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)

sample955.0ms (18.5%)

Results

714.0ms	8255×	0	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 353.0ms

ival-div: 124.0ms (35.1% of total)

ival-add: 117.0ms (33.1% of total)

ival-mult: 98.0ms (27.7% of total)

const: 11.0ms (3.1% of total)

backward-pass: 3.0ms (0.8% of total)

Bogosity

preprocess116.0ms (2.2%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

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

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

Call 2

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

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

explain133.0ms (2.6%)

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

90.0ms	510×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 72 to 26 computations (63.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-div: 39.0ms (79.6% of total)

ival-add: 5.0ms (10.2% of total)

ival-mult: 4.0ms (8.2% of total)

const: 1.0ms (2% 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)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize53.0ms (1%)

Localize:

Found 4 expressions of interest:

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

44.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 30 to 9 computations (70% saved)

Precisions

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

ival-add: 3.0ms (41.6% of total)

ival-div: 2.0ms (27.7% of total)

ival-mult: 2.0ms (27.7% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

4 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite318.0ms (6.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	49	18
2	501	17
3	7188	17
0	8003	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 182

Calls

Call 1

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

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

simplify390.0ms (7.6%)

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)

eval303.0ms (5.9%)

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

prune48.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	273	5	278
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	273	6	279

Accuracy

100.0%

Counts

279 → 6

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)
▶	73.1%	(+.f64 (*.f64 x y) z)
▶	67.7%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
▶	60.3%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
▶	33.9%	(*.f64 x y)
▶	41.4%	z

Compiler

Compiled 80 to 56 computations (30% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 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 x y)
✓	cost-diff	(+.f64 (*.f64 x y) z)

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	20	37
2	25	37
3	27	37
0	27	37

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize89.0ms (1.7%)

Localize:

Found 7 expressions of interest:

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

Results

75.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 43 to 11 computations (74.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-add: 6.0ms (50.1% of total)

ival-mult: 6.0ms (50.1% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

6 → 132

Calls

Call 1

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

Outputs
#<alt z>
#<alt (+ z (* x 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 (* 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

33 calls:

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

rewrite336.0ms (6.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3194×	`-lowering-.f32`
3194×	`-lowering-.f64`
1834×	`/-lowering-/.f32`
1834×	`/-lowering-/.f64`
1794×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	57	22
2	459	22
3	5078	22
0	8135	22

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 226

Calls

Call 1

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

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

simplify246.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

2346×	`fnmadd-define`
1784×	`fmsub-define`
1704×	`fnmsub-define`
1640×	`-lowering-.f32`
1640×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	508
1	211	463
2	588	463
3	1748	463
4	5114	463
0	8453	463

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval54.0ms (1.1%)

Compiler: Compiled 6721 to 655 computations (90.3% saved)

prune43.0ms (0.8%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	382	2	384
Fresh	0	0	0
Picked	0	5	5
Done	1	0	1
Total	383	7	390

Accuracy

100.0%

Counts

390 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.3%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	73.1%	(+.f64 (*.f64 x y) z)
✓	67.7%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	60.3%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	33.9%	(*.f64 x y)
▶	28.6%	(*.f64 x #s(literal 1/2 binary64))
✓	41.4%	z

Compiler

Compiled 50 to 36 computations (28% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 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 #s(literal 1/2 binary64))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	12	19
2	18	19
0	18	19

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize41.0ms (0.8%)

Localize:

Found 4 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 #s(literal 1/2 binary64))

Results

32.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

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

ival-mult: 12.0ms (88.7% of total)

ival-add: 1.0ms (7.4% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

3 → 60

Calls

Call 1

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

Outputs
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 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 (* 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

15 calls:

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

rewrite264.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2768×	`-lowering-.f32`
2768×	`-lowering-.f64`
1858×	`sum5-define`
1518×	`fmsub-define`
1518×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	25	11
2	222	11
3	2859	11
0	8124	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 112

Calls

Call 1

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

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

simplify136.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2190×	`sum3-define`
1814×	`fnmadd-define`
1430×	`fmsub-define`
1372×	`sum4-define`
1340×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	222
1	67	222
2	177	222
3	398	222
4	975	222
5	3143	222
6	7357	222
0	8866	222

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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)
(* 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)))))
(* 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
(* 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)
(* 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))
(* 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)

eval63.0ms (1.2%)

Compiler: Compiled 3754 to 334 computations (91.1% saved)

prune19.0ms (0.4%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	193	7	200

Accuracy

100.0%

Counts

200 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.3%	(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
✓	73.1%	(+.f64 (*.f64 x y) z)
✓	67.7%	(+.f64 (*.f64 x #s(literal 1/2 binary64)) z)
✓	60.3%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	33.9%	(*.f64 x y)
✓	28.6%	(*.f64 x #s(literal 1/2 binary64))
✓	41.4%	z

