Metrics for Numeric.Interval.Internal:bisect from intervals-0.7.1, A

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.1s (21.9%)

Memory

27.6MiB live, 881.3MiB allocated

Samples

649.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 492.0ms

ival-add: 298.0ms (60.5% of total)

ival-div: 117.0ms (23.8% of total)

ival-sub: 65.0ms (13.2% of total)

ival-true: 5.0ms (1% of total)

exact: 4.0ms (0.8% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

preprocess594.0ms (11.8%)

Memory

-3.9MiB live, 676.1MiB allocated

Algorithm

1×	egg-herbie

Rules

19 132×	`lower-fma.f64`
19 132×	`lower-fma.f32`
3 330×	`associate-+r+`
2 008×	`associate-+r-`
1 940×	`lower-+.f32`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	44	35
2	137	35
3	380	29
4	644	25
5	942	25
6	2325	25
7	3100	25
8	3417	25
9	3516	25
10	3581	25
11	3584	25
12	3600	25
13	3609	25
14	3609	25
15	3609	25
16	3609	25
0	6	7
0	9	7
1	15	7
2	26	7
3	46	7
4	87	7
5	150	7
6	326	7
7	532	6
8	1267	5
9	1983	5
10	2394	5
11	2412	5
12	2426	5
13	2426	5
14	3366	5
15	3909	5
16	4065	5
17	4124	5
18	4532	5
19	6372	5
20	7036	5
21	7968	5
0	8322	5

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

explain63.0ms (1.3%)

Memory

0.4MiB live, 157.7MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))`
-	-	`(-.f64 y x)`
-	-	`y`
-	-	`#s(literal 2 binary64)`
-	-	`(/.f64 (-.f64 y x) #s(literal 2 binary64))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

25.0ms

512×

valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sub: 6.0ms (47.4% of total)

ival-div: 3.0ms (23.7% of total)

ival-add: 2.0ms (15.8% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify507.0ms (10.1%)

Memory

3.6MiB live, 566.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 y x)
✓	cost-diff	192	(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
✓	cost-diff	384	(/.f64 (-.f64 y x) #s(literal 2 binary64))

Rules

19 132×	`lower-fma.f64`
19 132×	`lower-fma.f32`
1 940×	`lower-+.f32`
1 938×	`lower-+.f64`
1 884×	`lower--.f32`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	15	18
2	26	18
3	46	18
4	87	18
5	150	18
6	326	18
7	532	17
8	1267	16
9	1983	16
10	2394	16
11	2412	16
12	2426	16
13	2426	16
14	3366	16
15	3909	16
16	4065	16
17	4124	16
18	4532	16
19	6372	16
20	7036	16
21	7968	16
0	8322	16

Stop Event

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

Calls

Call 1

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

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

localize20.0ms (0.4%)

Memory

11.1MiB live, 48.7MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

13.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-div: 2.0ms (42.6% of total)

ival-sub: 1.0ms (21.3% of total)

ival-add: 1.0ms (21.3% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs
#<alt (/.f64 (-.f64 y x) #s(literal 2 binary64))>
#<alt (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))>
#<alt (-.f64 y x)>

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

Calls

18 calls:

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

simplify299.0ms (6%)

Memory

-55.1MiB live, 366.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12 600×	`lower-fma.f64`
12 600×	`lower-fma.f32`
1 834×	`lower-*.f64`
1 834×	`lower-*.f32`
1 602×	`lower--.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	315
1	177	315
2	498	279
3	1491	279
4	5234	279
5	7541	279
0	8288	279

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 69

Calls

Call 1

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

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

rewrite384.0ms (7.6%)

Memory

23.5MiB live, 333.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 080×	`lower-fma.f64`
4 080×	`lower-fma.f32`
3 840×	`lower-*.f64`
3 840×	`lower-*.f32`
2 598×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	48	15
2	400	15
3	5082	15
0	8211	14

Stop Event

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

Counts

3 → 344

Calls

Call 1

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

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

eval63.0ms (1.3%)

