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)

sample738.0ms (16.1%)

Results

545.0ms	8252×	0	valid
0.0ms	2×	2	valid
0.0ms	2×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 279.0ms

ival-mult: 101.0ms (36.1% of total)

ival-add: 92.0ms (32.9% of total)

ival-div: 73.0ms (26.1% of total)

const: 11.0ms (3.9% of total)

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

Bogosity

preprocess137.0ms (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))

explain83.0ms (1.8%)

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

44.0ms

512×

valid

Compiler

Compiled 72 to 26 computations (63.9% saved)

Precisions

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

ival-add: 5.0ms (35% of total)

ival-div: 4.0ms (28% of total)

ival-mult: 4.0ms (28% of total)

const: 1.0ms (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)

simplify9.0ms (0.2%)

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

localize29.0ms (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 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	100.0%	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))

Results

21.0ms

256×

valid

Compiler

Compiled 30 to 9 computations (70% saved)

Precisions

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

ival-div: 2.0ms (28.3% of total)

ival-add: 2.0ms (28.3% of total)

ival-mult: 2.0ms (28.3% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.2%)

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
3.0ms	x	@	-inf	(+ (+ (/ x 2) (* y x)) z)
1.0ms	x	@	-inf	(/ x 2)
1.0ms	x	@	inf	(+ (+ (/ x 2) (* y x)) z)
1.0ms	y	@	0	(+ (+ (/ x 2) (* y x)) z)
0.0ms	x	@	0	(+ (+ (/ x 2) (* y x)) z)

rewrite412.0ms (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	497	17
3	7165	17
0	8007	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 182

Calls

Call 1

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

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

simplify131.0ms (2.9%)

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)

eval92.0ms (2%)

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

prune64.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

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

Accuracy

100.0%

Counts

279 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 z (*.f64 x (-.f64 #s(literal -1/2 binary64) y)))
✓	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
	77.3%	(+.f64 (*.f64 x y) z)
▶	62.5%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
▶	60.5%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
▶	38.5%	(*.f64 x y)
▶	40.8%	z

Compiler

Compiled 100 to 70 computations (30% saved)

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

756×	`fnmadd-define`
588×	`fmsub-define`
576×	`fnmsub-define`
548×	`fma-lowering-fma.f32`
548×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	29	46
2	60	45
3	154	45
4	335	45
5	824	45
6	1643	45
7	2448	45
8	2675	45
9	2732	45
0	2732	45

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize327.0ms (7.1%)

Localize:

Found 8 expressions of interest:

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

Results

313.0ms

256×

valid

Compiler

Compiled 51 to 14 computations (72.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 159.0ms

ival-mult: 153.0ms (96.2% of total)

ival-sub: 3.0ms (1.9% of total)

ival-add: 3.0ms (1.9% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

8 → 168

Calls

Call 1

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

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

42 calls:

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

rewrite366.0ms (8%)

Algorithm

1×	batch-egg-rewrite

Rules

3924×	`-lowering-.f32`
3924×	`-lowering-.f64`
2544×	`/-lowering-/.f32`
2544×	`/-lowering-/.f64`
2012×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	76	33
2	599	32
3	7144	32
0	8584	32

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 361

Calls

Call 1

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

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

simplify204.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1888×	`fnmadd-define`
1854×	`-lowering-.f32`
1854×	`-lowering-.f64`
1654×	`sum3-define`
1102×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	813
1	256	704
2	730	698
3	2448	698
4	7457	698
0	8168	698

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

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

eval88.0ms (1.9%)

Compiler: Compiled 10856 to 1067 computations (90.2% saved)

prune55.0ms (1.2%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	527	2	529
Fresh	0	1	1
Picked	0	5	5
Done	1	0	1
Total	528	8	536

Accuracy

100.0%

Counts

536 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 z (*.f64 x (-.f64 #s(literal -1/2 binary64) y)))
▶	60.5%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
▶	77.3%	(+.f64 (*.f64 x y) z)
✓	62.5%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	60.5%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	38.5%	(*.f64 x y)
▶	24.0%	(*.f64 x #s(literal 1/2 binary64))
✓	40.8%	z

Compiler

Compiled 60 to 43 computations (28.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	16	29
2	23	29
0	23	29

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize39.0ms (0.8%)

Localize:

Found 6 expressions of interest:

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

Results

28.0ms

256×

valid

Compiler

Compiled 36 to 9 computations (75% saved)

Precisions

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

ival-mult: 4.0ms (58% of total)

ival-add: 3.0ms (43.5% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Counts

4 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite288.0ms (6.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	39	15
2	350	15
3	4478	15
0	8159	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 148

