Metrics for Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

analyze12.0ms (0.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (55.9% of total)

ival-div: 1.0ms (28% of total)

const: 0.0ms (0% of total)

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

sample667.0ms (23.3%)

Results

452.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 198.0ms

ival-add: 119.0ms (60.1% of total)

ival-div: 69.0ms (34.8% of total)

const: 8.0ms (4% of total)

backward-pass: 3.0ms (1.5% of total)

Bogosity

preprocess94.0ms (3.3%)

Algorithm

2×	egg-herbie

Rules

1008×	`times-frac`
972×	`div-sub`
948×	`distribute-lft-in`
880×	`distribute-rgt-in`
648×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	48
1	44	42
2	108	42
3	320	42
4	1302	42
5	2669	42
6	3640	42
7	4208	42
8	4632	42
9	4891	42
10	5045	42
11	5458	42
12	5607	42
0	5	7
1	8	7
2	11	7
3	13	7
0	13	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ (+ x y) (+ y y))

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

Call 2

Inputs
(/ (+ x y) (+ y y))
(/ (+ (neg x) y) (+ y y))
(/ (+ x (neg y)) (+ (neg y) (neg y)))
(neg (/ (+ (neg x) y) (+ y y)))
(neg (/ (+ x (neg y)) (+ (neg y) (neg y))))
(/ (+ y x) (+ x x))

Outputs
(/ (+ x y) (+ y y))
(* (+ x y) (/ 1/2 y))
(/ (+ (neg x) y) (+ y y))
(* (- y x) (/ 1/2 y))
(/ (+ x (neg y)) (+ (neg y) (neg y)))
(* (- y x) (/ 1/2 y))
(neg (/ (+ (neg x) y) (+ y y)))
(- -1/2 (* x (/ -1/2 y)))
(neg (/ (+ x (neg y)) (+ (neg y) (neg y))))
(- -1/2 (* x (/ -1/2 y)))
(/ (+ y x) (+ x x))
(+ 1/2 (* 1/2 (/ y x)))

explain58.0ms (2%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(+.f64 x y)`
-	-	`(/.f64 (+.f64 x y) (+.f64 y y))`
-	-	`y`
-	-	`(+.f64 y y)`

Results

40.0ms

512×

valid

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

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

ival-add: 6.0ms (56.9% of total)

ival-div: 4.0ms (38% of total)

const: 0.0ms (0% of total)

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

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize72.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(/.f64 (+.f64 x y) (+.f64 y y))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))

Rules

10×	`/-lowering-/.f32`
10×	`/-lowering-/.f64`
6×	`+-lowering-+.f64`
6×	`+-lowering-+.f32`
4×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
1	8	15
2	11	15
3	13	15
0	13	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (+ x y) (+ y y))
(+ x y)
x
y
(+ y y)

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

Results

55.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

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

ival-add: 3.0ms (57.4% of total)

ival-div: 2.0ms (38.3% of total)

const: 0.0ms (0% of total)

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

series12.0ms (0.4%)

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (/ (+ x y) (+ y y))>
#<alt (+ x y)>
#<alt (+ y y)>

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

Calls

15 calls:

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

rewrite144.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

150×	`/-lowering-/.f32`
150×	`/-lowering-/.f64`
128×	`-lowering-.f32`
128×	`-lowering-.f64`
76×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	35	13
0	302	13

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

3 → 61

Calls

Call 1

Inputs
(/ (+ x y) (+ y y))
(+ x y)
(+ y y)

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

simplify289.0ms (10.1%)

Algorithm

1×	egg-herbie

Rules

4752×	`accelerator-lowering-fma.f32`
4752×	`accelerator-lowering-fma.f64`
2672×	`-lowering-.f32`
2672×	`-lowering-.f64`
1714×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	95	240
2	195	240
3	539	240
4	2494	240
5	4900	240
6	6147	240
7	7103	240
8	7625	240
0	8012	222

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval34.0ms (1.2%)

Compiler: Compiled 1212 to 492 computations (59.4% saved)

prune13.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	3	122

Accuracy

100.0%

Counts

122 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
▶	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
▶	51.9%	#s(literal 1/2 binary64)

Compiler

Compiled 19 to 15 computations (21.1% saved)

localize91.0ms (3.2%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	accuracy	100.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)

Rules

16×	`-lowering-.f32`
16×	`-lowering-.f64`
8×	`*-commutative`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	10	18
2	13	18
3	17	18
4	21	18
5	23	18
0	23	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

46.0ms

256×

valid

Compiler

Compiled 33 to 21 computations (36.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-div: 16.0ms (58.4% of total)

ival-mult: 8.0ms (29.2% of total)

ival-add: 1.0ms (3.7% of total)

const: 1.0ms (3.7% of total)