Memory: -6.7MiB live, 119.5MiB allocated
Compiler: Compiled 8 747 to 1 085 computations (87.6% saved)

prune44.0ms (0.9%)

Memory

-4.1MiB live, 112.9MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	410	3	413
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	411	3	414

Accuracy

100.0%

Counts

414 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.5%	#s(approx (+ x (/ (- y x) 2)) (*.f64 x #s(literal 1/2 binary64)))
▶	100.0%	#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))
▶	48.2%	#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y))

Status

Accuracy

Program

▶

53.5%

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

▶

100.0%

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

▶

48.2%

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

Compiler

Compiled 20 to 13 computations (35% saved)

simplify521.0ms (10.4%)

Memory

12.2MiB live, 533.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

18 004×	`lower-fma.f64`
18 004×	`lower-fma.f32`
2 208×	`lower--.f64`
2 208×	`lower--.f32`
1 676×	`lower-*.f32`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	14	56
0	18	58
1	31	58
2	43	58
3	63	58
4	104	58
5	173	58
6	371	58
7	625	50
8	1619	50
9	2293	50
10	2670	50
11	2686	50
12	2698	50
13	2698	50
14	3653	50
15	4208	50
16	4364	50
17	4422	50
18	4830	50
19	6669	50
20	7333	50
0	8031	50

Stop Event

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

Calls

Call 1

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

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

localize138.0ms (2.8%)

Memory

-15.4MiB live, 62.2MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	53.5%	#s(approx (+ x (/ (- y x) 2)) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))
✓	accuracy	100.0%	#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) y)
✓	accuracy	48.2%	#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y))

Samples

19.0ms

256×

valid

Compiler

Compiled 44 to 13 computations (70.5% saved)

Precisions

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

ival-mult: 4.0ms (40.2% of total)

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

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

ival-sub: 1.0ms (10% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

7 → 144

Calls

Call 1

Inputs
#<alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y))>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))>
#<alt (*.f64 #s(literal 1/2 binary64) (+.f64 x y))>
#<alt (+.f64 x y)>
#<alt #s(approx (+ x (/ (- y x) 2)) (*.f64 x #s(literal 1/2 binary64)))>
#<alt (*.f64 x #s(literal 1/2 binary64))>

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

36 calls:

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

simplify282.0ms (5.6%)

Memory

25.8MiB live, 492.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 724×	`lower-fma.f64`
14 724×	`lower-fma.f32`
2 174×	`lower-*.f64`
2 174×	`lower-*.f32`
1 654×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	564
1	153	564
2	370	564
3	1193	564
4	4200	564
5	6780	564
0	8063	564

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 138

Calls

Call 1

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

rewrite294.0ms (5.9%)

Memory

-1.1MiB live, 439.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 656×	`lower-fma.f64`
4 656×	`lower-fma.f32`
3 888×	`lower-*.f32`
3 882×	`lower-*.f64`
3 454×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
0	18	49
1	71	49
2	532	49
3	6745	49
0	8317	46

Stop Event

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

Counts

7 → 159

Calls

Call 1

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

Outputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))
(neg.f64 (/.f64 y #s(literal -2 binary64)))
(/.f64 y #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) y)))
(/.f64 (neg.f64 y) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 y)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) y) #s(literal -1 binary64))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(.f64 #s(literal 1 binary64) (.f64 y #s(literal 1/2 binary64)))
(*.f64 (neg.f64 y) #s(literal -1/2 binary64))
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))
(+.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (-.f64 y x) #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 (-.f64 y x) #s(literal -1/2 binary64))))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 y #s(literal 1/2 binary64)))
(fma.f64 y #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 y #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) y (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (*.f64 y #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)) (.f64 y #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 y) #s(literal -1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (-.f64 y x) #s(literal 1/2 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 y x) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (-.f64 y x) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 x y) (-.f64 x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (.f64 y (-.f64 y x))) (.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 x x) (.f64 y (*.f64 y y))))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (-.f64 y x) #s(literal 1/2 binary64)) (.f64 (*.f64 x x) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (fma.f64 (.f64 y y) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 y (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
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eval32.0ms (0.6%)

