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)

sample1.4s (21%)

Results

1.0s	8254×	0	valid
0.0ms	2×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 534.0ms

ival-add: 245.0ms (45.9% of total)

ival-div: 180.0ms (33.7% of total)

ival-mult: 94.0ms (17.6% of total)

const: 12.0ms (2.2% of total)

backward-pass: 3.0ms (0.6% of total)

Bogosity

preprocess150.0ms (2.3%)

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))

explain129.0ms (2%)

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

89.0ms

512×

valid

Compiler

Compiled 72 to 26 computations (63.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-add: 5.0ms (33.6% of total)

ival-div: 4.0ms (26.9% of total)

ival-mult: 4.0ms (26.9% of total)

const: 1.0ms (6.7% 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)

simplify6.0ms (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

localize37.0ms (0.6%)

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

Results

28.0ms

256×

valid

Compiler

Compiled 30 to 9 computations (70% saved)

Precisions

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

ival-div: 3.0ms (38.6% of total)

ival-add: 3.0ms (38.6% of total)

ival-mult: 2.0ms (25.7% 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))

rewrite318.0ms (4.9%)

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	501	17
3	7188	17
0	8003	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 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x 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 1/4 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 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))) (/.f64 (.f64 y (.f64 x (.f64 x 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 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 y (.f64 x (.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 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1/2 binary64) y)) z)
(neg.f64 (/.f64 (+.f64 (.f64 x (.f64 (+.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 x (.f64 (+.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 (+.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 x (.f64 (+.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 1/4 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 x (.f64 (+.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 (+.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 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 1/4 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 1/4 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x y) z))))))
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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 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (.f64 y (.f64 x (.f64 x y))) (.f64 (.f64 x (-.f64 y #s(literal 1/2 binary64))) (.f64 x (-.f64 y #s(literal 1/2 binary64))))))) (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 y (.f64 x (.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 1/4 binary64) x)) (.f64 (.f64 x (.f64 x y)) (+.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)

simplify288.0ms (4.5%)

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)

eval48.0ms (0.7%)

Compiler: Compiled 6769 to 647 computations (90.4% saved)

prune31.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	271	7	278
Fresh	0	0	0
Picked	1	0	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)
	64.3%	(-.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
	77.3%	(+.f64 (*.f64 x y) z)
▶	68.3%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
▶	54.8%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
▶	33.0%	(*.f64 x y)
▶	46.6%	z

Compiler

Compiled 146 to 92 computations (37% saved)

simplify6.0ms (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

localize69.0ms (1.1%)

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

Results

55.0ms

256×

valid

Compiler

Compiled 45 to 12 computations (73.3% saved)

Precisions

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

ival-mult: 7.0ms (40.5% of total)

ival-add: 6.0ms (34.7% of total)

compiled-spec: 4.0ms (23.1% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

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

rewrite305.0ms (4.7%)

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	582	27
0	8412	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 x (.f64 (+.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 z (.f64 x y)) (.f64 x #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 (+.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 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 x (.f64 (+.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 (.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z)))) (.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 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x (.f64 (+.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 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x (.f64 (+.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 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x (.f64 (+.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 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x (.f64 (+.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 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 z (.f64 z z)) (-.f64 (.f64 z (.f64 z z)) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (*.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (*.f64 x (+.f64 y #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.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 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 z (.f64 z z)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z)))) (.f64 (-.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) z) (+.f64 (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 z z) (+.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (*.f64 z z))))))
(/.f64 (-.f64 (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (.f64 z z))))
(/.f64 (-.f64 (.f64 z z) (.f64 x (.f64 (+.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 #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 x (.f64 (+.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 (.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 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 z (.f64 z z)) (-.f64 (.f64 z (.f64 z z)) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z)))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.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 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 z z) (+.f64 (.f64 x (.f64 (+.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 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.f64 y #s(literal 1/2 binary64)))))) (.f64 z (.f64 z (.f64 z z)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 (+.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 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (+.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 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (.f64 z 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 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.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)))))))
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(.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)))))
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(+.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) z))))))
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(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 z z) (.f64 (.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 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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) z)))))
(/.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))) (+.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 x (.f64 x #s(literal 1/4 binary64))))))
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(/.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 x (.f64 x #s(literal 1/4 binary64)))) (+.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) 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)))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 z (.f64 z z))) (+.f64 (.f64 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) 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)))) #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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) z))))))
(/.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 x (.f64 x #s(literal 1/4 binary64))))) (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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))))
(/.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))))) (+.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))))) (-.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z)))))
(.f64 (+.f64 (.f64 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))) (.f64 (+.f64 z (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) z))))))
(.f64 (+.f64 (.f64 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))) (/.f64 (+.f64 z (.f64 x #s(literal 1/2 binary64))) (+.f64 (.f64 z z) (.f64 (.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 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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z))))))
(.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 z z) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) z)))) (+.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 x (.f64 x #s(literal 1/4 binary64)))) (/.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)