Compiler

Compiled 91 to 52 computations (42.9% saved)

regimes28.0ms (0.5%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

14.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
3.0ms	z
3.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
3.0ms	x
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)

regimes36.0ms (0.7%)

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	x
3.0ms	y

Results

Accuracy	Segments	Branch
86.3%	3	`x`
98.9%	3	`y`
88.0%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes8.0ms (0.2%)

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 y)

Calls

3 calls:

3.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
81.4%	3	`x`
82.9%	3	`z`
85.4%	3	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0.1%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
76.6%	3	`x`
77.8%	3	`z`
64.7%	3	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes8.0ms (0.2%)

Counts

3 → 7

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
2.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
68.6%	7	`y`
57.7%	4	`x`
62.2%	5	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (0.1%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
2.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
54.4%	3	`x`
55.6%	3	`z`
51.0%	5	`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	z
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
41.4%	1	`y`
41.4%	1	`x`
41.4%	1	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch28.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.011519811241562473	195.2006309591807
11.0ms	-387.27444275700066	-47.62845725030513

Results

18.0ms

224×

valid

Compiler

Compiled 270 to 195 computations (27.8% saved)

Precisions

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

ival-div: 2.0ms (31.9% of total)

ival-add: 2.0ms (31.9% of total)

ival-mult: 2.0ms (31.9% of total)

const: 0.0ms (0% of total)

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

bsearch312.0ms (6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
301.0ms	3.6085462959974254e+79	1.0187891148629593e+82
9.0ms	-387.27444275700066	-47.62845725030513

Results

303.0ms

224×

valid

Compiler

Compiled 254 to 193 computations (24% saved)

Precisions

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

ival-div: 290.0ms (98.3% of total)

ival-add: 2.0ms (0.7% of total)

ival-mult: 2.0ms (0.7% of total)

const: 0.0ms (0% of total)

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

bsearch19.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	33899.96553769062	946876.4980489893
6.0ms	-3.868565925315511e+70	-2.3317695619415554e+70

Results

11.0ms

176×

valid

Compiler

Compiled 172 to 134 computations (22.1% saved)

Precisions

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

ival-add: 2.0ms (41.7% of total)

ival-div: 1.0ms (20.8% of total)

ival-mult: 1.0ms (20.8% of total)

const: 0.0ms (0% of total)

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

bsearch108.0ms (2.1%)

Algorithm

6×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	3.6085462959974254e+79	1.0187891148629593e+82
12.0ms	2.4511074143060973e-104	7.054661933052712e-103
16.0ms	2.615141742239536e-253	3.938285534180614e-241
30.0ms	-3.526756024603747e-222	-9.76429667963088e-231
6.0ms	-2.6767084637682143e-46	-1.417243122501575e-46
26.0ms	-1.4221863621473092e+60	-5.910927513510376e+53

Results

77.0ms

752×

valid

Compiler

Compiled 582 to 466 computations (19.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-div: 18.0ms (54.8% of total)

ival-add: 7.0ms (21.3% of total)

ival-mult: 6.0ms (18.3% of total)

const: 1.0ms (3% of total)

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

bsearch31.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	33899.96553769062	946876.4980489893
18.0ms	-1.397806764723568e-117	-4.903805319072813e-120

Results

21.0ms

240×

valid

Compiler

Compiled 198 to 163 computations (17.7% saved)

Precisions

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

ival-div: 2.0ms (30.9% of total)

ival-add: 2.0ms (30.9% of total)

ival-mult: 2.0ms (30.9% of total)

const: 0.0ms (0% of total)

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

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	117
1	74	117

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(if (<=.f64 y #s(literal -48 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 -215 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 y #s(literal 1249999999999999954258495703860821776378392903159195974210045480428385812692860928 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x y)))
(if (<=.f64 z #s(literal -23999999999999998675763391424923926311106931530898159694958799364292608 binary64)) z (if (<=.f64 z #s(literal 900000 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 y #s(literal -57999999999999997054697271205935946659469533894494126080 binary64)) (.f64 x y) (if (<=.f64 y #s(literal -498150793720287/3213876088517980551083924184682325205044405987565585670602752 binary64)) z (if (<=.f64 y #s(literal -8139666055761541/6511732844609232689531105264376228317524178049136629062886970519300817615056281319845148633663627237053642490813899648872938282865350942461292339894854326216889802323744154842249099888585755883524379898570201759747744871130348106729652224 binary64)) (.f64 x #s(literal 1/2 binary64)) (if (<=.f64 y #s(literal 2477480553505551/15015033657609400459942315391018513722623519187099007073355798781525263125238463415894820397160662761697108038369410925238365381332604486523522921813279810320079453845181805154673256699778290824639959535835805252308660678089369234238529227774479195332149248 binary64)) z (if (<=.f64 y #s(literal 6859101238668351/10086913586276986678343434265636765134100413253239154346994763111486904773503285916522052161250538404046496765518544896 binary64)) (.f64 x #s(literal 1/2 binary64)) (if (<=.f64 y #s(literal 2499999999999999908516991407721643552756785806318391948420090960856771625385721856 binary64)) z (.f64 x y)))))))
(if (<=.f64 z #s(literal -7722661445640823/22713710134237715329666368996500141698551292521478689383796568724394977753543685103943470334805111423773828800195818060422956300894208 binary64)) z (if (<=.f64 z #s(literal 35000 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

Outputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 x y)) z)
(if (<=.f64 y #s(literal -48 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 -48 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 -215 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 y #s(literal 1249999999999999954258495703860821776378392903159195974210045480428385812692860928 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) z) (*.f64 x y)))
(if (<=.f64 y #s(literal -215 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (if (<=.f64 y #s(literal 1249999999999999954258495703860821776378392903159195974210045480428385812692860928 binary64)) (+.f64 z (.f64 x #s(literal 1/2 binary64))) (*.f64 x y)))
(if (<=.f64 z #s(literal -23999999999999998675763391424923926311106931530898159694958799364292608 binary64)) z (if (<=.f64 z #s(literal 900000 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) y)) z))
(if (<=.f64 z #s(literal -23999999999999998675763391424923926311106931530898159694958799364292608 binary64)) z (if (<=.f64 z #s(literal 900000 binary64)) (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z))
(if (<=.f64 y #s(literal -57999999999999997054697271205935946659469533894494126080 binary64)) (.f64 x y) (if (<=.f64 y #s(literal -498150793720287/3213876088517980551083924184682325205044405987565585670602752 binary64)) z (if (<=.f64 y #s(literal -8139666055761541/6511732844609232689531105264376228317524178049136629062886970519300817615056281319845148633663627237053642490813899648872938282865350942461292339894854326216889802323744154842249099888585755883524379898570201759747744871130348106729652224 binary64)) (.f64 x #s(literal 1/2 binary64)) (if (<=.f64 y #s(literal 2477480553505551/15015033657609400459942315391018513722623519187099007073355798781525263125238463415894820397160662761697108038369410925238365381332604486523522921813279810320079453845181805154673256699778290824639959535835805252308660678089369234238529227774479195332149248 binary64)) z (if (<=.f64 y #s(literal 6859101238668351/10086913586276986678343434265636765134100413253239154346994763111486904773503285916522052161250538404046496765518544896 binary64)) (.f64 x #s(literal 1/2 binary64)) (if (<=.f64 y #s(literal 2499999999999999908516991407721643552756785806318391948420090960856771625385721856 binary64)) z (.f64 x y)))))))
(if (<=.f64 z #s(literal -7722661445640823/22713710134237715329666368996500141698551292521478689383796568724394977753543685103943470334805111423773828800195818060422956300894208 binary64)) z (if (<=.f64 z #s(literal 35000 binary64)) (*.f64 x #s(literal 1/2 binary64)) z))
z

soundness799.0ms (15.5%)

Rules

2520×	`-lowering-.f32`
2520×	`-lowering-.f64`
2346×	`fnmadd-define`
1784×	`fmsub-define`
1704×	`fnmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	508
1	211	463
2	588	463
3	1748	463
4	5114	463
0	8453	463
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 220 to 126 computations (42.7% saved)

preprocess83.0ms (1.6%)

Compiler: Compiled 272 to 126 computations (53.7% saved)

analyze0.0ms (0%)

sample955.0ms (18.5%)

preprocess116.0ms (2.2%)

explain133.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize53.0ms (1%)

series6.0ms (0.1%)

rewrite318.0ms (6.2%)

simplify390.0ms (7.6%)

eval303.0ms (5.9%)

prune48.0ms (0.9%)

simplify6.0ms (0.1%)

localize89.0ms (1.7%)

series5.0ms (0.1%)

rewrite336.0ms (6.5%)

simplify246.0ms (4.8%)

eval54.0ms (1.1%)

prune43.0ms (0.8%)

simplify15.0ms (0.3%)

localize41.0ms (0.8%)

series1.0ms (0%)

rewrite264.0ms (5.1%)

simplify136.0ms (2.6%)

eval63.0ms (1.2%)

prune19.0ms (0.4%)

regimes28.0ms (0.5%)

regimes36.0ms (0.7%)

regimes8.0ms (0.2%)

regimes7.0ms (0.1%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch28.0ms (0.5%)

bsearch312.0ms (6%)

bsearch19.0ms (0.4%)

bsearch108.0ms (2.1%)

bsearch31.0ms (0.6%)

simplify41.0ms (0.8%)

soundness799.0ms (15.5%)

preprocess83.0ms (1.6%)

end0.0ms (0%)

Profiling