Calls

Call 1

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

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

simplify153.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	376
1	161	349
2	468	349
3	1228	349
4	3448	349
0	8114	349

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval31.0ms (0.7%)

Compiler: Compiled 5927 to 441 computations (92.6% saved)

prune44.0ms (1%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	0	0
Picked	0	3	3
Done	0	5	5
Total	284	8	292

Accuracy

100.0%

Counts

292 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 z (*.f64 x (-.f64 #s(literal -1/2 binary64) y)))
✓	60.5%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	77.3%	(+.f64 (*.f64 x y) z)
✓	62.5%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	60.5%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	38.5%	(*.f64 x y)
✓	24.0%	(*.f64 x #s(literal 1/2 binary64))
✓	40.8%	z

Compiler

Compiled 108 to 63 computations (41.7% saved)

regimes49.0ms (1.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

5 calls:

34.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
4.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
4.0ms	x
4.0ms	z
3.0ms	y

Results

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

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes10.0ms (0.2%)

Counts

7 → 3

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	z
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
84.9%	3	`x`
98.3%	3	`y`
88.3%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (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 (+.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))

Calls

2 calls:

3.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
82.5%	3	`z`
88.1%	3	`y`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes18.0ms (0.4%)

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:

13.0ms	y
2.0ms	z
2.0ms	x

Results

Accuracy	Segments	Branch
76.7%	3	`z`
69.6%	3	`x`
69.5%	3	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
66.5%	3	`y`
54.9%	4	`x`
60.5%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (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:

3.0ms	x
2.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
48.5%	3	`x`
51.6%	3	`z`
40.8%	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	z
1.0ms	x

Results

Accuracy	Segments	Branch
40.8%	1	`y`
40.8%	1	`x`
40.8%	1	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch27.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.0059921821795038644	194.32691614696503
14.0ms	-1074.2277579338831	-0.0005215801844676802

Results

15.0ms

272×

valid

Compiler

Compiled 324 to 234 computations (27.8% saved)

Precisions

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

ival-add: 3.0ms (40.7% of total)

ival-div: 2.0ms (27.1% of total)

ival-mult: 2.0ms (27.1% of total)

const: 0.0ms (0% of total)

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

bsearch28.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	339.1650892621509	7303.538647005885
15.0ms	-1074.2277579338831	-0.0005215801844676802

Results

17.0ms

256×

valid

Compiler

Compiled 306 to 237 computations (22.5% saved)

Precisions

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

ival-mult: 5.0ms (53.6% of total)

ival-div: 2.0ms (21.4% of total)

ival-add: 2.0ms (21.4% of total)

const: 0.0ms (0% of total)

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

bsearch25.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
7.0ms	1.8268946315553821e+50	6.157521896915403e+50
15.0ms	-5.937053547634982e+70	-1.162059855839861e+54

Results

14.0ms

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 (30.7% of total)

ival-add: 2.0ms (30.7% of total)

ival-mult: 2.0ms (30.7% of total)

const: 0.0ms (0% of total)

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

bsearch25.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	5.450553220051631e+48	1.2263694619219298e+51
12.0ms	-1074.2277579338831	-0.0005215801844676802

Results

15.0ms

256×

valid

Compiler

Compiled 210 to 157 computations (25.2% saved)

Precisions

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

ival-div: 2.0ms (29.7% of total)

ival-add: 2.0ms (29.7% of total)

ival-mult: 2.0ms (29.7% of total)

const: 0.0ms (0% of total)

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

bsearch26.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	5.793417005117727e-55	1.1648533349726026e-52
11.0ms	-9.887025965959201e-51	-5.277331187499053e-55

Results

16.0ms

240×

valid

Compiler

Compiled 198 to 163 computations (17.7% saved)

Precisions

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

ival-div: 4.0ms (44.3% of total)

ival-add: 2.0ms (22.2% of total)

ival-mult: 2.0ms (22.2% of total)

const: 0.0ms (0% of total)

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

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

172×	`unsub-neg_binary64`
106×	`neg-mul-1_binary64`
102×	`distribute-lft-neg-in_binary64`
54×	`neg-sub0_binary64`
52×	`cancel-sign-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	87
1	71	87
2	86	87
3	98	87
4	118	87
5	146	87
6	170	87
7	221	87
8	311	87
9	372	87
10	391	87
11	417	87
12	444	87
13	465	87
14	488	87
15	492	87
16	503	87