simplify146.0ms (2.2%)

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	8267	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 (0.8%)

Compiler: Compiled 10697 to 884 computations (91.7% saved)

prune51.0ms (0.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	483	2	485
Fresh	0	2	2
Picked	1	4	5
Done	0	0	0
Total	484	8	492

Accuracy

100.0%

Counts

492 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.7%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 y #s(literal 1/2 binary64))))
▶	64.3%	(-.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
▶	77.3%	(+.f64 (*.f64 x y) z)
✓	68.3%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	54.8%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	33.0%	(*.f64 x y)
▶	23.7%	(*.f64 x #s(literal 1/2 binary64))
✓	46.6%	z

Compiler

Compiled 80 to 53 computations (33.8% saved)

simplify145.0ms (2.2%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 y #s(literal 1/2 binary64)))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 y #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 x (.f64 #s(literal 1/4 binary64) x))
✓	cost-diff	256	(/.f64 (.f64 y (.f64 x (.f64 x y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))
✓	cost-diff	256	(/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
✓	cost-diff	384	(-.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
✓	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

1812×	`-lowering-.f32`
1812×	`-lowering-.f64`
1776×	`sum5-define`
1560×	`sum3-define`
1292×	`sum4-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	134
1	64	114
2	194	105
3	708	98
4	2919	97
5	6209	97
0	8156	97

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize109.0ms (1.7%)

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 y #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 y #s(literal 1/2 binary64))))
✓	accuracy	99.8%	(.f64 x (.f64 x y))
✓	accuracy	95.2%	(.f64 y (.f64 x (*.f64 x y)))
✓	accuracy	68.4%	(/.f64 (.f64 y (.f64 x (.f64 x y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))
✓	accuracy	59.3%	(/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
✓	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

80.0ms

256×

valid

Compiler

Compiled 141 to 23 computations (83.7% saved)

Precisions

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

ival-mult: 13.0ms (45.8% of total)

ival-div: 7.0ms (24.7% of total)

ival-sub: 4.0ms (14.1% of total)

ival-add: 3.0ms (10.6% of total)

const: 1.0ms (3.5% of total)

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

series21.0ms (0.3%)