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

series8.0ms (0.3%)

Counts

3 → 60

Calls

Call 1

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

Calls

15 calls:

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

rewrite499.0ms (17.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4298×	`/-lowering-/.f32`
4298×	`/-lowering-/.f64`
3366×	`-lowering-.f32`
3366×	`-lowering-.f64`
2896×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	33	15
2	261	15
3	4246	15
0	9193	14

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 181

Calls

Call 1

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

Outputs
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(*.f64 x #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))) (neg.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x))))) #s(literal -1 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))) (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))))
(-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) y) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) y) #s(literal 1/2 binary64))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))) (neg.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) y) (exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1/2 binary64) y) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) y) (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) y) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x (/.f64 #s(literal -1 binary64) y)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) y) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) y) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) y) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x))) (neg.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x))))))
(fma.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x y) (+.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)))) (neg.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x))))))
(fma.f64 (exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(fma.f64 (exp.f64 (log.f64 (/.f64 x y))) (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(fma.f64 (exp.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64)))) (exp.f64 (log.f64 (/.f64 #s(literal -1 binary64) y))) #s(literal 1/2 binary64))
(fma.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (exp.f64 (log.f64 (/.f64 x y))) #s(literal 1/2 binary64))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) y))) #s(literal 1/2 binary64))
(neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) (+.f64 #s(literal -1/4 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x))))))
(neg.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
(neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)))))
(neg.f64 (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) #s(literal -1/4 binary64)))))
(/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x))))
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(/.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x))))) (.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))) (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x))))))) (neg.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))) (/.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x))))) #s(literal 1 binary64))) (+.f64 #s(literal -1/4 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) #s(literal 1 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (.f64 #s(literal 1/512 binary64) (.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (/.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)))))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (/.f64 (.f64 y (.f64 y y)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 #s(literal 1/64 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)))))) (+.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64)))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 #s(literal 1/64 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))))) (neg.f64 (+.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 x x) (*.f64 y y))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal -1/2 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)))))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
(*.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x))))))
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal -1/2 binary64))))
(.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x))))))
(*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 x y) (+.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x))) (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) (/.f64 y x)))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/64 binary64) (.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)) (.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)))))) (+.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 y x)) #s(literal 1/4 binary64)) (/.f64 y x))))
(exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))
(-.f64 (/.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))
(neg.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(/.f64 (*.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 y (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 y x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) y) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 y x)))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) y)
(/.f64 (exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x))) y)
(/.f64 (exp.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64)))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) y))))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (/.f64 (/.f64 y x) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) y))
(/.f64 (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) y))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1 binary64))
(pow.f64 (/.f64 y (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 y (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) y)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 y (*.f64 #s(literal 1/2 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x y) #s(literal 1 binary64)))
(*.f64 x (/.f64 #s(literal 1/2 binary64) y))
(.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) y)))
(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y))
(*.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) y))
(.f64 (.f64 x #s(literal -1/2 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(.f64 (/.f64 #s(literal 1 binary64) y) (.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) y) (exp.f64 (log.f64 (.f64 #s(literal 1/2 binary64) x))))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 y x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) y)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1/2 binary64) y))
(.f64 (/.f64 #s(literal -1 binary64) y) (.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) y))
(.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 #s(literal -1 binary64) y)))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(.f64 (.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) y))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) y))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) y))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) y))
(*.f64 (exp.f64 (log.f64 (/.f64 x y))) (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal -1/2 binary64)))) (exp.f64 (log.f64 (/.f64 #s(literal -1 binary64) y))))
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (exp.f64 (log.f64 (/.f64 x y))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) y))))

simplify20.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

132×	`-lowering-.f32`
132×	`-lowering-.f64`
72×	`accelerator-lowering-fma.f32`
72×	`accelerator-lowering-fma.f64`
66×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	300
1	47	300
2	79	300
3	114	300
4	121	300
5	169	300
6	200	300
7	229	300
8	229	300
9	255	300
10	260	300
11	260	300
0	260	282

Stop Event

1×	iter limit
1×	saturated

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

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

eval65.0ms (2.3%)

Compiler: Compiled 5382 to 2973 computations (44.8% saved)

prune43.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	343	2	345
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	343	5	348

Accuracy

100.0%

Counts

348 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
▶	48.9%	(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
✓	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
▶	48.9%	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
✓	51.9%	#s(literal 1/2 binary64)

Compiler

Compiled 33 to 25 computations (24.2% saved)

localize114.0ms (4%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 y x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
✓	accuracy	100.0%	(/.f64 y x)
✓	accuracy	99.2%	(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) y)
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
10×	`/-lowering-/.f32`
10×	`/-lowering-/.f64`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	10	19
2	14	19
3	15	19
0	15	19

