Metrics for Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

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 13 to 9 computations (30.8% saved)

Precisions

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

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

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

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

const: 0.0ms (0% of total)

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

sample974.0ms (18.1%)

Results

647.0ms	8255×	0	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 293.0ms

ival-div: 100.0ms (34.2% of total)

ival-mult: 95.0ms (32.5% of total)

ival-add: 85.0ms (29% of total)

const: 10.0ms (3.4% of total)

backward-pass: 3.0ms (1% of total)

Bogosity

preprocess109.0ms (2%)

Algorithm

2×	egg-herbie

Rules

3140×	`sum3-define`
2416×	`sum5-define`
1524×	`fnmadd-define`
1200×	`fmsub-define`
1126×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	89
1	101	80
2	289	80
3	952	72
4	3235	64
5	5997	63
6	6928	63
7	7272	63
8	7466	63
9	7602	63
0	8	8
1	14	8
2	26	8
3	33	8
4	34	8
0	34	8

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

Inputs
(+ (+ (/ x 2) (* y x)) z)

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

Call 2

Inputs
(+ (+ (/ x 2) (* y x)) z)
(+ (+ (/ (neg x) 2) (* y (neg x))) z)
(+ (+ (/ x 2) (* (neg y) x)) z)
(+ (+ (/ x 2) (* y x)) (neg z))
(neg (+ (+ (/ (neg x) 2) (* y (neg x))) z))
(neg (+ (+ (/ x 2) (* (neg y) x)) z))
(neg (+ (+ (/ x 2) (* y x)) (neg z)))
(+ (+ (/ y 2) (* x y)) z)
(+ (+ (/ z 2) (* y z)) x)
(+ (+ (/ x 2) (* z x)) y)

Outputs
(+ (+ (/ x 2) (* y x)) z)
(fma x (+ y 1/2) z)
(+ (+ (/ (neg x) 2) (* y (neg x))) z)
(fma x (- -1/2 y) z)
(+ (+ (/ x 2) (* (neg y) x)) z)
(fnmadd x (+ y -1/2) z)
(+ (+ (/ x 2) (* y x)) (neg z))
(fnmsub x (- -1/2 y) z)
(neg (+ (+ (/ (neg x) 2) (* y (neg x))) z))
(fnmsub x (- -1/2 y) z)
(neg (+ (+ (/ x 2) (* (neg y) x)) z))
(fmsub x (+ y -1/2) z)
(neg (+ (+ (/ x 2) (* y x)) (neg z)))
(fma x (- -1/2 y) z)
(+ (+ (/ y 2) (* x y)) z)
(+ z (* y (+ x 1/2)))
(+ (+ (/ z 2) (* y z)) x)
(fma y z (fma z 1/2 x))
(+ (+ (/ x 2) (* z x)) y)
(fma x z (fma x 1/2 y))

explain370.0ms (6.9%)

FPErrors

Click to see full error table

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

Results

177.0ms

512×

valid

Compiler

Compiled 72 to 26 computations (63.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-div: 144.0ms (93.8% of total)

ival-add: 5.0ms (3.3% of total)

ival-mult: 4.0ms (2.6% of total)

const: 1.0ms (0.7% of total)

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

eval0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
12×	`fma-lowering-fma.f32`
12×	`sum3-define`
12×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	14	24
2	26	24
3	33	24
4	34	24
0	34	24

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (+ (/ x 2) (* y x)) z)
(+ (/ x 2) (* y x))
(/ x 2)
x
2
(* y x)
y
z

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

localize54.0ms (1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
✓	accuracy	100.0%	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))

Results

46.0ms

256×

valid

Compiler

Compiled 30 to 9 computations (70% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-add: 29.0ms (85.5% of total)

ival-div: 2.0ms (5.9% of total)

ival-mult: 2.0ms (5.9% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

4 → 96

Calls

Call 1

Inputs
#<alt (+ (+ (/ x 2) (* y x)) z)>
#<alt (+ (/ x 2) (* y x))>
#<alt (/ x 2)>
#<alt (* y x)>

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

Calls

24 calls:

