracy

100.0%

Counts

293 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.9%	(/.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))
▶	33.3%	(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #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))))))
▶	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
	53.4%	(+.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)))
▶	99.9%	(+.f64 x (/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #s(literal 2 binary64)))
	60.2%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
	99.2%	(+.f64 x (*.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))))
	51.8%	(.f64 (/.f64 #s(literal 1 binary64) (+.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))))
▶	11.1%	x

Compiler

Compiled 354 to 197 computations (44.4% saved)

simplify189.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #s(literal 3/2 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #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))))))
✓	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	512	(*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))
✓	cost-diff	512	(fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y))))
✓	cost-diff	512	(/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #s(literal 2 binary64))
✓	cost-diff	512	(+.f64 x (/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #s(literal 2 binary64)))

Rules

2174×	`fma-lowering-fma.f32`
2174×	`fma-lowering-fma.f64`
1534×	`fmsub-define`
1492×	`-lowering-.f32`
1492×	`-lowering-.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	419
1	77	415
2	167	415
3	359	305
4	1292	285
5	5995	285
0	8284	285

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize236.0ms (2.7%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(pow.f64 (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #s(literal 3/2 binary64))
✓	accuracy	96.8%	(+.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)))))
✓	accuracy	82.4%	(+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #s(literal 3/2 binary64)))
✓	accuracy	36.1%	(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #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))))))
✓	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	78.6%	(-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))
✓	accuracy	54.2%	(/.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	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y))))
✓	accuracy	100.0%	(/.f64 (-.f64 y x) (+.f64 x y))
✓	accuracy	99.9%	(*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))
✓	accuracy	99.9%	(+.f64 x (/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #s(literal 2 binary64)))

Results

141.0ms	227×	0	valid
11.0ms	6×	3	valid
10.0ms	13×	1	valid
10.0ms	8×	2	valid
6.0ms	2×	5	exit

Compiler

Compiled 345 to 34 computations (90.1% saved)

Precisions

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

ival-pow: 33.0ms (30.8% of total)

ival-add: 28.0ms (26.2% of total)

ival-div: 21.0ms (19.6% of total)

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

ival-sub: 5.0ms (4.7% of total)

ival-fabs: 4.0ms (3.7% of total)

backward-pass: 4.0ms (3.7% of total)

const: 1.0ms (0.9% of total)

series45.0ms (0.5%)

Counts

21 → 480

Calls

Call 1

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

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

Calls

120 calls:

Time	Variable		Point	Expression
6.0ms	y	@	inf	(/ (+ (* x (* x x)) (pow (/ (* (- y x) (- y x)) 4) 3/2)) (+ (/ (* (- y x) (- y x)) 4) (* x (+ x (/ (fabs (- y x)) -2)))))
5.0ms	y	@	-inf	(/ (- (/ (* (- y x) (- y x)) 4) (* x x)) (- (/ (fabs (- y x)) 2) x))
3.0ms	y	@	0	(/ (+ (* x (* x x)) (pow (/ (* (- y x) (- y x)) 4) 3/2)) (+ (/ (* (- y x) (- y x)) 4) (* x (+ x (/ (fabs (- y x)) -2)))))
2.0ms	x	@	inf	(/ (+ (* x (* x x)) (pow (/ (* (- y x) (- y x)) 4) 3/2)) (+ (/ (* (- y x) (- y x)) 4) (* x (+ x (/ (fabs (- y x)) -2)))))
1.0ms	x	@	0	(/ (+ (* x (* x x)) (pow (/ (* (- y x) (- y x)) 4) 3/2)) (+ (/ (* (- y x) (- y x)) 4) (* x (+ x (/ (fabs (- y x)) -2)))))

rewrite485.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4502×	`-lowering-.f32`
4502×	`-lowering-.f64`
3230×	`/-lowering-/.f32`
3230×	`/-lowering-/.f64`
3050×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	252
1	241	169
2	2414	164
0	11460	164

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1223

Calls

Call 1

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

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 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) x))
(+.f64 (/.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))))
(+.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)))
(+.f64 (fma.f64 (-.f64 y x) (/.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) x))) (fma.f64 (neg.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))) x (.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) x)))
(+.f64 (fma.f64 (-.f64 y x) (/.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (.f64 x x)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))) (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (*.f64 x x))))
(+.f64 (fma.f64 (-.f64 y x) (/.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (.f64 (+.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (/.f64 (.f64 x x) (-.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)) (.f64 x (.f64 x x))))))) (fma.f64 (neg.f64 (+.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))) (/.f64 (.f64 x x) (-.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (/.f64 (.f64 x x) (-.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)) (.f64 x (.f64 x x)))))))
(+.f64 (fma.f64 (-.f64 y x) (/.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (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 (-.f64 y x) #s(literal 4 binary64))) (.f64 x x)))))) (fma.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) x) (/.f64 (.f64 x x) (-.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x x))) (.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (/.f64 (.f64 x x) (-.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (*.f64 x x))))))
(+.f64 (fma.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) x))) (fma.f64 (neg.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))) x (*.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) x)))
(+.f64 (fma.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (.f64 x x)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))) (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (.f64 x x))))
(+.f64 (fma.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (.f64 (+.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (/.f64 (.f64 x x) (-.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)) (.f64 x (.f64 x x))))))) (fma.f64 (neg.f64 (+.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))) (/.f64 (.f64 x x) (-.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))) (/.f64 (.f64 x x) (-.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)) (.f64 x (*.f64 x x)))))))
(+.f64 (fma.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (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 (-.f64 y x) #s(literal 4 binary64))) (.f64 x x)))))) (fma.f64 (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) x) (/.f64 (.f64 x x) (-.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x x))) (.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (/.f64 (.f64 x x) (-.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 x x))))))
(+.f64 (fma.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (neg.f64 (.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) x))) (fma.f64 (neg.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))) x (*.f64 (/.f64 x (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) x)))
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(exp.f64 (*.f64 (log.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 16 binary64))) #s(literal 3/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64)))) #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64)))) #s(literal 3/4 binary64)) (.f64 (log.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64)))) #s(literal 3/4 binary64))))
(neg.f64 (pow.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 #s(literal -2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (/.f64 #s(literal -2 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 3 binary64)))
(/.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 8 binary64))
(/.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal -8 binary64))
(/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 8 binary64))
(/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -8 binary64))
(/.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 3 binary64)) #s(literal 8 binary64))
(/.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 3 binary64)) #s(literal -8 binary64))
(pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64))
(pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) #s(literal 3 binary64))
(pow.f64 (/.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal 16 binary64)) #s(literal 3/4 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -3/2 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (-.f64 y x))) #s(literal -3 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 3/2 binary64)) (log.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64)))))
(pow.f64 (exp.f64 (log.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) #s(literal 3 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))) #s(literal 3 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)))
(.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))))
(.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)))
(.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))))
(.f64 (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/4 binary64)) (pow.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/4 binary64)))
(.f64 (.f64 (fabs.f64 (-.f64 y x)) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal 1/8 binary64))
(.f64 (.f64 (fabs.f64 (-.f64 y x)) (*.f64 (-.f64 y x) (-.f64 y x))) #s(literal -1/8 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 (fabs.f64 (-.f64 y x)) (*.f64 (-.f64 y x) (-.f64 y x))))
(.f64 (.f64 (-.f64 y x) (*.f64 (-.f64 y x) (-.f64 y x))) (pow.f64 #s(literal 1/4 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (-.f64 y x) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (-.f64 y x) #s(literal 3/2 binary64)) (pow.f64 (.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (-.f64 y x) #s(literal 3/2 binary64)) (pow.f64 (.f64 #s(literal 1/4 binary64) (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64)))) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 y x) #s(literal 3/2 binary64)))
(.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/2 binary64)) (.f64 (-.f64 y x) (*.f64 (-.f64 y x) (-.f64 y x))))
(.f64 (pow.f64 (-.f64 y x) #s(literal 3/4 binary64)) (pow.f64 (.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64)))) #s(literal 3/4 binary64)))
(.f64 #s(literal -1/8 binary64) (.f64 (fabs.f64 (-.f64 y x)) (*.f64 (-.f64 y x) (-.f64 y x))))
(.f64 (.f64 (*.f64 (-.f64 y x) (-.f64 y x)) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal 1/8 binary64))
(.f64 (.f64 (*.f64 (-.f64 y x) (-.f64 y x)) (-.f64 #s(literal 0 binary64) (fabs.f64 (-.f64 y x)))) #s(literal -1/8 binary64))
(*.f64 (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal -2 binary64)) #s(literal 3/2 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (pow.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 3/2 binary64)) (pow.f64 #s(literal -1/4 binary64) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 3/4 binary64)) (pow.f64 #s(literal 1/16 binary64) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (-.f64 y x)) #s(literal 3/4 binary64)) (pow.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 3/4 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 y x) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal 4 binary64)) #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 y x) #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (fabs.f64 (+.f64 x y)) #s(literal 3 binary64)) (pow.f64 (.f64 (fabs.f64 (/.f64 (-.f64 y x) (+.f64 x y))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (fabs.f64 (+.f64 x y)) #s(literal 3 binary64)) (pow.f64 (/.f64 (fabs.f64 (/.f64 (-.f64 y x) (+.f64 x y))) #s(literal 2 binary64)) #s(literal 3 binary64)))

