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

analyze119.0ms (3.7%)

Memory

-19.1MiB live, 19.8MiB allocated

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 9 to 7 computations (22.2% saved)

sample710.0ms (21.8%)

Memory

68.6MiB live, 993.2MiB allocated

Samples

476.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 293.0ms

ival-div: 192.0ms (65.5% of total)

ival-add: 92.0ms (31.4% of total)

ival-true: 6.0ms (2% of total)

ival-assert: 3.0ms (1% of total)

Bogosity

preprocess147.0ms (4.5%)

Memory

-47.0MiB live, 66.5MiB allocated

Algorithm

1×	egg-herbie

Rules

856×	`times-frac`
820×	`distribute-lft-in`
772×	`distribute-rgt-in`
636×	`div-sub`
544×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	42	35
2	106	35
3	310	35
4	1262	35
5	2388	35
6	3252	35
7	3801	35
8	4253	35
9	4303	35
10	4335	35
11	4411	35
12	4595	35
0	5	7
0	8	7
1	11	7
2	14	7
3	16	7
0	16	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))

explain115.0ms (3.5%)

Memory

-7.2MiB live, 110.4MiB allocated

FPErrors

Click to see full error table

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

28.0ms

512×

valid

Compiler

Compiled 52 to 24 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-div: 11.0ms (66.5% of total)

ival-add: 5.0ms (30.2% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

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)

simplify6.0ms (0.2%)

Memory

5.1MiB live, 5.1MiB allocated

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×	`lower-/.f32`
8×	`lower-/.f64`
6×	`lower-+.f32`
4×	`lift-+.f64`
4×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	11	15
2	14	15
3	16	15
0	16	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(+.f64 x y)
x
y
(+.f64 y y)

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(+.f64 x y)
x
y
(+.f64 y y)

localize18.0ms (0.5%)

Memory

-7.8MiB live, 30.7MiB allocated

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))

Samples

11.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-div: 2.0ms (39% of total)

ival-add: 2.0ms (39% of total)

ival-true: 1.0ms (19.5% of total)

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

series5.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (/.f64 (+.f64 x y) (+.f64 y y))>
#<alt (+.f64 x y)>
#<alt (+.f64 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))

rewrite54.0ms (1.6%)

Memory

21.8MiB live, 97.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

150×	`lower-/.f32`
148×	`lower-/.f64`
128×	`lower-*.f64`
128×	`lower-*.f32`
76×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	38	13
0	305	13

Stop Event

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

Counts

3 → 61

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(+.f64 x y)
(+.f64 y y)

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

simplify181.0ms (5.5%)

Memory

-8.7MiB live, 308.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 672×	`lower-*.f64`
2 672×	`lower-*.f32`
1 714×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

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

eval15.0ms (0.5%)

Memory: -26.6MiB live, 32.9MiB allocated
Compiler: Compiled 1 129 to 160 computations (85.8% saved)

prune10.0ms (0.3%)

Memory

-6.2MiB live, 32.2MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Accuracy

100.0%

Counts

116 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
▶	46.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
▶	4.4%	(*.f64 (+.f64 y y) (+.f64 x y))
▶	54.9%	#s(literal 1/2 binary64)

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify9.0ms (0.3%)

Memory

23.3MiB live, 23.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

114×	`lower-fma.f32`
112×	`lower-fma.f64`
84×	`lower-+.f32`
80×	`lower-+.f64`
78×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
0	18	39
1	31	39
2	57	39
3	99	39
4	139	39
5	173	39
0	173	39

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize42.0ms (1.3%)

Memory

-21.5MiB live, 92.5MiB allocated

Localize:

Found 7 expressions of interest:

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

Samples

23.0ms

256×

valid

Compiler

Compiled 42 to 13 computations (69% saved)

Precisions

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

ival-add: 4.0ms (34.3% of total)

ival-mult: 4.0ms (34.3% of total)

ival-div: 3.0ms (25.7% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.3%)

Memory

28.6MiB live, 28.6MiB allocated

Counts

7 → 144

Calls

Call 1

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

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

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ (* 1/2 x) y)
1.0ms	x	@	inf	(* (+ y y) (+ x y))
0.0ms	x	@	0	(/ (* 1/2 x) y)
0.0ms	y	@	0	(/ (* 1/2 x) y)
0.0ms	y	@	inf	(/ (* 1/2 x) y)

rewrite81.0ms (2.5%)