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

rewrite342.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3950×	`-lowering-.f32`
3950×	`-lowering-.f64`
2598×	`/-lowering-/.f32`
2598×	`/-lowering-/.f64`
1388×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	49	18
2	497	17
3	7165	17
0	8007	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 182

Calls

Call 1

Inputs
(+ (+ (/ x 2) (* y x)) z)
(+ (/ x 2) (* y x))
(/ x 2)
(* y x)

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

simplify170.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

2520×	`-lowering-.f32`
2520×	`-lowering-.f64`
1302×	`sum4-define`
1010×	`sum5-define`
914×	`fnmadd-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	440
1	184	412
2	569	412
3	1683	412
4	5094	412
0	8271	412

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval46.0ms (0.9%)

Compiler: Compiled 6769 to 644 computations (90.5% saved)

prune66.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	272	6	278
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	272	7	279

Accuracy

100.0%

Counts

279 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)
✓	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
	76.7%	(+.f64 (*.f64 x y) z)
▶	64.8%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
▶	59.4%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
▶	36.3%	(*.f64 x y)
▶	43.3%	z

Compiler

Compiled 98 to 68 computations (30.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(+.f64 y #s(literal 1/2 binary64))
✓	cost-diff	6272	(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)

Rules

28×	`fma-lowering-fma.f32`
28×	`fma-define`
28×	`+-lowering-+.f64`
28×	`+-lowering-+.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	23	40
2	37	40
3	48	40
4	49	40
0	49	40

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* x (+ y 1/2)) z)
x
(+ y 1/2)
y
1/2
z
z
(* x y)
x
y
(* x (+ 1/2 y))
x
(+ 1/2 y)
1/2
y
(+ (* x 1/2) z)
(* x 1/2)
x
1/2
z

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

localize73.0ms (1.4%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) y)
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(+.f64 y #s(literal 1/2 binary64))
✓	accuracy	100.0%	(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)

Results

59.0ms

256×

valid

Compiler

Compiled 45 to 12 computations (73.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 19.0ms (67% of total)

ival-add: 5.0ms (17.6% of total)

compiled-spec: 4.0ms (14.1% of total)

const: 0.0ms (0% of total)

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

series33.0ms (0.6%)

Counts

7 → 144

Calls

Call 1

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

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

Calls

36 calls:

Time	Variable		Point	Expression
29.0ms	z	@	-inf	(+ (* x (+ y 1/2)) z)
0.0ms	x	@	-inf	(+ (* x (+ y 1/2)) z)
0.0ms	y	@	inf	(+ (* x (+ y 1/2)) z)
0.0ms	x	@	0	(+ (* x (+ y 1/2)) z)
0.0ms	x	@	0	(* x (+ 1/2 y))

rewrite276.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4118×	`-lowering-.f32`
4118×	`-lowering-.f64`
2988×	`/-lowering-/.f32`
2988×	`/-lowering-/.f64`
1646×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	68	27
2	578	27
0	8381	27

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 341

Calls

Call 1

Inputs
(+ (* x (+ y 1/2)) z)
(+ y 1/2)
(* x y)
(* x (+ 1/2 y))
(+ 1/2 y)
(+ (* x 1/2) z)
(* x 1/2)

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

simplify139.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1986×	`-lowering-.f32`
1986×	`-lowering-.f64`
998×	`sum4-define`
956×	`/-lowering-/.f32`
956×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	602
1	233	556
2	712	556
3	2259	556
4	5212	556
0	8266	556

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval53.0ms (1%)

Compiler: Compiled 10697 to 885 computations (91.7% saved)

prune50.0ms (0.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	482	3	485
Fresh	0	1	1
Picked	1	4	5
Done	1	0	1
Total	484	8	492

Accuracy

100.0%

Counts

492 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.7%	(fma.f64 x y z)
▶	59.5%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
▶	76.7%	(+.f64 (*.f64 x y) z)
✓	64.8%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	59.4%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	36.3%	(*.f64 x y)
▶	24.2%	(*.f64 x #s(literal 1/2 binary64))
✓	43.3%	z

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	6272	(fma.f64 x y z)
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	128	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(+.f64 (*.f64 x y) z)
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))

Rules

12×	`fma-lowering-fma.f32`
12×	`fma-define`
12×	`+-lowering-+.f64`
12×	`-lowering-.f32`
12×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	16	36
2	23	36
0	23	36