Counts

12 → 264

Calls

Call 1

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

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 z>
#<alt (+ z (* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y)))))>
#<alt (+ z (* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y)))))>
#<alt (+ z (* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y)))))>
#<alt (* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y))))>
#<alt (* x (- (+ (* 1/4 (/ 1 (- 1/2 y))) (/ z x)) (/ (pow y 2) (- 1/2 y))))>
#<alt (* x (- (+ (* 1/4 (/ 1 (- 1/2 y))) (/ z x)) (/ (pow y 2) (- 1/2 y))))>
#<alt (* x (- (+ (* 1/4 (/ 1 (- 1/2 y))) (/ z x)) (/ (pow y 2) (- 1/2 y))))>
#<alt (* x (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))>
#<alt (* -1 (* x (- (* -1 (/ z x)) (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))))>
#<alt (* -1 (* x (- (* -1 (/ z x)) (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))))>
#<alt (* -1 (* x (- (* -1 (/ z x)) (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))))>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (+ z (+ (* 1/2 x) (* y (+ x (* (pow y 2) (+ (* -4 x) (* 4 x)))))))>
#<alt (+ z (+ (* 1/2 x) (* y (+ x (* (pow y 2) (+ (* -4 x) (+ (* 4 x) (* y (+ (* -8 x) (* 8 x))))))))))>
#<alt (* x y)>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ z y)) (* -1 x)))>
#<alt (* y (- (+ (* -1/4 (/ x (pow y 2))) (+ (* 1/4 (/ x (pow y 2))) (+ (* 1/2 (/ x y)) (/ z y)))) (* -1 x)))>
#<alt (* y (- (+ (* -1/4 (/ x (pow y 2))) (+ (* -1/8 (/ x (pow y 3))) (+ (* 1/8 (/ x (pow y 3))) (+ (* 1/4 (/ x (pow y 2))) (+ (* 1/2 (/ x y)) (/ z y)))))) (* -1 x)))>
#<alt (* x y)>
#<alt (* -1 (* y (- (* -1 (/ (+ z (* 1/2 x)) y)) x)))>
#<alt (* -1 (* y (- (* -1 (/ (+ z (+ (* -1 (/ (+ (* -1/4 x) (* 1/4 x)) y)) (* 1/2 x))) y)) x)))>
#<alt (* -1 (* y (- (* -1 (/ (+ z (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 x) (* 1/8 x)) y)) (+ (* -1/4 x) (* 1/4 x))) y)) (* 1/2 x))) y)) x)))>
#<alt (- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y)))>
#<alt (- (+ z (* 1/4 (/ x (- 1/2 y)))) (/ (* x (pow y 2)) (- 1/2 y)))>
#<alt (- (+ z (* 1/4 (/ x (- 1/2 y)))) (/ (* x (pow y 2)) (- 1/2 y)))>
#<alt (- (+ z (* 1/4 (/ x (- 1/2 y)))) (/ (* x (pow y 2)) (- 1/2 y)))>
#<alt z>
#<alt (* z (- (+ 1 (* 1/4 (/ x (* z (- 1/2 y))))) (/ (* x (pow y 2)) (* z (- 1/2 y)))))>
#<alt (* z (- (+ 1 (* 1/4 (/ x (* z (- 1/2 y))))) (/ (* x (pow y 2)) (* z (- 1/2 y)))))>
#<alt (* z (- (+ 1 (* 1/4 (/ x (* z (- 1/2 y))))) (/ (* x (pow y 2)) (* z (- 1/2 y)))))>
#<alt z>
#<alt (* -1 (* z (- (* -1 (/ (- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y))) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y))) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y))) z)) 1)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/4 (/ x (- 1/2 y)))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ (* 1/2 x) (* y (+ x (* 2 (* x y)))))>
#<alt (+ (* 1/2 x) (* y (+ x (* y (+ (* 2 x) (* 4 (* x y)))))))>
#<alt (* -1/4 (/ x y))>
#<alt (/ (+ (* -1/4 x) (* -1/8 (/ x y))) y)>
#<alt (/ (+ (* -1/4 x) (+ (* -1/8 (/ x y)) (* -1/16 (/ x (pow y 2))))) y)>
#<alt (/ (+ (* -1/4 x) (+ (* -1/8 (/ x y)) (+ (* -1/16 (/ x (pow y 2))) (* -1/32 (/ x (pow y 3)))))) y)>
#<alt (* -1/4 (/ x y))>
#<alt (* -1 (/ (+ (* 1/8 (/ x y)) (* 1/4 x)) y))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/8 x) (* -1/16 (/ x y))) y)) (* 1/4 x)) y))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/32 (/ x y)) (* 1/16 x)) y)) (* -1/8 x)) y)) (* 1/4 x)) y))>
#<alt (* 2 (* x (pow y 2)))>
#<alt (* (pow y 2) (+ (* 2 x) (* 4 (* x y))))>
#<alt (* (pow y 2) (+ (* 2 x) (* y (- (* 8 (* x y)) (* -4 x)))))>
#<alt (* (pow y 2) (+ (* 2 x) (* y (- (* y (- (* 16 (* x y)) (* -8 x))) (* -4 x)))))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (* -1/2 (/ x y))))>
#<alt (* y (- (+ (* -1 x) (* -1/4 (/ x (pow y 2)))) (* 1/2 (/ x y))))>
#<alt (* y (- (+ (* -1 x) (* -1/8 (/ x (pow y 3)))) (+ (* 1/4 (/ x (pow y 2))) (* 1/2 (/ x y)))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* 1/2 (/ x y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (* -1/4 (/ x y)) (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ x y)) (* -1/4 x)) y)) (* 1/2 x)) y)))))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (/ (* x (pow y 2)) (- 1/2 y))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* x (+ 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 2>
#<alt (+ 2 (* -4 y))>
#<alt (+ 2 (* y (- (* 8 y) 4)))>
#<alt (+ 2 (* y (- (* y (+ 8 (* -16 y))) 4)))>
#<alt (/ 1 y)>
#<alt (/ (- 1 (* 1/2 (/ 1 y))) y)>
#<alt (/ (- (+ 1 (/ 1/4 (pow y 2))) (* 1/2 (/ 1 y))) y)>
#<alt (/ (- (+ 1 (/ 1/4 (pow y 2))) (+ (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow y 3))))) y)>
#<alt (/ 1 y)>
#<alt (* -1 (/ (- (* 1/2 (/ 1 y)) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 y)) 1/2) y)) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 y)) 1/4) y)) 1/2) y)) 1) 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 (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>
#<alt (* (pow x 2) y)>

