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

analyze17.0ms (0.7%)

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 (52.7% of total)

ival-div: 1.0ms (26.4% of total)

const: 0.0ms (0% of total)

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

sample693.0ms (31.3%)

Results

520.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 240.0ms

ival-add: 151.0ms (63% of total)

ival-div: 78.0ms (32.5% of total)

const: 8.0ms (3.3% of total)

backward-pass: 3.0ms (1.3% of total)

Bogosity

preprocess75.0ms (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)

explain70.0ms (3.2%)

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

54.0ms

512×

valid

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-div: 16.0ms (54.6% of total)

ival-add: 12.0ms (40.9% 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)

simplify29.0ms (1.3%)

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))

localize30.0ms (1.4%)

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

19.0ms

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 (56% of total)

ival-div: 2.0ms (37.3% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.2%)

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))

rewrite72.0ms (3.2%)

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

simplify179.0ms (8.1%)

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	6905	222
0	8033	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 x y)))
(+ 1/2 (* 1/2 (/ x y)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(+ 1/2 (* 1/2 (/ x y)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* 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 x y)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* 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 x y)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* 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 x y)))
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 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 -1/2 binary64) (/.f64 x y)))
(+ 1/2 (* 1/2 (/ x y)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(+ 1/2 (* 1/2 (/ x y)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 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 -1/2 binary64) (/.f64 x y)))
(+ 1/2 (* 1/2 (/ x y)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(+ 1/2 (* 1/2 (/ x y)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 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))

eval33.0ms (1.5%)

Compiler: Compiled 1196 to 166 computations (86.1% saved)

prune9.0ms (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
▶	49.7%	(/.f64 x (+.f64 y y))
▶	100.0%	(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
▶	52.4%	#s(literal 1/2 binary64)

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify73.0ms (3.3%)

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 x y)
✓	cost-diff	(*.f64 #s(literal -1/2 binary64) (/.f64 x y))
✓	cost-diff	(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))

Rules

1112×	`fnmadd-define`
910×	`fmsub-define`
878×	`fnmsub-define`
836×	`fma-define`
792×	`fmm-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	19	30
2	40	29
3	73	29
4	121	29
5	181	29
6	271	29
7	353	29
8	460	29
9	624	29
10	716	29
11	978	29
12	1733	29
13	3282	29
14	3794	29
15	3867	29
16	3922	29
17	3930	29
0	3930	29

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize63.0ms (2.8%)

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 x y)
✓	accuracy	100.0%	(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) (/.f64 x y))

Results

48.0ms

256×

valid

Compiler

Compiled 33 to 10 computations (69.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-sub: 12.0ms (47.8% of total)

ival-div: 10.0ms (39.9% of total)

ival-mult: 2.0ms (8% of total)

ival-add: 1.0ms (4% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.4%)

Counts

5 → 108

Calls

Call 1

Inputs
#<alt (- 1/2 (* -1/2 (/ x y)))>
#<alt (* -1/2 (/ x y))>
#<alt (/ x y)>
#<alt (/ x (+ y 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 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 y) (* -1/2 x)) y)>
#<alt (/ (- (* 1/2 y) (* -1/2 x)) y)>
#<alt (/ (- (* 1/2 y) (* -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 (* -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 (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (* 1/2 (/ 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
3.0ms	y	@	-inf	(/ x y)
0.0ms	x	@	-inf	(/ x y)
0.0ms	x	@	inf	(- 1/2 (* -1/2 (/ x y)))
0.0ms	x	@	inf	(* -1/2 (/ x y))
0.0ms	y	@	0	(- 1/2 (* -1/2 (/ x y)))

rewrite82.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

198×	`/-lowering-/.f32`
198×	`/-lowering-/.f64`
194×	`-lowering-.f32`
194×	`-lowering-.f64`
76×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	56	23
0	422	23

Stop Event

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

Counts

5 → 81

Calls

Call 1

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

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

simplify148.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

2950×	`fma-define`
2630×	`fnmadd-define`
1620×	`sum3-define`
1196×	`fmsub-define`
1006×	`fnmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	492
1	64	474
2	127	474
3	317	474
4	511	474
5	790	474
6	1508	474
7	2856	474
8	4210	474
9	5605	474
10	7356	474
11	7441	474
12	7441	474
13	7445	474
0	7445	474

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

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

eval16.0ms (0.7%)

Compiler: Compiled 1615 to 220 computations (86.4% saved)

prune12.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	189	3	192

Accuracy

100.0%

Counts

192 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(/.f64 x (+.f64 y y))
✓	100.0%	(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x y)))
✓	52.4%	#s(literal 1/2 binary64)

Compiler

Compiled 41 to 25 computations (39% saved)

regimes6.0ms (0.3%)

Counts

4 → 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 x y)))
(/.f64 (+.f64 x y) (+.f64 y y))

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

regimes3.0ms (0.2%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
80.0%	3	`x`
76.7%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (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:

20.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
52.4%	1	`y`
52.4%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch11.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
4.0ms	2.570540101628655e-50	3.3247736621847546e-50
6.0ms	-8.039498808710765e+34	-4.887150158627437e+34

Results

6.0ms

112×

valid

Compiler

Compiled 98 to 72 computations (26.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (42.6% of total)

ival-add: 1.0ms (42.6% of total)

const: 0.0ms (0% of total)

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

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	24	23
2	36	23
3	46	23
4	54	23
5	59	23
6	61	23

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal -74000000000000001737174616075403264 binary64)) (/.f64 x (+.f64 y y)) (if (<=.f64 x #s(literal 710857968762761/26328072917139296674479506920917608079723773850137277813577744384 binary64)) #s(literal 1/2 binary64) (/.f64 x (+.f64 y y))))

#s(literal 1/2 binary64)

Outputs

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

(if (<=.f64 x #s(literal -74000000000000001737174616075403264 binary64)) (/.f64 x (+.f64 y y)) (if (<=.f64 x #s(literal 710857968762761/26328072917139296674479506920917608079723773850137277813577744384 binary64)) #s(literal 1/2 binary64) (/.f64 x (+.f64 y y))))

#s(literal 1/2 binary64)

soundness489.0ms (22.1%)

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	6905	222
0	8033	222

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 51 to 32 computations (37.3% saved)

preprocess59.0ms (2.7%)

Compiler: Compiled 94 to 52 computations (44.7% saved)

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

analyze17.0ms (0.7%)

sample693.0ms (31.3%)

preprocess75.0ms (3.4%)

explain70.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify29.0ms (1.3%)

localize30.0ms (1.4%)

series5.0ms (0.2%)

rewrite72.0ms (3.2%)

simplify179.0ms (8.1%)

eval33.0ms (1.5%)

prune9.0ms (0.4%)

simplify73.0ms (3.3%)

localize63.0ms (2.8%)

series8.0ms (0.4%)

rewrite82.0ms (3.7%)

simplify148.0ms (6.7%)

eval16.0ms (0.7%)

prune12.0ms (0.6%)

regimes6.0ms (0.3%)

regimes3.0ms (0.2%)

regimes22.0ms (1%)

bsearch11.0ms (0.5%)

simplify10.0ms (0.4%)

soundness489.0ms (22.1%)

preprocess59.0ms (2.7%)

end0.0ms (0%)

Profiling