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x 1/2)
x
1/2
(+ (* x y) z)
(* x y)
x
y
z
(+ (* x y) (* x 1/2))
(* x y)
x
y
(* x 1/2)
1/2
(+ (* x y) z)
x
y
z

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

localize63.0ms (1.2%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x y z)
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(+.f64 (*.f64 x y) z)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))

Results

30.0ms

256×

valid

Compiler

Compiled 43 to 10 computations (76.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 6.0ms (44.2% of total)

ival-add: 4.0ms (29.5% of total)

compiled-spec: 3.0ms (22.1% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

5 → 132

Calls

Call 1

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

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

Calls

33 calls:

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

rewrite242.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4096×	`-lowering-.f32`
4096×	`-lowering-.f64`
1888×	`sum3-define`
1748×	`pow-lowering-pow.f64`
1748×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	39	19
2	350	19
3	4478	19
0	8159	19

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 214

Calls

Call 1

Inputs
(* x 1/2)
(+ (* x y) z)
(* x y)
(+ (* x y) (* x 1/2))
(+ (* x y) z)

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

simplify144.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1964×	`-lowering-.f32`
1964×	`-lowering-.f64`
1642×	`fnmadd-define`
1596×	`fmsub-define`
1364×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	530
1	161	476
2	468	476
3	1228	476
4	3448	476
0	8114	476

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval41.0ms (0.8%)

Compiler: Compiled 8645 to 441 computations (94.9% saved)

prune24.0ms (0.4%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	385	1	386
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	386	8	394

Accuracy

100.0%

Counts

394 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	59.5%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	76.7%	(+.f64 (*.f64 x y) z)
✓	64.8%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
▶	48.4%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal -1/2 binary64))))))
✓	59.4%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	36.3%	(*.f64 x y)
✓	24.2%	(*.f64 x #s(literal 1/2 binary64))
✓	43.3%	z

Compiler

Compiled 72 to 49 computations (31.9% saved)

simplify223.0ms (4.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	cost-diff	768	(.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal -1/2 binary64)))))
✓	cost-diff	896	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal -1/2 binary64))))))

Rules

3968×	`-lowering-.f32`
3968×	`-lowering-.f64`
2648×	`+-lowering-+.f64`
2648×	`+-lowering-+.f32`
2280×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	43	33
2	115	33
3	423	33
4	3347	33
5	7396	33
0	8733	33

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize43.0ms (0.8%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x (+.f64 y #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal -1/2 binary64))))
✓	accuracy	89.2%	(.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal -1/2 binary64)))))

Results

29.0ms

256×

valid

Compiler

Compiled 64 to 14 computations (78.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 8.0ms (60.8% of total)

ival-add: 3.0ms (22.8% of total)

ival-div: 2.0ms (15.2% of total)

const: 1.0ms (7.6% of total)

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

series6.0ms (0.1%)

Counts

6 → 132

Calls

Call 1

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

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

Calls

33 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ 1 (* x (+ y -1/2)))
1.0ms	x	@	0	(/ 1 (* x (+ y -1/2)))
0.0ms	y	@	0	(/ 1 (* x (+ y -1/2)))
0.0ms	x	@	inf	(/ 1 (* x (+ y -1/2)))
0.0ms	y	@	inf	(/ 1 (* x (+ y -1/2)))

rewrite277.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3316×	`-lowering-.f32`
3316×	`-lowering-.f64`
2744×	`/-lowering-/.f32`
2744×	`/-lowering-/.f64`
1428×	`frac-times`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	77	25
2	518	25
3	6660	25
0	8211	25

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 540

Calls

Call 1

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

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

simplify206.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2634×	`fma-lowering-fma.f32`
2634×	`fma-lowering-fma.f64`
2044×	`-lowering-.f32`
2044×	`-lowering-.f64`
1890×	`fmm-def`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	100	626
1	301	622
2	732	618
3	2106	613
4	6338	609
0	8186	609

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval150.0ms (2.8%)

Compiler: Compiled 21062 to 1822 computations (91.3% saved)

prune145.0ms (2.7%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	798	1	799
Fresh	0	0	0
Picked	1	0	1
Done	0	7	7
Total	799	8	807