simplify443.0ms (5%)

Algorithm

1×	egg-herbie

Rules

5118×	`-lowering-.f32`
5118×	`-lowering-.f64`
4918×	`+-lowering-+.f64`
4918×	`+-lowering-+.f32`
1168×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	969	7295
1	3474	7125
0	8365	7125

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

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

Outputs
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(.f64 (.f64 x x) (+.f64 #s(literal 5/4 binary64) (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 y x) (/.f64 (fabs.f64 (-.f64 y x)) x)))))
(* (pow x 2) (+ 5/4 (+ (* -1/2 (/ y x)) (+ (* -1/2 (/ (fabs (- y x)) x)) (* 1/4 (/ (pow y 2) (pow x 2)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 5/4 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 y x) (/.f64 (fabs.f64 (-.f64 y x)) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x x)))))
(* (pow x 2) (+ 5/4 (+ (* -1/2 (/ y x)) (+ (* -1/2 (/ (fabs (- y x)) x)) (* 1/4 (/ (pow y 2) (pow x 2)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 5/4 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 y x) (/.f64 (fabs.f64 (-.f64 y x)) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x x)))))
(* 5/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 5/4 binary64))
(* (pow x 2) (+ 5/4 (* -1 (/ (+ (* 1/2 y) (* 1/2 (fabs (+ y (* -1 x))))) x))))
(.f64 (.f64 x x) (-.f64 #s(literal 5/4 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 y (fabs.f64 (-.f64 y x)))) x)))
(* (pow x 2) (+ 5/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (+ (* 1/2 y) (* 1/2 (fabs (+ y (* -1 x)))))) x))))
(.f64 (.f64 x x) (-.f64 #s(literal 5/4 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 y y) x)) (*.f64 #s(literal 1/2 binary64) (+.f64 y (fabs.f64 (-.f64 y x))))) x)))
(* (pow x 2) (+ 5/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (+ (* 1/2 y) (* 1/2 (fabs (+ y (* -1 x)))))) x))))
(.f64 (.f64 x x) (-.f64 #s(literal 5/4 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 y y) x)) (*.f64 #s(literal 1/2 binary64) (+.f64 y (fabs.f64 (-.f64 y x))))) x)))
(* -1/8 (pow x 3))
(.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x)))
(+ (* -1/8 (pow x 3)) (* 1/8 (* y (+ (* 2 (pow x 2)) (pow x 2)))))
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 y (.f64 #s(literal 3 binary64) (*.f64 x x)))))
(+ (* -1/8 (pow x 3)) (* y (+ (* 1/8 (* y (+ (* -2 x) (* -1 x)))) (* 1/8 (+ (* 2 (pow x 2)) (pow x 2))))))
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 y (.f64 #s(literal 1/8 binary64) (+.f64 (.f64 y (.f64 x #s(literal -3 binary64))) (.f64 #s(literal 3 binary64) (*.f64 x x))))))
(+ (* -1/8 (pow x 3)) (* y (+ (* 1/8 (+ (* 2 (pow x 2)) (pow x 2))) (* y (+ (* 1/8 y) (* 1/8 (+ (* -2 x) (* -1 x))))))))
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 y (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) (.f64 x x))) (.f64 y (.f64 #s(literal 1/8 binary64) (+.f64 (.f64 x #s(literal -3 binary64)) y))))))
(* 1/8 (pow y 3))
(.f64 #s(literal 1/8 binary64) (.f64 y (*.f64 y y)))
(* (pow y 3) (+ 1/8 (* 1/8 (/ (+ (* -2 x) (* -1 x)) y))))
(.f64 (.f64 y (.f64 y y)) (.f64 (+.f64 (/.f64 (*.f64 x #s(literal -3 binary64)) y) #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(* (pow y 3) (+ 1/8 (+ (* 1/8 (/ (+ (* -2 x) (* -1 x)) y)) (* 1/8 (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow y 2))))))
(.f64 (.f64 y (.f64 y y)) (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 (.f64 x #s(literal -3 binary64)) y) (/.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) (.f64 y y))))))
(* (pow y 3) (+ 1/8 (+ (* -1/8 (/ (pow x 3) (pow y 3))) (+ (* 1/8 (/ (+ (* -2 x) (* -1 x)) y)) (* 1/8 (/ (+ (* 2 (pow x 2)) (pow x 2)) (pow y 2)))))))
(.f64 (.f64 y (.f64 y y)) (+.f64 #s(literal 1/8 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 (.f64 x #s(literal -3 binary64)) y) (/.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) (.f64 y y)))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 y (*.f64 y y))))))
(* -1/8 (pow y 3))
(.f64 #s(literal -1/8 binary64) (.f64 y (*.f64 y y)))
(* -1 (* (pow y 3) (+ 1/8 (* -1/8 (/ (+ x (* 2 x)) y)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 #s(literal 3 binary64) x)) y)) (neg.f64 (.f64 y (*.f64 y y))))
(* -1 (* (pow y 3) (+ 1/8 (* -1 (/ (+ (* -1/8 (/ (+ (* 2 (pow x 2)) (pow x 2)) y)) (* 1/8 (+ x (* 2 x)))) y)))))
(.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) y)) (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) x))) y)) (neg.f64 (.f64 y (.f64 y y))))
(* -1 (* (pow y 3) (+ 1/8 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 3) y)) (* 1/8 (+ (* 2 (pow x 2)) (pow x 2)))) y)) (* 1/8 (+ x (* 2 x)))) y)))))
(.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) x)) (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) (.f64 x x))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) y)) y)) y)) (neg.f64 (.f64 y (*.f64 y y))))
(* 1/8 (pow y 3))
(.f64 #s(literal 1/8 binary64) (.f64 y (*.f64 y y)))
(+ (* 1/8 (* x (+ (* -2 (pow y 2)) (* -1 (pow y 2))))) (* 1/8 (pow y 3)))
(.f64 #s(literal 1/8 binary64) (+.f64 (.f64 x (.f64 (.f64 y y) #s(literal -3 binary64))) (.f64 y (.f64 y y))))
(+ (* 1/8 (pow y 3)) (* x (+ (* 1/8 (* x (+ y (* 2 y)))) (* 1/8 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))) (.f64 x (.f64 #s(literal 1/8 binary64) (+.f64 (.f64 x (.f64 #s(literal 3 binary64) y)) (.f64 (*.f64 y y) #s(literal -3 binary64))))))
(+ (* 1/8 (pow y 3)) (* x (+ (* 1/8 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (* x (+ (* -1/8 x) (* 1/8 (+ y (* 2 y))))))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))) (.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 y y) #s(literal -3 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) y)) (*.f64 x #s(literal -1/8 binary64)))))))
(* -1/8 (pow x 3))
(.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/8 (/ (+ y (* 2 y)) x)) 1/8))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 3 binary64) y)) x) #s(literal -1/8 binary64)))
(* (pow x 3) (- (+ (* 1/8 (/ (+ y (* 2 y)) x)) (* 1/8 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow x 2)))) 1/8))
(.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 (.f64 #s(literal 3 binary64) y) x) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) (.f64 x x)))) #s(literal -1/8 binary64)))
(* (pow x 3) (- (+ (* 1/8 (/ (+ y (* 2 y)) x)) (+ (* 1/8 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow x 2))) (* 1/8 (/ (pow y 3) (pow x 3))))) 1/8))
(.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 (/.f64 (.f64 #s(literal 3 binary64) y) x) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) (.f64 x x))) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) #s(literal -1/8 binary64)))
(* -1/8 (pow x 3))
(.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (+ 1/8 (* -1/8 (/ (+ y (* 2 y)) x)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 3 binary64) y) x))) (.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(* -1 (* (pow x 3) (+ 1/8 (* -1 (/ (+ (* -1/8 (/ (+ (* 2 (pow y 2)) (pow y 2)) x)) (* 1/8 (+ y (* 2 y)))) x)))))
(.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) y)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 #s(literal 3 binary64) (.f64 y y))) x)) x)) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (+ 1/8 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow y 3) x)) (* 1/8 (+ (* 2 (pow y 2)) (pow y 2)))) x)) (* 1/8 (+ y (* 2 y)))) x)))))
(.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) y)) (/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) x) (.f64 #s(literal 1/8 binary64) (.f64 #s(literal 3 binary64) (.f64 y y)))) x)) x)) (.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))