Calls

66 calls:

Time	Variable		Point	Expression
4.0ms	y	@	-inf	(* x (* x y))
2.0ms	x	@	inf	(- (/ (* x (* 1/4 x)) (* x (- 1/2 y))) (- (/ (* y (* x (* x y))) (* x (- 1/2 y))) z))
1.0ms	z	@	-inf	(+ (* x y) z)
1.0ms	x	@	0	(- (/ (* x (* 1/4 x)) (* x (- 1/2 y))) (- (/ (* y (* x (* x y))) (* x (- 1/2 y))) z))
1.0ms	z	@	0	(- (/ (* x (* 1/4 x)) (* x (- 1/2 y))) (- (/ (* y (* x (* x y))) (* x (- 1/2 y))) z))

rewrite352.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3004×	`/-lowering-/.f32`
3004×	`/-lowering-/.f64`
2836×	`-lowering-.f32`
2836×	`-lowering-.f64`
2226×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	91
1	148	70
2	1570	69
0	8700	69

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 373

Calls

Call 1

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

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

simplify250.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

3690×	`-lowering-.f32`
3690×	`-lowering-.f64`
1902×	`+-lowering-+.f64`
1902×	`+-lowering-+.f32`
1668×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	1996
1	1030	1781
2	3446	1724
0	8966	1724