Memory

7.0MiB live, 156.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

346×	`lower-*.f32`
342×	`lower-*.f64`
290×	`lower-/.f32`
286×	`lower-/.f64`
240×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
0	18	30
1	77	30
0	603	30

Stop Event

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

Counts

7 → 130

Calls

Call 1

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

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

simplify204.0ms (6.3%)

Memory

-13.1MiB live, 350.9MiB allocated

Algorithm

1×	egg-herbie

Rules

5 472×	`lower-fma.f64`
5 472×	`lower-fma.f32`
3 286×	`lower-*.f64`
3 286×	`lower-*.f32`
1 314×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	624
1	176	624
2	395	624
3	1173	624
4	2736	624
5	5983	624
0	8140	606

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 138

Calls

Call 1

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

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

eval28.0ms (0.9%)

Memory: -14.1MiB live, 61.4MiB allocated
Compiler: Compiled 2 522 to 308 computations (87.8% saved)

prune19.0ms (0.6%)

Memory

3.8MiB live, 48.0MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	265	7	272

Accuracy

100.0%

Counts

272 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.0%	(fma.f64 (+.f64 y y) x (+.f64 y y))
✓	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
✓	46.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	4.4%	(*.f64 (+.f64 y y) (+.f64 x y))
▶	3.5%	(.f64 #s(literal 2 binary64) (.f64 y y))
▶	3.9%	(.f64 #s(literal 2 binary64) (.f64 x y))
✓	54.9%	#s(literal 1/2 binary64)

Compiler

Compiled 51 to 32 computations (37.3% saved)

simplify11.0ms (0.4%)

Memory

27.3MiB live, 27.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	64	(fma.f64 (+.f64 y y) x (+.f64 y y))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	128	(.f64 #s(literal 2 binary64) (.f64 y y))
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	128	(.f64 #s(literal 2 binary64) (.f64 x y))

Rules

210×	`lower-fma.f32`
208×	`lower-fma.f64`
126×	`lower-*.f32`
118×	`lower-*.f64`
76×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
0	16	34
1	27	33
2	41	33
3	71	33
4	112	33
5	134	33
6	189	33
7	189	33
0	189	32

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize31.0ms (0.9%)

Memory

-9.8MiB live, 68.1MiB allocated

Localize:

Found 6 expressions of interest:

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

Samples

20.0ms

256×

valid

Compiler

Compiled 37 to 12 computations (67.6% saved)

Precisions

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

ival-mult: 8.0ms (72.8% of total)

ival-add: 2.0ms (18.2% 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

8.8MiB live, 8.8MiB allocated

Counts

6 → 108

Calls

Call 1

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

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

rewrite61.0ms (1.9%)

Memory

-22.5MiB live, 97.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

382×	`lower-fma.f32`
380×	`lower-fma.f64`
184×	`lower-*.f32`
176×	`lower-*.f64`
112×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
0	16	27
1	48	26
0	382	26

Stop Event

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

Counts

6 → 103

Calls

Call 1

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

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

simplify250.0ms (7.7%)

Memory

3.0MiB live, 236.6MiB allocated

Algorithm

1×	egg-herbie

Rules

5 328×	`lower-fma.f64`
5 328×	`lower-fma.f32`
3 150×	`lower-*.f64`
3 150×	`lower-*.f32`
1 068×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	484
1	79	484
2	193	484
3	397	484
4	759	484
5	1661	484
6	3759	484
7	6033	484
8	7793	484
0	8018	463

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

eval48.0ms (1.5%)

Memory: -14.1MiB live, 40.1MiB allocated
Compiler: Compiled 2 554 to 252 computations (90.1% saved)

prune19.0ms (0.6%)

Memory

-1.9MiB live, 36.9MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	251	4	255
Fresh	0	0	0
Picked	3	0	3
Done	0	4	4
Total	254	8	262

Accuracy

100.0%

Counts

262 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
✓	46.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	4.4%	(*.f64 (+.f64 y y) (+.f64 x y))
▶	3.5%	(*.f64 (+.f64 y y) y)
▶	3.9%	(*.f64 (+.f64 y y) x)
▶	4.0%	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 y y))
▶	3.2%	(*.f64 #s(literal 2 binary64) y)
✓	54.9%	#s(literal 1/2 binary64)