eval395.0ms (4.4%)

Compiler: Compiled 89044 to 5637 computations (93.7% saved)

prune271.0ms (3.1%)

Pruning

18 alts after pruning (13 fresh and 5 done)

	Pruned	Kept	Total
New	2240	12	2252
Fresh	3	1	4
Picked	1	4	5
Done	0	1	1
Total	2244	18	2262

Accuracy

100.0%

Counts

2262 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	72.5%	(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))
	50.4%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
✓	51.9%	(/.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))
	6.8%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
▶	53.3%	(/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
	26.5%	(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
▶	11.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #s(literal 2 binary64)))
▶	60.2%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
	51.8%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (-.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (*.f64 x x)))
	45.3%	(.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3 binary64) x)) x) y)))
	24.7%	(*.f64 y #s(literal -1/2 binary64))
▶	87.8%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)))
	11.2%	(*.f64 x #s(literal 7/10 binary64))
▶	30.4%	(*.f64 #s(literal 1/2 binary64) y)
✓	11.1%	x

Compiler

Compiled 487 to 298 computations (38.8% saved)

simplify158.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(.f64 #s(literal 1/4 binary64) (.f64 y y))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64)))))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	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 #s(literal 1 binary64) x)
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
✓	cost-diff	256	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)))

Rules

2312×	`fnmadd-define`
1648×	`sum5-define`
1550×	`-lowering-.f32`
1550×	`-lowering-.f64`
1140×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	30	162
1	70	160
2	188	160
3	444	156
4	713	156
5	1093	154
6	3011	154
7	7204	153
0	8731	153

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize149.0ms (1.7%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))))
✓	accuracy	99.9%	(+.f64 (.f64 x #s(literal -3/4 binary64)) (.f64 y #s(literal -1/2 binary64)))
✓	accuracy	94.1%	(+.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64)))))
✓	accuracy	53.8%	(/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	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 #s(literal 1 binary64) x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) y)
✓	accuracy	100.0%	(fabs.f64 (-.f64 y x))
✓	accuracy	100.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
✓	accuracy	87.9%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)))

Results

68.0ms	216×	0	valid
19.0ms	10×	3	valid
12.0ms	20×	1	valid
8.0ms	10×	2	valid

Compiler

Compiled 176 to 31 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-mult: 20.0ms (34.1% of total)

ival-div: 18.0ms (30.7% of total)

ival-add: 6.0ms (10.2% of total)

ival-fabs: 5.0ms (8.5% of total)

ival-sub: 4.0ms (6.8% of total)

backward-pass: 4.0ms (6.8% of total)

const: 1.0ms (1.7% of total)

series26.0ms (0.3%)

Counts

17 → 324

Calls

Call 1

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

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

Calls

81 calls:

Time	Variable		Point	Expression
5.0ms	y	@	inf	(* 1/4 (* y y))
3.0ms	y	@	0	(* x (+ 1 (/ (* 1/2 (fabs (- y x))) x)))
1.0ms	y	@	-inf	(* x (+ (* x -3/4) (* y -1/2)))
1.0ms	y	@	inf	(* x (+ 1 (/ (* 1/2 (fabs (- y x))) x)))
1.0ms	y	@	-inf	(* x (+ 1 (/ (* 1/2 (fabs (- y x))) x)))

rewrite645.0ms (7.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3834×	`/-lowering-/.f32`
3834×	`/-lowering-/.f64`
3602×	`-lowering-.f32`
3602×	`-lowering-.f64`
1612×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	115
1	184	111
2	2073	109
0	8873	109

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 611

Calls

Call 1

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

Outputs
(+.f64 x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(+.f64 (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(fma.f64 x #s(literal 1 binary64) (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64))) x)
(fma.f64 #s(literal 1 binary64) x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (fabs.f64 (-.f64 y x)) x) x) x)
(fma.f64 (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64))) x x)
(fma.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64) x)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) x) x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (fabs.f64 (-.f64 y x)) x) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #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 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64)))) (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #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 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)))) (.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #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 #s(literal 1 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 #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 #s(literal -1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (pow.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 x x) (-.f64 (pow.f64 (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (-.f64 x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64)))) (+.f64 #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 (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) x) (+.f64 #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 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #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 (neg.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))))) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #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 (neg.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))))) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 #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 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (+.f64 #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 #s(literal -1 binary64) x))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) #s(literal 1 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) #s(literal -1 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) x))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (pow.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (pow.f64 (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))))) (neg.f64 (+.f64 #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 (neg.f64 (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) x)) (neg.f64 (+.f64 #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 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x))) x)) (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64))))))
(/.f64 (+.f64 (/.f64 (pow.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (.f64 x (*.f64 x x))) (+.f64 (pow.f64 (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (/.f64 (-.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))))
(.f64 x (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) x)
(*.f64 (+.f64 x (/.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) x)))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) x)
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 y x)) (.f64 x #s(literal 2 binary64)))) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #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 #s(literal 1 binary64) x)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #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)))) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #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 #s(literal -1 binary64) x)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) #s(literal 3/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #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)))) (pow.f64 x #s(literal -1/2 binary64))))
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(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -27/64 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 9/16 binary64)) (.f64 (.f64 y #s(literal -1/2 binary64)) (-.f64 (.f64 y #s(literal -1/2 binary64)) (*.f64 x #s(literal -3/4 binary64)))))) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 9/16 binary64)) (/.f64 (.f64 y y) #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -3/4 binary64)) (.f64 #s(literal 1/2 binary64) y))) (/.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 9/16 binary64)) (/.f64 (.f64 y y) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -3/4 binary64)) (.f64 #s(literal 1/2 binary64) y))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 9/16 binary64)) (/.f64 (.f64 y y) #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -3/4 binary64)) (.f64 #s(literal 1/2 binary64) y))) (/.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 9/16 binary64)) (/.f64 (.f64 y y) #s(literal 4 binary64))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -3/4 binary64)) (.f64 #s(literal 1/2 binary64) y))) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))) #s(literal 1 binary64)) x)
(.f64 (/.f64 (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))))

simplify635.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

4554×	`-lowering-.f32`
4554×	`-lowering-.f64`
2870×	`+-lowering-+.f64`
2870×	`+-lowering-+.f32`
1922×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	2836
1	845	2735
2	2640	2672
0	8152	2672