Accuracy

100.0%

Counts

807 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	59.5%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	76.7%	(+.f64 (*.f64 x y) z)
✓	64.8%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
	25.6%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x y))))
✓	59.4%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	36.3%	(*.f64 x y)
✓	24.2%	(*.f64 x #s(literal 1/2 binary64))
✓	43.3%	z

Compiler

Compiled 157 to 79 computations (49.7% saved)

regimes23.0ms (0.4%)

Counts

12 → 1

Calls

Call 1

Inputs
z
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x y)
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
(+.f64 (*.f64 x y) z)
(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x y))))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x (+.f64 y #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal -1/2 binary64))))))
(fma.f64 x y z)
(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)

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

Calls

5 calls:

5.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
4.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
4.0ms	z
4.0ms	x
4.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
100.0%	1	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes10.0ms (0.2%)

Counts

7 → 3

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	z
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
86.1%	3	`x`
98.0%	3	`y`
90.5%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Counts

5 → 3

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
81.9%	3	`z`
87.2%	3	`y`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes8.0ms (0.2%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	y
2.0ms	z
2.0ms	x

Results

Accuracy	Segments	Branch
78.8%	3	`z`
72.3%	3	`x`
67.6%	3	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

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

Outputs
(*.f64 x y)
z
(*.f64 x y)

Calls

3 calls:

2.0ms	z
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
65.6%	3	`y`
55.1%	3	`x`
59.1%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes3.0ms (0.1%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
56.0%	3	`z`
43.3%	1	`y`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
z

Outputs
z

Calls

3 calls:

3.0ms	z
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
43.3%	1	`y`
43.3%	1	`x`
43.3%	1	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch31.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
21.0ms	0.0009573939225751705	0.8089585468826352
9.0ms	-2.373408683342256	-0.45865315162773207

Results

13.0ms

224×

valid

Compiler

Compiled 270 to 195 computations (27.8% saved)

Precisions

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

ival-div: 2.0ms (33.6% of total)

ival-add: 2.0ms (33.6% of total)

ival-mult: 2.0ms (33.6% of total)

const: 0.0ms (0% of total)

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

bsearch30.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	2.2160243361050006e-14	8.984941504976227e-10
11.0ms	-2.2829733117756415e+45	-6.477759516606534e+42

Results

14.0ms

256×

valid

Compiler

Compiled 290 to 221 computations (23.8% saved)

Precisions

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

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

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

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

const: 0.0ms (0% of total)

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

bsearch37.0ms (0.7%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
20.0ms	3.070414458752759e+110	3.1902074597430135e+130
14.0ms	-1.5360620779248398e+68	-2.190557742140945e+58

Results

24.0ms

336×

valid

Compiler

Compiled 312 to 244 computations (21.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-add: 3.0ms (33.4% of total)

ival-mult: 3.0ms (33.4% of total)

ival-div: 2.0ms (22.3% of total)

const: 0.0ms (0% of total)

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

bsearch41.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
28.0ms	8.934343450462013e+61	4.356713606500542e+62
11.0ms	-2.2829733117756415e+45	-6.477759516606534e+42

Results

32.0ms

224×

valid

Compiler

Compiled 186 to 139 computations (25.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-div: 21.0ms (82.4% of total)

ival-add: 2.0ms (7.8% of total)

ival-mult: 2.0ms (7.8% of total)

const: 0.0ms (0% of total)

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

bsearch33.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1.1605428385576816e-40	8.411082342309835e-40
13.0ms	-117255.08413958021	-0.5120223073928506

Results

24.0ms

240×

valid

Compiler

Compiled 198 to 163 computations (17.7% saved)

Precisions

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

ival-add: 12.0ms (72.8% of total)

ival-div: 2.0ms (12.1% of total)

ival-mult: 2.0ms (12.1% of total)

const: 0.0ms (0% of total)

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`if-if-or-not_binary32`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	91
1	65	91