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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)
z
(+ z (* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y)))))
(+ z (* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y)))))
(+ z (* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y)))))
(* x (- (* 1/4 (/ 1 (- 1/2 y))) (/ (pow y 2) (- 1/2 y))))
(* x (- (+ (* 1/4 (/ 1 (- 1/2 y))) (/ z x)) (/ (pow y 2) (- 1/2 y))))
(* x (- (+ (* 1/4 (/ 1 (- 1/2 y))) (/ z x)) (/ (pow y 2) (- 1/2 y))))
(* x (- (+ (* 1/4 (/ 1 (- 1/2 y))) (/ z x)) (/ (pow y 2) (- 1/2 y))))
(* x (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))
(* -1 (* x (- (* -1 (/ z x)) (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))))
(* -1 (* x (- (* -1 (/ z x)) (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))))
(* -1 (* x (- (* -1 (/ z x)) (+ (* -1 (/ (pow y 2) (- 1/2 y))) (* 1/4 (/ 1 (- 1/2 y)))))))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* y (+ x (* (pow y 2) (+ (* -4 x) (* 4 x)))))))
(+ z (+ (* 1/2 x) (* y (+ x (* (pow y 2) (+ (* -4 x) (+ (* 4 x) (* y (+ (* -8 x) (* 8 x))))))))))
(* x y)
(* y (- (+ (* 1/2 (/ x y)) (/ z y)) (* -1 x)))
(* y (- (+ (* -1/4 (/ x (pow y 2))) (+ (* 1/4 (/ x (pow y 2))) (+ (* 1/2 (/ x y)) (/ z y)))) (* -1 x)))
(* y (- (+ (* -1/4 (/ x (pow y 2))) (+ (* -1/8 (/ x (pow y 3))) (+ (* 1/8 (/ x (pow y 3))) (+ (* 1/4 (/ x (pow y 2))) (+ (* 1/2 (/ x y)) (/ z y)))))) (* -1 x)))
(* x y)
(* -1 (* y (- (* -1 (/ (+ z (* 1/2 x)) y)) x)))
(* -1 (* y (- (* -1 (/ (+ z (+ (* -1 (/ (+ (* -1/4 x) (* 1/4 x)) y)) (* 1/2 x))) y)) x)))
(* -1 (* y (- (* -1 (/ (+ z (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 x) (* 1/8 x)) y)) (+ (* -1/4 x) (* 1/4 x))) y)) (* 1/2 x))) y)) x)))
(- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y)))
(- (+ z (* 1/4 (/ x (- 1/2 y)))) (/ (* x (pow y 2)) (- 1/2 y)))
(- (+ z (* 1/4 (/ x (- 1/2 y)))) (/ (* x (pow y 2)) (- 1/2 y)))
(- (+ z (* 1/4 (/ x (- 1/2 y)))) (/ (* x (pow y 2)) (- 1/2 y)))
z
(* z (- (+ 1 (* 1/4 (/ x (* z (- 1/2 y))))) (/ (* x (pow y 2)) (* z (- 1/2 y)))))
(* z (- (+ 1 (* 1/4 (/ x (* z (- 1/2 y))))) (/ (* x (pow y 2)) (* z (- 1/2 y)))))
(* z (- (+ 1 (* 1/4 (/ x (* z (- 1/2 y))))) (/ (* x (pow y 2)) (* z (- 1/2 y)))))
z
(* -1 (* z (- (* -1 (/ (- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y))) z)) 1)))
(* -1 (* z (- (* -1 (/ (- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y))) z)) 1)))
(* -1 (* z (- (* -1 (/ (- (* 1/4 (/ x (- 1/2 y))) (/ (* x (pow y 2)) (- 1/2 y))) z)) 1)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/4 (/ x (- 1/2 y)))
(* 1/2 x)
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* y (+ x (* 2 (* x y)))))
(+ (* 1/2 x) (* y (+ x (* y (+ (* 2 x) (* 4 (* x y)))))))
(* -1/4 (/ x y))
(/ (+ (* -1/4 x) (* -1/8 (/ x y))) y)
(/ (+ (* -1/4 x) (+ (* -1/8 (/ x y)) (* -1/16 (/ x (pow y 2))))) y)
(/ (+ (* -1/4 x) (+ (* -1/8 (/ x y)) (+ (* -1/16 (/ x (pow y 2))) (* -1/32 (/ x (pow y 3)))))) y)
(* -1/4 (/ x y))
(* -1 (/ (+ (* 1/8 (/ x y)) (* 1/4 x)) y))
(* -1 (/ (+ (* -1 (/ (+ (* -1/8 x) (* -1/16 (/ x y))) y)) (* 1/4 x)) y))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/32 (/ x y)) (* 1/16 x)) y)) (* -1/8 x)) y)) (* 1/4 x)) y))
(* 2 (* x (pow y 2)))
(* (pow y 2) (+ (* 2 x) (* 4 (* x y))))
(* (pow y 2) (+ (* 2 x) (* y (- (* 8 (* x y)) (* -4 x)))))
(* (pow y 2) (+ (* 2 x) (* y (- (* y (- (* 16 (* x y)) (* -8 x))) (* -4 x)))))
(* -1 (* x y))
(* y (+ (* -1 x) (* -1/2 (/ x y))))
(* y (- (+ (* -1 x) (* -1/4 (/ x (pow y 2)))) (* 1/2 (/ x y))))
(* y (- (+ (* -1 x) (* -1/8 (/ x (pow y 3)))) (+ (* 1/4 (/ x (pow y 2))) (* 1/2 (/ x y)))))
(* -1 (* x y))
(* -1 (* y (+ x (* 1/2 (/ x y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1/4 (/ x y)) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ x y)) (* -1/4 x)) y)) (* 1/2 x)) y)))))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(/ (* x (pow y 2)) (- 1/2 y))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* x (+ 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)))))
2
(+ 2 (* -4 y))
(+ 2 (* y (- (* 8 y) 4)))
(+ 2 (* y (- (* y (+ 8 (* -16 y))) 4)))
(/ 1 y)
(/ (- 1 (* 1/2 (/ 1 y))) y)
(/ (- (+ 1 (/ 1/4 (pow y 2))) (* 1/2 (/ 1 y))) y)
(/ (- (+ 1 (/ 1/4 (pow y 2))) (+ (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow y 3))))) y)
(/ 1 y)
(* -1 (/ (- (* 1/2 (/ 1 y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 y)) 1/2) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 y)) 1/4) y)) 1/2) y)) 1) 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))))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)
(* (pow x 2) y)