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 324

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

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

eval162.0ms (1.8%)

Compiler: Compiled 23361 to 2370 computations (89.9% saved)

prune100.0ms (1.1%)

Pruning

19 alts after pruning (10 fresh and 9 done)

	Pruned	Kept	Total
New	978	2	980
Fresh	0	8	8
Picked	1	4	5
Done	0	5	5
Total	979	19	998

Accuracy

100.0%

Counts

998 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.5%	(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))
	50.4%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
✓	51.9%	(/.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))
	6.8%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
▶	26.5%	(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
	26.6%	(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
▶	5.9%	(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
✓	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
✓	11.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #s(literal 2 binary64)))
✓	60.2%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
	51.8%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (-.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (*.f64 x x)))
▶	45.3%	(.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3 binary64) x)) x) y)))
	24.7%	(*.f64 y #s(literal -1/2 binary64))
✓	87.8%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)))
▶	11.2%	(*.f64 x #s(literal 7/10 binary64))
✓	30.4%	(*.f64 #s(literal 1/2 binary64) y)
✓	11.1%	x

Compiler

Compiled 451 to 273 computations (39.5% saved)

simplify131.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal -3/4 binary64))
✓	cost-diff	0	(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
✓	cost-diff	256	(-.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3 binary64) x)) x)
✓	cost-diff	256	(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3 binary64) x)) x) y)
✓	cost-diff	256	(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3 binary64) x)) x) y))
✓	cost-diff	640	(.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3 binary64) x)) x) y)))
✓	cost-diff	0	(*.f64 x #s(literal 7/10 binary64))
✓	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	64	(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	12928	(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))

Rules

2162×	`-lowering-.f32`
2162×	`-lowering-.f64`
2126×	`sum3-define`
1976×	`sum4-define`
760×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	30	163
1	63	153
2	124	149
3	335	149
4	1200	144
5	5104	143
0	8248	143

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(pow (pow (+ x (/ (fabs (- y x)) 2)) 1/2) 2)
(pow (+ x (/ (fabs (- y x)) 2)) 1/2)
(+ x (/ (fabs (- y x)) 2))
x
(/ (fabs (- y x)) 2)
(fabs (- y x))
(- y x)
y
2
1/2
(* x 7/10)
x
7/10
(* (- 0 y) (- 1/2 (/ (- (* 1/2 (* 3 x)) x) y)))
(- 0 y)
0
y
(- 1/2 (/ (- (* 1/2 (* 3 x)) x) y))
1/2
(/ (- (* 1/2 (* 3 x)) x) y)
(- (* 1/2 (* 3 x)) x)
(* 1/2 (* 3 x))
(* 3 x)
3
x
(/ 1 (pow (* x x) -1/2))
1
(pow (* x x) -1/2)
(* x x)
x
-1/2
(/ (* (* x x) -3/4) (- (/ (fabs (- y x)) 2) x))
(* (* x x) -3/4)
(* x x)
x
-3/4
(- (/ (fabs (- y x)) 2) x)
(/ (fabs (- y x)) 2)
(fabs (- y x))
(- y x)
y
2

Outputs
(pow (pow (+ x (/ (fabs (- y x)) 2)) 1/2) 2)
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(pow (+ x (/ (fabs (- y x)) 2)) 1/2)
(sqrt.f64 (+.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)))
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)
1/2
#s(literal 1/2 binary64)
(* x 7/10)
(*.f64 x #s(literal 7/10 binary64))
x
7/10
#s(literal 7/10 binary64)
(* (- 0 y) (- 1/2 (/ (- (* 1/2 (* 3 x)) x) y)))
(*.f64 #s(literal 1/2 binary64) (-.f64 x y))
(- 0 y)
(-.f64 #s(literal 0 binary64) y)
0
#s(literal 0 binary64)
y
(- 1/2 (/ (- (* 1/2 (* 3 x)) x) y))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) y))
1/2
#s(literal 1/2 binary64)
(/ (- (* 1/2 (* 3 x)) x) y)
(/.f64 (*.f64 x #s(literal 1/2 binary64)) y)
(- (* 1/2 (* 3 x)) x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 (* 3 x))
(*.f64 x #s(literal 3/2 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
3
#s(literal 3 binary64)
x
(/ 1 (pow (* x x) -1/2))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
1
#s(literal 1 binary64)
(pow (* x x) -1/2)
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* x x)
(*.f64 x x)
x
-1/2
#s(literal -1/2 binary64)
(/ (* (* x x) -3/4) (- (/ (fabs (- y x)) 2) x))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(* (* x x) -3/4)
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* x x)
(*.f64 x x)
x
-3/4
#s(literal -3/4 binary64)
(- (/ (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))
(fabs (- y x))
(fabs.f64 (-.f64 y x))
(- y x)
(-.f64 y x)
y
2
#s(literal 2 binary64)

localize183.0ms (2.1%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fabs.f64 (-.f64 y x))
✓	accuracy	100.0%	(-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -3/4 binary64))
✓	accuracy	84.7%	(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
✓	accuracy	65.5%	(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 3 binary64) x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3 binary64) x))
✓	accuracy	98.9%	(-.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3 binary64) x)) x)
✓	accuracy	94.5%	(.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3 binary64) x)) x) y)))
✓	accuracy	99.5%	(*.f64 x #s(literal 7/10 binary64))
✓	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%	(pow.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	accuracy	99.5%	(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))

Results

94.0ms	168×	0	valid
21.0ms	69×	0	invalid
12.0ms	6×	5	exit
6.0ms	4×	3	valid
5.0ms	4×	2	valid
4.0ms	5×	1	valid

Compiler

Compiled 178 to 31 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 19.0ms (25% of total)

ival-pow: 19.0ms (25% of total)

ival-div: 15.0ms (19.7% of total)

ival-sub: 8.0ms (10.5% of total)

...c/correct-round.rkt:119:19: 6.0ms (7.9% of total)

backward-pass: 4.0ms (5.3% of total)

ival-fabs: 2.0ms (2.6% of total)

ival-add: 2.0ms (2.6% of total)

const: 1.0ms (1.3% of total)

series34.0ms (0.4%)

Counts

18 → 336

Calls

Call 1

Inputs
#<alt (pow (pow (+ x (/ (fabs (- y x)) 2)) 1/2) 2)>
#<alt (pow (+ x (/ (fabs (- y x)) 2)) 1/2)>
#<alt (+ x (/ (fabs (- y x)) 2))>
#<alt (/ (fabs (- y x)) 2)>
#<alt (* x 7/10)>
#<alt (* (- 0 y) (- 1/2 (/ (- (* 1/2 (* 3 x)) x) y)))>
#<alt (- 1/2 (/ (- (* 1/2 (* 3 x)) x) y))>
#<alt (/ (- (* 1/2 (* 3 x)) x) y)>
#<alt (- (* 1/2 (* 3 x)) x)>
#<alt (/ 1 (pow (* x x) -1/2))>
#<alt (pow (* x x) -1/2)>
#<alt (* x x)>
#<alt (/ (* (* x x) -3/4) (- (/ (fabs (- y x)) 2) x))>
#<alt (* (* x x) -3/4)>
#<alt (- (/ (fabs (- y x)) 2) x)>
#<alt (fabs (- y x))>
#<alt (* 1/2 (* 3 x))>
#<alt (* 3 x)>