Memory: -1.8MiB live, 73.2MiB allocated
Compiler: Compiled 3 823 to 443 computations (88.4% saved)

prune24.0ms (0.5%)

Memory

15.4MiB live, 56.3MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	297	3	300

Accuracy

100.0%

Counts

300 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

53.5%

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

✓

100.0%

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

✓

48.2%

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

Compiler

Compiled 43 to 24 computations (44.2% saved)

regimes8.0ms (0.2%)

Memory

-20.8MiB live, 17.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
2.0ms	(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
2.0ms	y

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
2.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
84.0%	2	`x`
84.5%	2	`y`
98.5%	2	`(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms	(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
48.2%	1	`x`
48.2%	1	`y`
48.2%	1	`(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.480839360780554e-268	2.1796577051208817e-273

Compiler

Compiled 12 to 11 computations (8.3% saved)

simplify8.0ms (0.2%)

Memory

-22.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
8×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	56
1	27	56
2	32	56
3	34	56
4	35	56

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #s(literal -7435084542388915/18587711355972288284975781226873757001640752520742430738197148241449258214505054669314603931201954382372484047377412163130682315569311321347385382263779932822287135505593248424283580122928721710877989947279392965075846858835973501101963736754358226037650563818176798910297066860183552 binary64)) #s(approx (+ x (/ (- y x) 2)) (*.f64 x #s(literal 1/2 binary64))) #s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y)))

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

Outputs
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))
(if (<=.f64 (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #s(literal -7435084542388915/18587711355972288284975781226873757001640752520742430738197148241449258214505054669314603931201954382372484047377412163130682315569311321347385382263779932822287135505593248424283580122928721710877989947279392965075846858835973501101963736754358226037650563818176798910297066860183552 binary64)) #s(approx (+ x (/ (- y x) 2)) (.f64 x #s(literal 1/2 binary64))) #s(approx (+ x (/ (- y x) 2)) (.f64 #s(literal 1/2 binary64) y)))
(if (<=.f64 (+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64))) #s(literal -7435084542388915/18587711355972288284975781226873757001640752520742430738197148241449258214505054669314603931201954382372484047377412163130682315569311321347385382263779932822287135505593248424283580122928721710877989947279392965075846858835973501101963736754358226037650563818176798910297066860183552 binary64)) #s(approx (+ x (/ (- y x) 2)) (.f64 x #s(literal 1/2 binary64))) #s(approx (+ x (/ (- y x) 2)) (.f64 y #s(literal 1/2 binary64))))
#s(approx (+ x (/ (- y x) 2)) (*.f64 #s(literal 1/2 binary64) y))
#s(approx (+ x (/ (- y x) 2)) (*.f64 y #s(literal 1/2 binary64)))

soundness568.0ms (11.3%)

Memory

-10.5MiB live, 166.4MiB allocated

Rules

12 600×	`lower-fma.f64`
12 600×	`lower-fma.f32`
1 834×	`lower-*.f64`
1 834×	`lower-*.f32`
1 602×	`lower--.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	315
1	177	315
2	498	279
3	1491	279
4	5234	279
5	7541	279
0	8288	279

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 47 to 28 computations (40.4% saved)

preprocess55.0ms (1.1%)

Memory: -3.0MiB live, 112.6MiB allocated
Remove: (sort x y)
Compiler: Compiled 124 to 70 computations (43.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.1s (21.9%)

preprocess594.0ms (11.8%)

explain63.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify507.0ms (10.1%)

localize20.0ms (0.4%)

series3.0ms (0.1%)

simplify299.0ms (6%)

rewrite384.0ms (7.6%)

eval63.0ms (1.3%)

prune44.0ms (0.9%)

simplify521.0ms (10.4%)

localize138.0ms (2.8%)

series4.0ms (0.1%)

simplify282.0ms (5.6%)

rewrite294.0ms (5.9%)

eval32.0ms (0.6%)

prune24.0ms (0.5%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify8.0ms (0.2%)

soundness568.0ms (11.3%)

preprocess55.0ms (1.1%)

end0.0ms (0%)

Profiling