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

analyze19.0ms (0.9%)

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: 3.0ms (76.8% of total)

ival-div: 1.0ms (25.6% of total)

const: 0.0ms (0% of total)

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

sample581.0ms (25.7%)

Results

407.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 196.0ms

ival-add: 116.0ms (59.2% of total)

ival-div: 69.0ms (35.2% of total)

const: 8.0ms (4.1% of total)

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

Bogosity

preprocess77.0ms (3.4%)

Algorithm

2×	egg-herbie

Rules

1700×	`fnmsub-define`
1686×	`fmsub-define`
1656×	`sum3-define`
1554×	`fmm-def`
914×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	48
1	44	42
2	112	42
3	349	42
4	1512	38
5	3788	37
6	6433	37
7	7694	36
0	5	7
1	8	7
2	11	7
3	13	7
0	13	7

Stop Event

1×	iter limit
1×	saturated
1×	node limit

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))
(fnmsub x (/ -1/2 y) -1/2)
(/ (+ (neg x) y) (+ y y))
(fnmsub x (/ 1/2 y) -1/2)
(/ (+ x (neg y)) (+ (neg y) (neg y)))
(fnmsub x (/ 1/2 y) -1/2)
(neg (/ (+ (neg x) y) (+ y y)))
(fnmsub x (/ -1/2 y) 1/2)
(neg (/ (+ x (neg y)) (+ (neg y) (neg y))))
(fnmsub x (/ -1/2 y) 1/2)
(/ (+ y x) (+ x x))
(fnmsub y (/ -1/2 x) -1/2)

explain79.0ms (3.5%)

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

53.0ms

512×

valid

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

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

ival-add: 6.0ms (59.1% of total)

ival-div: 4.0ms (39.4% 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)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 y y)
✓	cost-diff	(+.f64 x y)
✓	cost-diff	(/.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))

localize21.0ms (0.9%)

Localize:

Found 3 expressions of interest:

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

Results

15.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

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

ival-add: 4.0ms (65.7% of total)

ival-div: 2.0ms (32.8% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.3%)

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))

rewrite67.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	35	13
0	323	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 x y) (/.f64 #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 x) (.f64 y 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 x) (.f64 y 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 x) (*.f64 y 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 x y) (/.f64 #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 x) (.f64 y y))))
(/.f64 (-.f64 (.f64 x x) (.f64 y 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 x) (.f64 y 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 x) (*.f64 y 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))

simplify167.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

1732×	`-lowering-.f32`
1732×	`-lowering-.f64`
1516×	`times-frac`
1452×	`fmsub-define`
1444×	`fnmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	103	222
2	224	222
3	607	222
4	2820	222
5	6903	222
0	8026	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 #s(literal 1/2 binary64) (/.f64 y x)))
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(* 1/2 (/ x y))
(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(* 1/2 (/ x y))
(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(* 1/2 (/ x y))
(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(+ 1/2 (* 1/2 (/ x y)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
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))

eval11.0ms (0.5%)

Compiler: Compiled 1212 to 163 computations (86.6% saved)

prune10.0ms (0.4%)

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
▶	50.6%	(/.f64 x (+.f64 y y))
▶	99.9%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
▶	50.3%	#s(literal 1/2 binary64)

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

20×	`-lowering-.f32`
20×	`-lowering-.f64`
18×	`/-lowering-/.f32`
18×	`/-lowering-/.f64`
10×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	13	28
2	20	28
3	26	28
4	28	28
5	32	28
6	36	28
7	38	28
0	38	28

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize34.0ms (1.5%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x (+.f64 y y))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(/.f64 y x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
✓	accuracy	99.4%	(/.f64 #s(literal 1/2 binary64) (/.f64 y x))

Results

23.0ms

256×

valid

Compiler

Compiled 32 to 9 computations (71.9% saved)

Precisions

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

ival-div: 7.0ms (70.4% of total)

ival-add: 2.0ms (20.1% of total)

const: 0.0ms (0% of total)

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

series7.0ms (0.3%)

Counts

5 → 108

Calls

Call 1

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

Outputs
#<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>
#<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 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)>
#<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 (* 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

27 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(/ y x)
0.0ms	x	@	inf	(/ 1/2 (/ y x))
0.0ms	x	@	inf	(+ 1/2 (/ 1/2 (/ y x)))
0.0ms	y	@	0	(+ 1/2 (/ 1/2 (/ y x)))
0.0ms	x	@	0	(+ 1/2 (/ 1/2 (/ y x)))

rewrite64.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

246×	`/-lowering-/.f32`
246×	`/-lowering-/.f64`
208×	`-lowering-.f32`
208×	`-lowering-.f64`
72×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	58	22
0	491	22

Stop Event

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

Counts

5 → 110

Calls

Call 1

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

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

simplify55.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

270×	`fma-define`
148×	`-lowering-.f32`
148×	`-lowering-.f64`
96×	`fma-lowering-fma.f32`
96×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	22	492
1	56	492
2	101	492
3	155	492
4	164	492
5	221	492
6	293	474
7	358	474
8	375	474
9	409	474
10	420	474
11	420	474
0	420	474

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

Inputs
(* 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
(+ 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 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)
(* 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))
(* 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 (/ 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
#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 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)
(* 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)
(* 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))

eval23.0ms (1%)

Compiler: Compiled 1871 to 232 computations (87.6% saved)

prune17.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	218	3	221

Accuracy

100.0%

Counts

221 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.6%	(/.f64 x (+.f64 y y))
▶	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) y))
✓	50.3%	#s(literal 1/2 binary64)