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 (* (sqrt (fabs (- y x))) (sqrt 1/2))>
#<alt (+ (* 1/2 (* (/ x (sqrt 1/2)) (sqrt (/ 1 (fabs (- y x)))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))>
#<alt (+ (* x (+ (* -1/8 (* (/ x (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow (fabs (- y x)) 3))))) (* 1/2 (* (sqrt (/ 1 (fabs (- y x)))) (/ 1 (sqrt 1/2)))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))>
#<alt (+ (* x (+ (* 1/2 (* (sqrt (/ 1 (fabs (- y x)))) (/ 1 (sqrt 1/2)))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow (fabs (- y x)) 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/16 (* (/ x (pow (sqrt 1/2) 5)) (sqrt (/ 1 (pow (fabs (- y x)) 5))))))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (pow (fabs (- y x)) 2))) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (pow (fabs (- y x)) 2))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (pow (fabs (- y x)) 3))) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (pow (fabs (+ y (* -1 x))) 2) (pow (sqrt -1) 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (pow (fabs (+ y (* -1 x))) 2) (pow (sqrt -1) 2)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (pow (fabs (+ y (* -1 x))) 3) (pow (sqrt -1) 4)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (- y x)))))>
#<alt (sqrt (+ x (* 1/2 (fabs (neg (+ x (* -1 y)))))))>
#<alt (sqrt (+ x (* 1/2 (fabs (neg (+ x (* -1 y)))))))>
#<alt (sqrt (+ x (* 1/2 (fabs (neg (+ x (* -1 y)))))))>
#<alt (sqrt (+ 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))))>
#<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 (* 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 (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* 7/10 x)>
#<alt (* -1 (- x (* 3/2 x)))>
#<alt (+ (* -1 (- x (* 3/2 x))) (* -1/2 y))>
#<alt (+ (* -1 (- x (* 3/2 x))) (* -1/2 y))>
#<alt (+ (* -1 (- x (* 3/2 x))) (* -1/2 y))>
#<alt (* -1/2 y)>
#<alt (* y (- (* -1 (/ (- x (* 3/2 x)) y)) 1/2))>
#<alt (* y (- (* -1 (/ (- x (* 3/2 x)) y)) 1/2))>
#<alt (* y (- (* -1 (/ (- x (* 3/2 x)) y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 1/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 1/2 (* -1/2 (/ y x))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1/2)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/2 (/ x y)))>
#<alt (+ 1/2 (* -1/2 (/ x y)))>
#<alt (+ 1/2 (* -1/2 (/ x y)))>
#<alt (* -1/2 (/ x y))>
#<alt (* x (- (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (- (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (- (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* -1/2 (/ x y))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x)))))>
#<alt (/ (- x (* 3/2 x)) y)>
#<alt (/ (- (+ x (* 1/2 y)) (* 3/2 x)) y)>
#<alt (/ (- (+ x (* 1/2 y)) (* 3/2 x)) y)>
#<alt (/ (- (+ x (* 1/2 y)) (* 3/2 x)) y)>
#<alt 1/2>
#<alt (- (+ 1/2 (/ x y)) (* 3/2 (/ x y)))>
#<alt (- (+ 1/2 (/ x y)) (* 3/2 (/ x y)))>
#<alt (- (+ 1/2 (/ x y)) (* 3/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))>
#<alt (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))>
#<alt (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (/ (- (* 3/2 x) x) y)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -3/2 (/ (pow x 2) (fabs (- y x))))>
#<alt (* (pow x 2) (- (* -3 (/ x (pow (fabs (- y x)) 2))) (* 3/2 (/ 1 (fabs (- y x))))))>
#<alt (* (pow x 2) (- (* x (- (* -6 (/ x (pow (fabs (- y x)) 3))) (* 3 (/ 1 (pow (fabs (- y x)) 2))))) (* 3/2 (/ 1 (fabs (- y x))))))>
#<alt (* (pow x 2) (- (* x (- (* x (- (* -12 (/ x (pow (fabs (- y x)) 4))) (* 6 (/ 1 (pow (fabs (- y x)) 3))))) (* 3 (/ 1 (pow (fabs (- y x)) 2))))) (* 3/2 (/ 1 (fabs (- y x))))))>
#<alt (* 3/4 x)>
#<alt (* x (+ 3/4 (* 3/8 (/ (fabs (- y x)) x))))>
#<alt (* x (- (+ 3/4 (* 3/16 (/ (pow (fabs (- y x)) 2) (pow x 2)))) (* -3/8 (/ (fabs (- y x)) x))))>
#<alt (* x (- (+ 3/4 (* 3/32 (/ (pow (fabs (- y x)) 3) (pow x 3)))) (+ (* -3/8 (/ (fabs (- y x)) x)) (* -3/16 (/ (pow (fabs (- y x)) 2) (pow x 2))))))>
#<alt (* 3/4 x)>
#<alt (* -1 (* x (- (* -3/8 (/ (fabs (+ y (* -1 x))) x)) 3/4)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* 3/16 (/ (pow (fabs (+ y (* -1 x))) 2) x)) (* -3/8 (fabs (+ y (* -1 x))))) x)) 3/4)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -3/32 (/ (pow (fabs (+ y (* -1 x))) 3) x)) (* 3/16 (pow (fabs (+ y (* -1 x))) 2))) x)) (* -3/8 (fabs (+ y (* -1 x))))) x)) 3/4)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))>
#<alt (* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (* -3/4 (pow x 2))>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (- y x))) x)>
#<alt (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)>
#<alt (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)>
#<alt (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)>
#<alt (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)>
#<alt (* 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)>
#<alt (* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))>
#<alt (* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))>
#<alt (* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) 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 (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>
#<alt (* 3 x)>

Calls

84 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(* (- 0 y) (- 1/2 (/ (- (* 1/2 (* 3 x)) x) y)))
1.0ms	x	@	-inf	(pow (+ x (/ (fabs (- y x)) 2)) 1/2)
1.0ms	y	@	0	(/ (* (* x x) -3/4) (- (/ (fabs (- y x)) 2) x))
1.0ms	y	@	inf	(/ (* (* x x) -3/4) (- (/ (fabs (- y x)) 2) x))
1.0ms	y	@	-inf	(/ (* (* x x) -3/4) (- (/ (fabs (- y x)) 2) x))

rewrite430.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3868×	`/-lowering-/.f32`
3868×	`/-lowering-/.f64`
3660×	`-lowering-.f32`
3660×	`-lowering-.f64`
2006×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	121
1	183	104
2	1420	101
0	8663	101

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 556

Calls

Call 1

Inputs
(pow (pow (+ x (/ (fabs (- y x)) 2)) 1/2) 2)
(pow (+ x (/ (fabs (- y x)) 2)) 1/2)
(+ x (/ (fabs (- y x)) 2))
(/ (fabs (- y x)) 2)
(* x 7/10)
(* (- 0 y) (- 1/2 (/ (- (* 1/2 (* 3 x)) x) y)))
(- 1/2 (/ (- (* 1/2 (* 3 x)) x) y))
(/ (- (* 1/2 (* 3 x)) x) y)
(- (* 1/2 (* 3 x)) x)
(/ 1 (pow (* x x) -1/2))
(pow (* x x) -1/2)
(* x x)
(/ (* (* x x) -3/4) (- (/ (fabs (- y x)) 2) x))
(* (* x x) -3/4)
(- (/ (fabs (- y x)) 2) x)
(fabs (- y x))
(* 1/2 (* 3 x))
(* 3 x)