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 (.f64 x y) z) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (+.f64 (*.f64 x y) z)))
(if (<=.f64 y #s(literal -14500000000000000882956591198109594934050816 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 8510837770086989/9671406556917033397649408 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 z #s(literal -7000000000000000359333793432498072597888499801841438702960640 binary64)) z (if (<=.f64 z #s(literal 52000000000000000809089638732275837261946472639895194535228070182403356620567296569779240275582467279162726605127680 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 y #s(literal -68000000000000002433258442466472203967791104 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 89999999999999999726585254854541341201585959339692315725791232 binary64)) z (.f64 x y)))
(if (<=.f64 z #s(literal -607985949695017/1125899906842624 binary64)) z (if (<=.f64 z #s(literal 6497781093271369/12259964326927110866866776217202473468949912977468817408 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

Outputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 x y)) z)
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 (.f64 x y) z) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (+.f64 (*.f64 x y) z)))
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 z (.f64 x y)) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (+.f64 z (*.f64 x y))))
(if (<=.f64 y #s(literal -14500000000000000882956591198109594934050816 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 8510837770086989/9671406556917033397649408 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 y #s(literal -14500000000000000882956591198109594934050816 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 8510837770086989/9671406556917033397649408 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))))
(if (<=.f64 z #s(literal -7000000000000000359333793432498072597888499801841438702960640 binary64)) z (if (<=.f64 z #s(literal 52000000000000000809089638732275837261946472639895194535228070182403356620567296569779240275582467279162726605127680 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 z #s(literal -7000000000000000359333793432498072597888499801841438702960640 binary64)) z (if (<=.f64 z #s(literal 52000000000000000809089638732275837261946472639895194535228070182403356620567296569779240275582467279162726605127680 binary64)) (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z))
(if (<=.f64 y #s(literal -68000000000000002433258442466472203967791104 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 89999999999999999726585254854541341201585959339692315725791232 binary64)) z (.f64 x y)))
(if (<=.f64 z #s(literal -607985949695017/1125899906842624 binary64)) z (if (<=.f64 z #s(literal 6497781093271369/12259964326927110866866776217202473468949912977468817408 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

soundness736.0ms (13.7%)

Rules

2520×	`-lowering-.f32`
2520×	`-lowering-.f64`
1986×	`-lowering-.f32`
1986×	`-lowering-.f64`
1302×	`sum4-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	440
1	184	412
2	569	412
3	1683	412
4	5094	412
0	8271	412
0	66	602
1	233	556
2	712	556
3	2259	556
4	5212	556
0	8266	556

Stop Event

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

Compiler

Compiled 182 to 103 computations (43.4% saved)

preprocess56.0ms (1%)

Compiler: Compiled 224 to 102 computations (54.5% saved)

analyze0.0ms (0%)

sample974.0ms (18.1%)

preprocess109.0ms (2%)

explain370.0ms (6.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize54.0ms (1%)

series6.0ms (0.1%)

rewrite342.0ms (6.4%)

simplify170.0ms (3.2%)

eval46.0ms (0.9%)

prune66.0ms (1.2%)

simplify7.0ms (0.1%)

localize73.0ms (1.4%)

series33.0ms (0.6%)

rewrite276.0ms (5.1%)

simplify139.0ms (2.6%)

eval53.0ms (1%)

prune50.0ms (0.9%)

simplify5.0ms (0.1%)

localize63.0ms (1.2%)

series2.0ms (0%)

rewrite242.0ms (4.5%)

simplify144.0ms (2.7%)

eval41.0ms (0.8%)

prune24.0ms (0.4%)

simplify223.0ms (4.1%)

localize43.0ms (0.8%)

series6.0ms (0.1%)

rewrite277.0ms (5.1%)

simplify206.0ms (3.8%)

eval150.0ms (2.8%)

prune145.0ms (2.7%)

regimes23.0ms (0.4%)

regimes10.0ms (0.2%)

regimes6.0ms (0.1%)

regimes8.0ms (0.2%)

regimes6.0ms (0.1%)

regimes3.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch31.0ms (0.6%)

bsearch30.0ms (0.6%)

bsearch37.0ms (0.7%)

bsearch41.0ms (0.8%)

bsearch33.0ms (0.6%)

simplify9.0ms (0.2%)

soundness736.0ms (13.7%)

preprocess56.0ms (1%)

end0.0ms (0%)

Profiling