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

91.0ms

256×

valid

Compiler

Compiled 25 to 13 computations (48% saved)

Precisions

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

ival-div: 8.0ms (74.1% of total)

ival-mult: 2.0ms (18.5% of total)

const: 1.0ms (9.3% of total)

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

series8.0ms (0.3%)

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	y	@	-inf	(/ y x)
0.0ms	y	@	0	(/ y x)
0.0ms	x	@	-inf	(/ y x)
0.0ms	x	@	0	(/ y x)
0.0ms	y	@	inf	(/ y x)

rewrite340.0ms (11.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1708×	`-lowering-.f32`
1708×	`-lowering-.f64`
1228×	`/-lowering-/.f32`
1228×	`/-lowering-/.f64`
1070×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	31	16
2	149	16
3	681	16
4	3624	16
0	8994	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 359

Calls

Call 1

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

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

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
8×	`/-lowering-/.f32`
8×	`/-lowering-/.f64`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	348
1	10	348
2	12	348
3	13	348
4	14	348
0	14	348

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

Calls

Call 1

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

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

eval79.0ms (2.8%)

Compiler: Compiled 4347 to 2450 computations (43.6% saved)

prune40.0ms (1.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	443	5	448

Accuracy

100.0%

Counts

448 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	48.9%	(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
✓	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	48.9%	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
✓	51.9%	#s(literal 1/2 binary64)

Compiler

Compiled 65 to 45 computations (30.8% saved)

regimes7.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	y
2.0ms	x
1.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes11.0ms (0.4%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	y
4.0ms	x

Results

Accuracy	Segments	Branch
77.8%	3	`x`
74.8%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
77.7%	3	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/2 binary64)

Outputs
#s(literal 1/2 binary64)

Calls

2 calls:

0.0ms	x
0.0ms	y

Results

Accuracy	Segments	Branch
51.9%	1	`y`
51.9%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch16.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
4.0ms	2376194725603404300.0	3497366295531601400.0
12.0ms	-377621864.54323757	-497644.23873679305

Results

10.0ms

176×

valid

Compiler

Compiled 146 to 119 computations (18.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (57.1% of total)

ival-div: 1.0ms (28.5% of total)

const: 0.0ms (0% of total)

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

bsearch16.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
5.0ms	2376194725603404300.0	3497366295531601400.0
10.0ms	-377621864.54323757	-497644.23873679305

Results

8.0ms

176×

valid

Compiler

Compiled 146 to 119 computations (18.5% saved)

Precisions

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

ival-add: 2.0ms (58.8% of total)

ival-div: 1.0ms (29.4% of total)

const: 0.0ms (0% of total)

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

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 48 to 34 computations (29.2% saved)

preprocess87.0ms (3%)

Compiler: Compiled 132 to 92 computations (30.3% saved)

Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

analyze12.0ms (0.4%)

sample667.0ms (23.3%)

preprocess94.0ms (3.3%)

explain58.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize72.0ms (2.5%)

series12.0ms (0.4%)

rewrite144.0ms (5%)

simplify289.0ms (10.1%)

eval34.0ms (1.2%)

prune13.0ms (0.5%)

localize91.0ms (3.2%)

series8.0ms (0.3%)

rewrite499.0ms (17.4%)

simplify20.0ms (0.7%)

eval65.0ms (2.3%)

prune43.0ms (1.5%)

localize114.0ms (4%)

series8.0ms (0.3%)

rewrite340.0ms (11.9%)

simplify13.0ms (0.4%)

eval79.0ms (2.8%)

prune40.0ms (1.4%)

regimes7.0ms (0.2%)

regimes11.0ms (0.4%)

regimes4.0ms (0.1%)

regimes1.0ms (0%)

bsearch16.0ms (0.6%)

bsearch16.0ms (0.6%)

soundness1.0ms (0%)

preprocess87.0ms (3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	19	300
1	47	300
2	79	300
3	114	300
4	121	300
5	169	300
6	200	300
7	229	300
8	229	300
9	255	300
10	260	300
11	260	300
0	260	282

Iter	Nodes	Cost
0	19	300
1	47	300
2	79	300
3	114	300
4	121	300
5	169	300
6	200	300
7	229	300
8	229	300
9	255	300
10	260	300
11	260	300
0	260	282

Iter	Nodes	Cost
0	19	300
1	47	300
2	79	300
3	114	300
4	121	300
5	169	300
6	200	300
7	229	300
8	229	300
9	255	300
10	260	300
11	260	300
0	260	282