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

simplify300.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

3562×	`-lowering-.f32`
3562×	`-lowering-.f64`
1746×	`fma-define`
1700×	`fma-lowering-fma.f32`
1700×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	2507
1	846	2355
2	2441	2294
3	6962	2294
0	8008	2294

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

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))))))
(* (sqrt (fabs (- y x))) (sqrt 1/2))
(+ (* 1/2 (* (/ x (sqrt 1/2)) (sqrt (/ 1 (fabs (- y x)))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))
(+ (* x (+ (* -1/8 (* (/ x (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow (fabs (- y x)) 3))))) (* 1/2 (* (sqrt (/ 1 (fabs (- y x)))) (/ 1 (sqrt 1/2)))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))
(+ (* x (+ (* 1/2 (* (sqrt (/ 1 (fabs (- y x)))) (/ 1 (sqrt 1/2)))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow (fabs (- y x)) 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/16 (* (/ x (pow (sqrt 1/2) 5)) (sqrt (/ 1 (pow (fabs (- y x)) 5))))))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (pow (fabs (- y x)) 2))) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (pow (fabs (- y x)) 2))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (pow (fabs (- y x)) 3))) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (pow (fabs (+ y (* -1 x))) 2) (pow (sqrt -1) 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (pow (fabs (+ y (* -1 x))) 2) (pow (sqrt -1) 2)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (pow (fabs (+ y (* -1 x))) 3) (pow (sqrt -1) 4)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt (+ x (* 1/2 (fabs (neg (+ x (* -1 y)))))))
(sqrt (+ x (* 1/2 (fabs (neg (+ x (* -1 y)))))))
(sqrt (+ x (* 1/2 (fabs (neg (+ x (* -1 y)))))))
(sqrt (+ 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)))
(+ 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)))
(* 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))))
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* 7/10 x)
(* -1 (- x (* 3/2 x)))
(+ (* -1 (- x (* 3/2 x))) (* -1/2 y))
(+ (* -1 (- x (* 3/2 x))) (* -1/2 y))
(+ (* -1 (- x (* 3/2 x))) (* -1/2 y))
(* -1/2 y)
(* y (- (* -1 (/ (- x (* 3/2 x)) y)) 1/2))
(* y (- (* -1 (/ (- x (* 3/2 x)) y)) 1/2))
(* y (- (* -1 (/ (- x (* 3/2 x)) y)) 1/2))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))))
(* -1/2 y)
(+ (* -1/2 y) (* 1/2 x))
(+ (* -1/2 y) (* 1/2 x))
(+ (* -1/2 y) (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* -1/2 (/ y x))))
(* x (+ 1/2 (* -1/2 (/ y x))))
(* x (+ 1/2 (* -1/2 (/ y x))))
(* 1/2 x)
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
1/2
(+ 1/2 (* -1/2 (/ x y)))
(+ 1/2 (* -1/2 (/ x y)))
(+ 1/2 (* -1/2 (/ x y)))
(* -1/2 (/ x y))
(* x (- (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* x (- (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* x (- (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* -1/2 (/ x y))
(* -1 (* x (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x)))))
(* -1 (* x (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x)))))
(* -1 (* x (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x)))))
(/ (- x (* 3/2 x)) y)
(/ (- (+ x (* 1/2 y)) (* 3/2 x)) y)
(/ (- (+ x (* 1/2 y)) (* 3/2 x)) y)
(/ (- (+ x (* 1/2 y)) (* 3/2 x)) y)
1/2
(- (+ 1/2 (/ x y)) (* 3/2 (/ x y)))
(- (+ 1/2 (/ x y)) (* 3/2 (/ x y)))
(- (+ 1/2 (/ x y)) (* 3/2 (/ x y)))
1/2
(+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))
(+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))
(+ 1/2 (* -1 (/ (- (* 3/2 x) x) y)))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(/ (- (* 3/2 x) x) y)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
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)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -3/2 (/ (pow x 2) (fabs (- y x))))
(* (pow x 2) (- (* -3 (/ x (pow (fabs (- y x)) 2))) (* 3/2 (/ 1 (fabs (- y x))))))
(* (pow x 2) (- (* x (- (* -6 (/ x (pow (fabs (- y x)) 3))) (* 3 (/ 1 (pow (fabs (- y x)) 2))))) (* 3/2 (/ 1 (fabs (- y x))))))
(* (pow x 2) (- (* x (- (* x (- (* -12 (/ x (pow (fabs (- y x)) 4))) (* 6 (/ 1 (pow (fabs (- y x)) 3))))) (* 3 (/ 1 (pow (fabs (- y x)) 2))))) (* 3/2 (/ 1 (fabs (- y x))))))
(* 3/4 x)
(* x (+ 3/4 (* 3/8 (/ (fabs (- y x)) x))))
(* x (- (+ 3/4 (* 3/16 (/ (pow (fabs (- y x)) 2) (pow x 2)))) (* -3/8 (/ (fabs (- y x)) x))))
(* x (- (+ 3/4 (* 3/32 (/ (pow (fabs (- y x)) 3) (pow x 3)))) (+ (* -3/8 (/ (fabs (- y x)) x)) (* -3/16 (/ (pow (fabs (- y x)) 2) (pow x 2))))))
(* 3/4 x)
(* -1 (* x (- (* -3/8 (/ (fabs (+ y (* -1 x))) x)) 3/4)))
(* -1 (* x (- (* -1 (/ (- (* 3/16 (/ (pow (fabs (+ y (* -1 x))) 2) x)) (* -3/8 (fabs (+ y (* -1 x))))) x)) 3/4)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -3/32 (/ (pow (fabs (+ y (* -1 x))) 3) x)) (* 3/16 (pow (fabs (+ y (* -1 x))) 2))) x)) (* -3/8 (fabs (+ y (* -1 x))))) x)) 3/4)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(* -3/4 (pow x 2))
(- (* 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))))) x)
(* 1/2 (fabs (- y x)))
(+ (* -1 x) (* 1/2 (fabs (- y x))))
(+ (* -1 x) (* 1/2 (fabs (- y x))))
(+ (* -1 x) (* 1/2 (fabs (- y x))))
(* -1 x)
(* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))
(* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))
(* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) x)))))
(* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) x)))))
(* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) 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)))
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 x)
(* 3 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 binary64) (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x))))
x
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 #s(literal 0 binary64) 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))))
(* (sqrt (fabs (- y x))) (sqrt 1/2))
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 y x))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (* (/ x (sqrt 1/2)) (sqrt (/ 1 (fabs (- y x)))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))
(+.f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 y x))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (* x (+ (* -1/8 (* (/ x (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow (fabs (- y x)) 3))))) (* 1/2 (* (sqrt (/ 1 (fabs (- y x)))) (/ 1 (sqrt 1/2)))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))
(+.f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 y x))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x))) (.f64 (-.f64 y x) (-.f64 y x)))) (.f64 #s(literal -1/4 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))))
(+ (* x (+ (* 1/2 (* (sqrt (/ 1 (fabs (- y x)))) (/ 1 (sqrt 1/2)))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow (fabs (- y x)) 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/16 (* (/ x (pow (sqrt 1/2) 5)) (sqrt (/ 1 (pow (fabs (- y x)) 5))))))))) (* (sqrt (fabs (- y x))) (sqrt 1/2)))
(+.f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 y x))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x))) (.f64 (-.f64 y x) (-.f64 y x)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 5 binary64)))) (/.f64 (.f64 x #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (pow (fabs (- y x)) 2))) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x)))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (.f64 #s(literal -1/32 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (-.f64 y x) (-.f64 y x))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (pow (fabs (- y x)) 2))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (pow (fabs (- y x)) 3))) (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (- y x))))))))
(.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (.f64 #s(literal 1/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/32 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (-.f64 y x) (-.f64 y x)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (pow (fabs (+ y (* -1 x))) 2) (pow (sqrt -1) 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 1/32 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (pow (fabs (+ y (* -1 x))) 2) (pow (sqrt -1) 2)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (pow (fabs (+ y (* -1 x))) 3) (pow (sqrt -1) 4)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (fabs (+ y (* -1 x))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (-.f64 y x) (-.f64 y x))) #s(literal 1/32 binary64)) (/.f64 (.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) (.f64 #s(literal 1/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
(sqrt.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))))
(sqrt (+ x (* 1/2 (fabs (- y x)))))
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(.f64 x (+.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 3/16 binary64) x)) (.f64 (fabs.f64 (-.f64 y x)) #s(literal 3/8 binary64))) x)))
(* x (- (+ 3/4 (* 3/32 (/ (pow (fabs (- y x)) 3) (pow x 3)))) (+ (* -3/8 (/ (fabs (- y x)) x)) (* -3/16 (/ (pow (fabs (- y x)) 2) (pow x 2))))))
(.f64 x (+.f64 #s(literal 3/4 binary64) (+.f64 (.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x x)))) (/.f64 (+.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 3/16 binary64) x)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 3/8 binary64))) x))))
(* 3/4 x)
(*.f64 x #s(literal 3/4 binary64))
(* -1 (* x (- (* -3/8 (/ (fabs (+ y (* -1 x))) x)) 3/4)))
(.f64 x (+.f64 #s(literal 3/4 binary64) (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 3/8 binary64) x))))
(* -1 (* x (- (* -1 (/ (- (* 3/16 (/ (pow (fabs (+ y (* -1 x))) 2) x)) (* -3/8 (fabs (+ y (* -1 x))))) x)) 3/4)))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 #s(literal -3/4 binary64) (/.f64 (+.f64 (.f64 (.f64 (-.f64 y x) (-.f64 y x)) (/.f64 #s(literal 3/16 binary64) x)) (.f64 (fabs.f64 (-.f64 y x)) #s(literal 3/8 binary64))) x))))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -3/32 (/ (pow (fabs (+ y (* -1 x))) 3) x)) (* 3/16 (pow (fabs (+ y (* -1 x))) 2))) x)) (* -3/8 (fabs (+ y (* -1 x))))) x)) 3/4)))
(.f64 x (+.f64 #s(literal 3/4 binary64) (/.f64 (-.f64 (.f64 (fabs.f64 (-.f64 y x)) #s(literal 3/8 binary64)) (/.f64 (+.f64 (.f64 (.f64 (fabs.f64 (-.f64 y x)) (.f64 (-.f64 y x) (-.f64 y x))) (/.f64 #s(literal -3/32 binary64) x)) (.f64 (*.f64 (-.f64 y x) (-.f64 y x)) #s(literal -3/16 binary64))) x)) x)))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (- y x))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (/ (pow x 2) (- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(* -3/4 (pow x 2))
(.f64 x (.f64 x #s(literal -3/4 binary64)))
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (- y x))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(- (* 1/2 (fabs (neg (+ x (* -1 y))))) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(* 1/2 (fabs (- y x)))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
(+ (* -1 x) (* 1/2 (fabs (- y x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(+ (* -1 x) (* 1/2 (fabs (- y x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(+ (* -1 x) (* 1/2 (fabs (- y x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))
(.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))
(.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(* x (- (* 1/2 (/ (fabs (- y x)) x)) 1))
(.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) x)))))
(.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) x)))))
(.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (* -1/2 (/ (fabs (+ y (* -1 x))) x)))))
(.f64 x (+.f64 (.f64 (fabs.f64 (-.f64 y x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(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))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))