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

eval107.0ms (1.7%)

Compiler: Compiled 24408 to 1397 computations (94.3% saved)

prune69.0ms (1.1%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	661	2	663
Fresh	0	0	0
Picked	2	2	4
Done	0	4	4
Total	663	8	671

Accuracy

100.0%

Counts

671 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	33.0%	(/.f64 x (/.f64 #s(literal 1 binary64) y))
▶	69.7%	(-.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
✓	77.3%	(+.f64 (*.f64 x y) z)
✓	68.3%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	54.8%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	33.0%	(*.f64 x y)
✓	23.7%	(*.f64 x #s(literal 1/2 binary64))
✓	46.6%	z

Compiler

Compiled 70 to 48 computations (31.4% saved)

simplify139.0ms (2.2%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) y)
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) y))
✓	cost-diff	0	(-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) z)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	128	(-.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
✓	cost-diff	256	(/.f64 (.f64 y (.f64 x (.f64 x y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))

Rules

2058×	`fnmadd-define`
1712×	`sum5-define`
1420×	`-lowering-.f32`
1420×	`-lowering-.f64`
1274×	`fmm-def`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	84
1	47	71
2	138	71
3	580	63
4	2314	62
5	5037	62
0	8193	62

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize84.0ms (1.3%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) y)
✓	accuracy	99.7%	(/.f64 x (/.f64 #s(literal 1 binary64) y))
✓	accuracy	100.0%	(*.f64 x (-.f64 #s(literal 1/2 binary64) y))
✓	accuracy	99.8%	(.f64 x (.f64 x y))
✓	accuracy	95.2%	(.f64 y (.f64 x (*.f64 x y)))
✓	accuracy	68.4%	(/.f64 (.f64 y (.f64 x (.f64 x y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))

Results

66.0ms

256×

valid

Compiler

Compiled 92 to 17 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 9.0ms (42.8% of total)

ival-sub: 6.0ms (28.5% of total)

ival-div: 6.0ms (28.5% of total)

const: 1.0ms (4.8% of total)

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

series6.0ms (0.1%)

Counts

9 → 216

Calls

Call 1

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

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

Calls

54 calls:

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

rewrite306.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4102×	`-lowering-.f32`
4102×	`-lowering-.f64`
3722×	`/-lowering-/.f32`
3722×	`/-lowering-/.f64`
1448×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	72
1	107	58
2	949	52
0	8580	52

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 313

Calls

Call 1

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

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

simplify321.0ms (5%)

Algorithm

1×	egg-herbie

Rules

4902×	`-lowering-.f32`
4902×	`-lowering-.f64`
2680×	`+-lowering-+.f64`
2680×	`+-lowering-+.f32`
1544×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	1787
1	752	1565
2	2547	1490
0	8395	1490

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval85.0ms (1.3%)

Compiler: Compiled 15011 to 1298 computations (91.4% saved)

prune55.0ms (0.9%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	529	0	529
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	529	8	537

Accuracy

100.0%

Counts

537 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	33.0%	(/.f64 x (/.f64 #s(literal 1 binary64) y))
✓	69.7%	(-.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
✓	77.3%	(+.f64 (*.f64 x y) z)
✓	68.3%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	54.8%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	33.0%	(*.f64 x y)
✓	23.7%	(*.f64 x #s(literal 1/2 binary64))
✓	46.6%	z