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	10	19
2	13	19
0	13	19

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize26.0ms (1.1%)

Localize:

Found 3 expressions of interest:

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

Results

17.0ms

256×

valid

Compiler

Compiled 22 to 8 computations (63.6% saved)

Precisions

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

ival-div: 4.0ms (67.9% of total)

ival-add: 1.0ms (17% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

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

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 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))>
#<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

15 calls:

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

rewrite247.0ms (10.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2526×	`-lowering-.f32`
2526×	`-lowering-.f64`
1964×	`/-lowering-/.f32`
1964×	`/-lowering-/.f64`
1528×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	41	15
2	341	14
3	4196	14
0	8088	14

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 141

Calls

Call 1

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

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

simplify20.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

270×	`fma-define`
132×	`-lowering-.f32`
132×	`-lowering-.f64`
96×	`fma-lowering-fma.f32`
96×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	300
1	52	282
2	97	282
3	151	282
4	160	282
5	214	282
6	286	282
7	349	282
8	365	282
9	391	282
10	402	282
11	402	282
0	402	282

Stop Event

1×	iter limit
1×	saturated

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

eval23.0ms (1%)

Compiler: Compiled 3091 to 417 computations (86.5% saved)

prune20.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	201	3	204

Accuracy

100.0%

Counts

204 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.6%	(/.f64 x (+.f64 y y))
✓	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) y))
✓	50.3%	#s(literal 1/2 binary64)

Compiler

Compiled 48 to 28 computations (41.7% saved)

regimes7.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	y
2.0ms	x
2.0ms	(/.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)

regimes6.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.2%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
78.0%	3	`x`
78.5%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

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:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
50.3%	1	`x`
50.3%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch22.0ms (1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	4.5307208858365244e+27	1.327177283712887e+32
11.0ms	-4.3633285135098283e+24	-1.403131263714009e+23

Results

13.0ms

240×

valid

Compiler

Compiled 194 to 144 computations (25.8% saved)

Precisions

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

ival-add: 5.0ms (71.2% of total)

ival-div: 2.0ms (28.5% of total)

const: 0.0ms (0% of total)

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

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	30
1	23	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) y))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(if (<=.f64 y #s(literal -3999999999999999932891136 binary64)) #s(literal 1/2 binary64) (if (<=.f64 y #s(literal 110000000000000000498458871988224 binary64)) (/.f64 x (+.f64 y y)) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)

Outputs
(+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) y))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 y x)))
(if (<=.f64 y #s(literal -3999999999999999932891136 binary64)) #s(literal 1/2 binary64) (if (<=.f64 y #s(literal 110000000000000000498458871988224 binary64)) (/.f64 x (+.f64 y y)) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)

soundness581.0ms (25.7%)

Rules

1732×	`-lowering-.f32`
1732×	`-lowering-.f64`
1516×	`times-frac`
1452×	`fmsub-define`
1444×	`fnmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	103	222
2	224	222
3	607	222
4	2820	222
5	6903	222
0	8026	222
0	8	23
1	58	22
0	491	22

Stop Event

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

Compiler

Compiled 72 to 47 computations (34.7% saved)

preprocess37.0ms (1.6%)

Compiler: Compiled 100 to 58 computations (42% saved)

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

analyze19.0ms (0.9%)

sample581.0ms (25.7%)

preprocess77.0ms (3.4%)

explain79.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.2%)

localize21.0ms (0.9%)

series6.0ms (0.3%)

rewrite67.0ms (3%)

simplify167.0ms (7.4%)

eval11.0ms (0.5%)

prune10.0ms (0.4%)

simplify6.0ms (0.3%)

localize34.0ms (1.5%)

series7.0ms (0.3%)

rewrite64.0ms (2.8%)

simplify55.0ms (2.4%)

eval23.0ms (1%)

prune17.0ms (0.7%)

simplify5.0ms (0.2%)

localize26.0ms (1.1%)

series2.0ms (0.1%)

rewrite247.0ms (10.9%)

simplify20.0ms (0.9%)

eval23.0ms (1%)

prune20.0ms (0.9%)

regimes7.0ms (0.3%)

regimes6.0ms (0.3%)

regimes3.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch22.0ms (1%)

simplify10.0ms (0.4%)

soundness581.0ms (25.7%)

preprocess37.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	22	492
1	56	492
2	101	492
3	155	492
4	164	492
5	221	492
6	293	474
7	358	474
8	375	474
9	409	474
10	420	474
11	420	474
0	420	474

Iter	Nodes	Cost
0	19	300
1	52	282
2	97	282
3	151	282
4	160	282
5	214	282
6	286	282
7	349	282
8	365	282
9	391	282
10	402	282
11	402	282
0	402	282

Iter	Nodes	Cost
0	22	492
1	56	492
2	101	492
3	155	492
4	164	492
5	221	492
6	293	474
7	358	474
8	375	474
9	409	474
10	420	474
11	420	474
0	420	474

Iter	Nodes	Cost
0	19	300
1	52	282
2	97	282
3	151	282
4	160	282
5	214	282
6	286	282
7	349	282
8	365	282
9	391	282
10	402	282
11	402	282
0	402	282

Iter	Nodes	Cost
0	22	492
1	56	492
2	101	492
3	155	492
4	164	492
5	221	492
6	293	474
7	358	474
8	375	474
9	409	474
10	420	474
11	420	474
0	420	474

Iter	Nodes	Cost
0	19	300
1	52	282
2	97	282
3	151	282
4	160	282
5	214	282
6	286	282
7	349	282
8	365	282
9	391	282
10	402	282
11	402	282
0	402	282