eval154.0ms (1.7%)

Compiler: Compiled 21948 to 2251 computations (89.7% saved)

prune106.0ms (1.2%)

Pruning

21 alts after pruning (11 fresh and 10 done)

	Pruned	Kept	Total
New	1006	9	1015
Fresh	3	2	5
Picked	4	1	5
Done	0	9	9
Total	1013	21	1034

Accuracy

100.0%

Counts

1034 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	72.5%	(pow.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	51.9%	(/.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))
	6.8%	(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
	34.8%	(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y) (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y))) (-.f64 #s(literal 0 binary64) y)) (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 3/2 binary64)) x) y)))
	24.8%	(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.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)))) (/.f64 (.f64 x x) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
	8.5%	(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 #s(literal 0 binary64) x))
	26.6%	(/.f64 (.f64 (.f64 x #s(literal -3/4 binary64)) x) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
✓	5.9%	(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
✓	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
✓	11.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
✓	99.9%	(+.f64 x (/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #s(literal 2 binary64)))
✓	60.2%	(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
	26.5%	(.f64 (/.f64 #s(literal -3/4 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (.f64 x x))
	45.7%	(.f64 (-.f64 #s(literal 0 binary64) y) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) y))))
	24.7%	(*.f64 y #s(literal -1/2 binary64))
✓	87.8%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)))
✓	30.4%	(*.f64 #s(literal 1/2 binary64) y)
	31.1%	(*.f64 #s(literal 1/2 binary64) x)
	52.1%	(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
✓	11.1%	x

Compiler

Compiled 790 to 304 computations (61.5% saved)

regimes34.0ms (0.4%)

Counts

33 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 x #s(literal 7/10 binary64))
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) y) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) y))))
(.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3 binary64) x)) x) y)))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y) (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y))) (-.f64 #s(literal 0 binary64) y)) (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 3/2 binary64)) x) y)))
(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal -3/4 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (.f64 x x))
(/.f64 (.f64 x (.f64 x #s(literal -3/4 binary64))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(/.f64 (.f64 (.f64 x #s(literal -3/4 binary64)) x) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(+.f64 x (/.f64 (fabs.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 y x) (+.f64 x y)))) #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 (-.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 (/.f64 #s(literal 1 binary64) (+.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 #s(literal 1 binary64) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x)) (-.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (*.f64 x x)))
(/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 x (+.f64 (.f64 x #s(literal -3/4 binary64)) (*.f64 y #s(literal -1/2 binary64))))) (-.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x))
(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.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)))) (/.f64 (.f64 x x) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) #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 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 (/.f64 (.f64 (-.f64 y x) (/.f64 (-.f64 y x) #s(literal 4 binary64))) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))))))
(pow.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))) #s(literal 2 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))
(+.f64 x (*.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))))

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)

regimes17.0ms (0.2%)

Counts

14 → 2

Calls

Call 1

Inputs
x
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 x #s(literal 7/10 binary64))
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) y) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) y))))
(.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3 binary64) x)) x) y)))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y) (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y))) (-.f64 #s(literal 0 binary64) y)) (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 3/2 binary64)) x) y)))
(+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))

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

Calls

2 calls:

5.0ms	x
5.0ms	y

Results

Accuracy	Segments	Branch
73.1%	2	`x`
72.6%	2	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

12 → 2

Calls

Call 1

Inputs
x
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 x #s(literal 7/10 binary64))
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x x) #s(literal -3/4 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) y) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) y))))
(.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3 binary64) x)) x) y)))
(/.f64 (-.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) #s(literal 4 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y) (/.f64 (-.f64 (.f64 x #s(literal 3/2 binary64)) x) y))) (-.f64 #s(literal 0 binary64) y)) (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 3/2 binary64)) x) y)))

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

Calls

2 calls:

4.0ms	x
4.0ms	y

Results

Accuracy	Segments	Branch
70.4%	2	`y`
58.8%	5	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Counts