Compiler

Compiled 168 to 83 computations (50.6% saved)

regimes27.0ms (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 x (/.f64 #s(literal 1 binary64) y))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 y #s(literal 1/2 binary64))))
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(-.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
(-.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (/.f64 (.f64 y (.f64 x (.f64 x y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))) z))
(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)

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

Calls

5 calls:

7.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
4.0ms	z
4.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) 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)

regimes22.0ms (0.3%)

Counts

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

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

Calls

5 calls:

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

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)

regimes12.0ms (0.2%)

Counts

8 → 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 x (/.f64 #s(literal 1 binary64) y))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 y #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:

3.0ms	z
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
87.2%	3	`x`
98.7%	3	`y`
87.6%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes8.0ms (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 y)

Calls

3 calls:

2.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
81.8%	3	`x`
81.4%	3	`z`
84.1%	3	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0.1%)

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:

2.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
77.5%	3	`z`
75.3%	3	`x`
64.6%	3	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes10.0ms (0.2%)

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:

6.0ms	z
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
62.4%	3	`y`
59.9%	3	`x`
61.7%	4	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (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

3 calls:

2.0ms	x
2.0ms	z
1.0ms	y

Results

Accuracy	Segments	Branch
55.7%	3	`x`
56.9%	3	`z`
46.6%	1	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (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:

1.0ms	y
1.0ms	x
1.0ms	z

Results

Accuracy	Segments	Branch
46.6%	1	`y`
46.6%	1	`x`
46.6%	1	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch33.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	2.856133653826788e-7	430.9184119952419
16.0ms	-1153413169215.908	-1369839.0392851154

Results

19.0ms

288×

valid

Compiler

Compiled 342 to 247 computations (27.8% saved)

Precisions

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

ival-add: 3.0ms (37.1% of total)

ival-div: 2.0ms (24.8% of total)

ival-mult: 2.0ms (24.8% of total)

const: 0.0ms (0% of total)

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

bsearch30.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	2.6149667340403327e+139	5.798089448240038e+140
14.0ms	-4.7538950635686895e+51	-1.0918906710520159e+48

Results

20.0ms

240×

valid

Compiler

Compiled 258 to 193 computations (25.2% saved)

Precisions

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

ival-mult: 5.0ms (51.6% of total)

ival-div: 2.0ms (20.7% of total)

ival-add: 2.0ms (20.7% of total)

const: 0.0ms (0% of total)

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

bsearch30.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.1675775195185839e+98	2.8127296146754867e+103
9.0ms	-53300827733739.3	-4144052215414.9272

Results

17.0ms

240×

valid

Compiler

Compiled 228 to 178 computations (21.9% saved)

Precisions

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

ival-div: 2.0ms (30.2% of total)

ival-add: 2.0ms (30.2% of total)

ival-mult: 2.0ms (30.2% of total)

const: 0.0ms (0% of total)

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

bsearch40.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
25.0ms	2.0829638842354952e+136	2.4792476951658834e+138
12.0ms	-4.7538950635686895e+51	-1.0918906710520159e+48

Results

16.0ms

240×

valid

Compiler

Compiled 198 to 148 computations (25.3% saved)

Precisions

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

ival-div: 2.0ms (29.9% of total)

ival-add: 2.0ms (29.9% of total)

ival-mult: 2.0ms (29.9% of total)

const: 0.0ms (0% of total)

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

bsearch27.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	1.1991284261469577e-26	2.974006226268539e-26
14.0ms	-2.0734511122141144e-114	-4.861799946826616e-123

Results

15.0ms

224×

valid

Compiler

Compiled 186 to 153 computations (17.7% saved)

Precisions

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

ival-div: 2.0ms (31.7% of total)

ival-add: 2.0ms (31.7% of total)

ival-mult: 2.0ms (31.7% of total)

const: 0.0ms (0% of total)