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 z (*.f64 x (-.f64 #s(literal -1/2 binary64) y)))
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 (.f64 x y) z) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (+.f64 (*.f64 x y) z)))
(if (<=.f64 y #s(literal -8358680908399641/72057594037927936 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 y #s(literal 2050 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 z #s(literal -3200000000000000294089072260588103618689102710901905031168 binary64)) z (if (<=.f64 z #s(literal 359999999999999985928796559652172183617903261646848 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 y #s(literal -1050 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 44000000000000001280179986666499230037586055528448 binary64)) z (.f64 x y)))
(if (<=.f64 z #s(literal -2830794400050817/26959946667150639794667015087019630673637144422540572481103610249216 binary64)) z (if (<=.f64 z #s(literal 970558080017423/215679573337205118357336120696157045389097155380324579848828881993728 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

Outputs
(-.f64 z (*.f64 x (-.f64 #s(literal -1/2 binary64) y)))
(+.f64 z (*.f64 x (-.f64 y #s(literal -1/2 binary64))))
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 (.f64 x y) z) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (+.f64 (*.f64 x y) z)))
(if (<=.f64 y #s(literal -1/2 binary64)) (+.f64 z (.f64 x y)) (if (<=.f64 y #s(literal 1/2 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (+.f64 z (*.f64 x y))))
(if (<=.f64 y #s(literal -8358680908399641/72057594037927936 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 y #s(literal 2050 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x (+.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 y #s(literal -8358680908399641/72057594037927936 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (if (<=.f64 y #s(literal 2050 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))))
(if (<=.f64 z #s(literal -3200000000000000294089072260588103618689102710901905031168 binary64)) z (if (<=.f64 z #s(literal 359999999999999985928796559652172183617903261646848 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 z #s(literal -3200000000000000294089072260588103618689102710901905031168 binary64)) z (if (<=.f64 z #s(literal 359999999999999985928796559652172183617903261646848 binary64)) (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z))
(if (<=.f64 y #s(literal -1050 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 44000000000000001280179986666499230037586055528448 binary64)) z (.f64 x y)))
(if (<=.f64 z #s(literal -2830794400050817/26959946667150639794667015087019630673637144422540572481103610249216 binary64)) z (if (<=.f64 z #s(literal 970558080017423/215679573337205118357336120696157045389097155380324579848828881993728 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

soundness885.0ms (19.3%)

Rules

2520×	`-lowering-.f32`
2520×	`-lowering-.f64`
1888×	`fnmadd-define`
1854×	`-lowering-.f32`
1854×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	813
1	256	704
2	730	698
3	2448	698
4	7457	698
0	8168	698
0	57	440
1	184	412
2	569	412
3	1683	412
4	5094	412
0	8271	412

Stop Event

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

Compiler

Compiled 179 to 101 computations (43.6% saved)

preprocess42.0ms (0.9%)

Compiler: Compiled 224 to 100 computations (55.4% saved)

Iter	Nodes	Cost
0	42	87
1	71	87
2	86	87
3	98	87
4	118	87
5	146	87
6	170	87
7	221	87
8	311	87
9	372	87
10	391	87
11	417	87
12	444	87
13	465	87
14	488	87
15	492	87
16	503	87

Iter	Nodes	Cost
0	42	87
1	71	87
2	86	87
3	98	87
4	118	87
5	146	87
6	170	87
7	221	87
8	311	87
9	372	87
10	391	87
11	417	87
12	444	87
13	465	87
14	488	87
15	492	87
16	503	87

analyze0.0ms (0%)

sample738.0ms (16.1%)

preprocess137.0ms (3%)

explain83.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.2%)

localize29.0ms (0.6%)

series8.0ms (0.2%)

rewrite412.0ms (9%)

simplify131.0ms (2.9%)

eval92.0ms (2%)

prune64.0ms (1.4%)

simplify59.0ms (1.3%)

localize327.0ms (7.1%)

series6.0ms (0.1%)

rewrite366.0ms (8%)

simplify204.0ms (4.5%)

eval88.0ms (1.9%)

prune55.0ms (1.2%)

simplify5.0ms (0.1%)

localize39.0ms (0.8%)

series3.0ms (0.1%)

rewrite288.0ms (6.3%)

simplify153.0ms (3.4%)

eval31.0ms (0.7%)

prune44.0ms (1%)

regimes49.0ms (1.1%)

regimes10.0ms (0.2%)

regimes5.0ms (0.1%)

regimes18.0ms (0.4%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch27.0ms (0.6%)

bsearch28.0ms (0.6%)

bsearch25.0ms (0.5%)

bsearch25.0ms (0.5%)

bsearch26.0ms (0.6%)

simplify49.0ms (1.1%)

soundness885.0ms (19.3%)

preprocess42.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	42	87
1	71	87
2	86	87
3	98	87
4	118	87
5	146	87
6	170	87
7	221	87
8	311	87
9	372	87
10	391	87
11	417	87
12	444	87
13	465	87
14	488	87
15	492	87
16	503	87