5 → 3

Calls

Call 1

Inputs
x
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 x #s(literal 7/10 binary64))
(*.f64 y #s(literal -1/2 binary64))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
62.1%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes5.0ms (0.1%)

Counts

4 → 2

Calls

Call 1

Inputs
x
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 x #s(literal 7/10 binary64))

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

Calls

2 calls:

2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
47.0%	2	`x`
49.0%	2	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
31.1%	1	`x`
31.1%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

2.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
11.1%	1	`y`
11.1%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch11.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	-8.132891355585598e-33	-8.28730237768407e-35

Results

6.0ms

112×

valid

Compiler

Compiled 134 to 102 computations (23.9% saved)

Precisions

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

ival-sub: 1.0ms (33.7% of total)

ival-div: 1.0ms (33.7% of total)

ival-add: 1.0ms (33.7% of total)

ival-fabs: 1.0ms (33.7% of total)

const: 0.0ms (0% of total)

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

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	2.493784163899761e-5	0.0006611998554282129

Results

8.0ms	110×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 113 to 88 computations (22.1% saved)

Precisions

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

ival-div: 3.0ms (61% of total)

ival-add: 1.0ms (20.3% of total)

ival-fabs: 1.0ms (20.3% of total)

ival-sub: 1.0ms (20.3% of total)

const: 0.0ms (0% of total)

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

bsearch27.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	2.493784163899761e-5	0.0006611998554282129
10.0ms	-1.3176806025718052e-151	-1.1639031023999966e-153

Results

12.0ms	219×	0	valid
1.0ms	4×	2	valid
0.0ms	1×	3	valid

Compiler

Compiled 183 to 151 computations (17.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (31.3% of total)

ival-sub: 1.0ms (15.6% of total)

ival-fabs: 1.0ms (15.6% of total)

ival-add: 1.0ms (15.6% of total)

const: 0.0ms (0% of total)

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

bsearch12.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	2.493784163899761e-5	0.0006611998554282129

Results

6.0ms	111×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 99 to 81 computations (18.2% saved)

Precisions

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

ival-div: 1.0ms (33.3% of total)

ival-add: 1.0ms (33.3% of total)

ival-fabs: 1.0ms (33.3% of total)

ival-sub: 1.0ms (33.3% of total)

const: 0.0ms (0% of total)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
12×	`+-commutative_binary64`
8×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	66
1	41	66
2	48	66
3	53	66
4	56	66
5	57	66

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(if (<=.f64 x #s(literal -63940696633227/182687704666362864775460604089535377456991567872 binary64)) (*.f64 #s(literal -1/2 binary64) (-.f64 y x)) (+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64))))
(if (<=.f64 y #s(literal 700976274800963/18446744073709551616 binary64)) (.f64 #s(literal -1/2 binary64) (-.f64 y x)) (.f64 #s(literal 1/2 binary64) y))
(if (<=.f64 y #s(literal -3538089773270195/29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992 binary64)) (.f64 y #s(literal -1/2 binary64)) (if (<=.f64 y #s(literal 7378697629483821/295147905179352825856 binary64)) (.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y)))
(if (<=.f64 y #s(literal 8264141345021879/147573952589676412928 binary64)) (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) x)
x

Outputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(if (<=.f64 x #s(literal -63940696633227/182687704666362864775460604089535377456991567872 binary64)) (*.f64 #s(literal -1/2 binary64) (-.f64 y x)) (+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64))))
(if (<=.f64 x #s(literal -63940696633227/182687704666362864775460604089535377456991567872 binary64)) (*.f64 (-.f64 y x) #s(literal -1/2 binary64)) (+.f64 x (/.f64 (fabs.f64 y) #s(literal 2 binary64))))
(if (<=.f64 y #s(literal 700976274800963/18446744073709551616 binary64)) (.f64 #s(literal -1/2 binary64) (-.f64 y x)) (.f64 #s(literal 1/2 binary64) y))
(if (<=.f64 y #s(literal 700976274800963/18446744073709551616 binary64)) (.f64 (-.f64 y x) #s(literal -1/2 binary64)) (.f64 y #s(literal 1/2 binary64)))
(if (<=.f64 y #s(literal -3538089773270195/29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992 binary64)) (.f64 y #s(literal -1/2 binary64)) (if (<=.f64 y #s(literal 7378697629483821/295147905179352825856 binary64)) (.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y)))
(if (<=.f64 y #s(literal -3538089773270195/29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992 binary64)) (.f64 y #s(literal -1/2 binary64)) (if (<=.f64 y #s(literal 7378697629483821/295147905179352825856 binary64)) (.f64 x #s(literal 1/2 binary64)) (*.f64 y #s(literal 1/2 binary64))))
(if (<=.f64 y #s(literal 8264141345021879/147573952589676412928 binary64)) (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) y))
(if (<=.f64 y #s(literal 8264141345021879/147573952589676412928 binary64)) (.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
x

soundness1.6s (17.6%)

Rules

5118×	`-lowering-.f32`
5118×	`-lowering-.f64`
4918×	`+-lowering-+.f64`
4918×	`+-lowering-+.f32`
3562×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	275	2507
1	846	2355
2	2441	2294
3	6962	2294
0	8008	2294
0	7	21
1	47	20
2	399	20
3	5813	20
0	8172	20
0	43	479
1	117	458
2	293	458
3	903	458
4	3274	458
5	6167	458
0	8066	458
0	969	7295
1	3474	7125
0	8365	7125

Stop Event

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

Compiler

Compiled 231 to 155 computations (32.9% saved)

preprocess84.0ms (0.9%)

Compiler: Compiled 156 to 76 computations (51.3% saved)

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	28	24
4	50	24
5	123	24
6	278	24
7	436	24
8	581	23
9	722	23
10	871	23
11	943	23
12	957	23
13	970	23
14	990	23
15	998	23
0	998	23

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	28	24
4	50	24
5	123	24
6	278	24
7	436	24
8	581	23
9	722	23
10	871	23
11	943	23
12	957	23
13	970	23
14	990	23
15	998	23
0	998	23

analyze0.0ms (0%)

sample894.0ms (10.1%)

preprocess92.0ms (1%)

explain75.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify32.0ms (0.4%)

localize33.0ms (0.4%)

series4.0ms (0%)

rewrite450.0ms (5.1%)

simplify142.0ms (1.6%)

eval51.0ms (0.6%)

prune43.0ms (0.5%)

simplify189.0ms (2.1%)

localize236.0ms (2.7%)

series45.0ms (0.5%)

rewrite485.0ms (5.5%)

simplify443.0ms (5%)

eval395.0ms (4.4%)

prune271.0ms (3.1%)

simplify158.0ms (1.8%)

localize149.0ms (1.7%)

series26.0ms (0.3%)

rewrite645.0ms (7.3%)

simplify635.0ms (7.1%)

eval162.0ms (1.8%)

prune100.0ms (1.1%)

simplify131.0ms (1.5%)

localize183.0ms (2.1%)

series34.0ms (0.4%)

rewrite430.0ms (4.8%)

simplify300.0ms (3.4%)

eval154.0ms (1.7%)

prune106.0ms (1.2%)

regimes34.0ms (0.4%)

regimes17.0ms (0.2%)

regimes9.0ms (0.1%)

regimes3.0ms (0%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes4.0ms (0%)

bsearch11.0ms (0.1%)

bsearch13.0ms (0.1%)

bsearch27.0ms (0.3%)

bsearch12.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.6s (17.6%)

preprocess84.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	24
1	12	24
2	19	24
3	28	24
4	50	24
5	123	24
6	278	24
7	436	24
8	581	23
9	722	23
10	871	23
11	943	23
12	957	23
13	970	23
14	990	23
15	998	23
0	998	23