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	93
1	70	93

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(if (<=.f64 y #s(literal -1400000 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 -19500000000000000449345747305952439936418903490560 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 26500000000000002522941327939552038472944103090457309502088013206559843894439870067930512954913140999097687976072756661812215064365000294400 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x y)))
(if (<=.f64 z #s(literal -52000000000000 binary64)) z (if (<=.f64 z #s(literal 1750000000000000053084755041014334503916146287396170029563021230283685561403378012248112955192653119488 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 y #s(literal -6200000000000000109584950050259060207153085153280 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 39000000000000001900560907819850178597914091368747705964109613903104776348410977395971480593523255805788915473821654532184052408193646592 binary64)) z (.f64 x y)))
(if (<=.f64 z #s(literal -2772669694120815/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912 binary64)) z (if (<=.f64 z #s(literal 7317432018267861/348449143727040986586495598010130648530944 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

Outputs
(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 z (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 x y)))
(if (<=.f64 y #s(literal -1400000 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 -1400000 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 -19500000000000000449345747305952439936418903490560 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 26500000000000002522941327939552038472944103090457309502088013206559843894439870067930512954913140999097687976072756661812215064365000294400 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x y)))
(if (<=.f64 y #s(literal -19500000000000000449345747305952439936418903490560 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 26500000000000002522941327939552038472944103090457309502088013206559843894439870067930512954913140999097687976072756661812215064365000294400 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (*.f64 x y)))
(if (<=.f64 z #s(literal -52000000000000 binary64)) z (if (<=.f64 z #s(literal 1750000000000000053084755041014334503916146287396170029563021230283685561403378012248112955192653119488 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 z #s(literal -52000000000000 binary64)) z (if (<=.f64 z #s(literal 1750000000000000053084755041014334503916146287396170029563021230283685561403378012248112955192653119488 binary64)) (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z))
(if (<=.f64 y #s(literal -6200000000000000109584950050259060207153085153280 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 39000000000000001900560907819850178597914091368747705964109613903104776348410977395971480593523255805788915473821654532184052408193646592 binary64)) z (.f64 x y)))
(if (<=.f64 z #s(literal -2772669694120815/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912 binary64)) z (if (<=.f64 z #s(literal 7317432018267861/348449143727040986586495598010130648530944 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

soundness1.1s (16.9%)

Rules

3950×	`-lowering-.f32`
3950×	`-lowering-.f64`
2598×	`/-lowering-/.f32`
2598×	`/-lowering-/.f64`
2520×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	440
1	184	412
2	569	412
3	1683	412
4	5094	412
0	8271	412
0	8	21
1	49	18
2	501	17
3	7188	17
0	8003	17
0	66	602
1	233	556
2	712	556
3	2259	556
4	5212	556
0	8267	556

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 187 to 104 computations (44.4% saved)

preprocess56.0ms (0.9%)

Compiler: Compiled 232 to 104 computations (55.2% saved)

analyze0.0ms (0%)

sample1.4s (21%)

preprocess150.0ms (2.3%)

explain129.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize37.0ms (0.6%)

series6.0ms (0.1%)

rewrite318.0ms (4.9%)

simplify288.0ms (4.5%)

eval48.0ms (0.7%)

prune31.0ms (0.5%)

simplify6.0ms (0.1%)

localize69.0ms (1.1%)

series4.0ms (0.1%)

rewrite305.0ms (4.7%)

simplify146.0ms (2.2%)

eval53.0ms (0.8%)

prune51.0ms (0.8%)

simplify145.0ms (2.2%)

localize109.0ms (1.7%)

series21.0ms (0.3%)

rewrite352.0ms (5.4%)

simplify250.0ms (3.9%)

eval107.0ms (1.7%)

prune69.0ms (1.1%)

simplify139.0ms (2.2%)

localize84.0ms (1.3%)

series6.0ms (0.1%)

rewrite306.0ms (4.7%)

simplify321.0ms (5%)

eval85.0ms (1.3%)

prune55.0ms (0.9%)

regimes27.0ms (0.4%)

regimes22.0ms (0.3%)

regimes12.0ms (0.2%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes10.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch33.0ms (0.5%)

bsearch30.0ms (0.5%)

bsearch30.0ms (0.5%)

bsearch40.0ms (0.6%)

bsearch27.0ms (0.4%)

simplify10.0ms (0.2%)

soundness1.1s (16.9%)

preprocess56.0ms (0.9%)

end0.0ms (0%)

Profiling