Compiler

Compiled 55 to 36 computations (34.5% saved)

simplify12.0ms (0.4%)

Memory

13.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(*.f64 (+.f64 y y) y)
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(*.f64 (+.f64 y y) x)
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 y y))
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) y)

Rules

210×	`lower-fma.f64`
210×	`lower-fma.f32`
126×	`lower-*.f32`
118×	`lower-*.f64`
76×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	40
0	16	40
1	27	40
2	62	40
3	124	40
4	193	40
5	227	40
6	227	40
0	227	39

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize31.0ms (0.9%)

Memory

8.6MiB live, 47.5MiB allocated

Localize:

Found 8 expressions of interest:

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

Samples

18.0ms

256×

valid

Compiler

Compiled 42 to 12 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 6.0ms (67.8% of total)

ival-add: 2.0ms (22.6% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

6 → 96

Calls

Call 1

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

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

Calls

24 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	(* (+ x 1) (+ y y))
1.0ms	y	@	0	(* (+ x 1) (+ y y))
0.0ms	x	@	-inf	(* (+ x 1) (+ y y))
0.0ms	x	@	0	(* (+ x 1) (+ y y))
0.0ms	y	@	-inf	(* 2 y)

rewrite72.0ms (2.2%)

Memory

-33.5MiB live, 50.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

194×	`lower-*.f32`
186×	`lower-*.f64`
130×	`lower-/.f64`
130×	`lower-/.f32`
100×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
0	16	24
1	48	24
0	341	24

Stop Event

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

Counts

6 → 135

Calls

Call 1

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

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

simplify234.0ms (7.2%)

Memory

31.2MiB live, 228.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4 076×	`lower-fma.f64`
4 076×	`lower-fma.f32`
3 192×	`lower-*.f64`
3 192×	`lower-*.f32`
1 734×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	442
1	84	442
2	196	442
3	563	442
4	1613	442
5	4165	442
6	6623	442
0	8020	421

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 94

Calls

Call 1

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

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

eval29.0ms (0.9%)

Memory: 2.9MiB live, 41.6MiB allocated
Compiler: Compiled 2 499 to 250 computations (90% saved)

prune45.0ms (1.4%)

Memory

3.8MiB live, 41.0MiB allocated

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	290	3	293
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	291	10	301

Accuracy

100.0%

Counts

301 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
✓	46.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
	3.5%	(/.f64 #s(literal 1 binary64) (+.f64 y y))
	3.2%	(+.f64 y y)
✓	4.4%	(*.f64 (+.f64 y y) (+.f64 x y))
✓	3.5%	(*.f64 (+.f64 y y) y)
✓	3.9%	(*.f64 (+.f64 y y) x)
✓	4.0%	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 y y))
	2.6%	(.f64 (.f64 (+.f64 y y) y) y)
✓	54.9%	#s(literal 1/2 binary64)

Compiler

Compiled 152 to 70 computations (53.9% saved)

regimes31.0ms (1%)

Memory

-28.6MiB live, 16.2MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

3 calls:

21.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
5.0ms	y
5.0ms	x

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)

regimes14.0ms (0.4%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))

Calls

3 calls:

5.0ms	x
5.0ms	y
4.0ms	(/.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)

regimes48.0ms (1.5%)

Memory

-18.8MiB live, 20.1MiB allocated

Counts

13 → 3

Calls

Call 1

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

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

Calls

3 calls:

39.0ms	x
4.0ms	y
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
79.5%	3	`x`
75.2%	3	`y`
98.3%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes12.0ms (0.4%)

Memory

26.5MiB live, 26.5MiB allocated

Accuracy

Total -34.2b remaining (-118.5%)

Threshold costs -34.2b (-118.5%)

Counts

12 → 1

Calls

Call 1

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

Outputs
#s(literal 1/2 binary64)

Calls

3 calls:

4.0ms	x
4.0ms	y
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
54.9%	1	`y`
54.9%	1	`x`
54.9%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5000018882334968	9217636.352173796
0.0ms	-5.001486332934084	0.4990986530689326

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify14.0ms (0.4%)

Memory

-23.2MiB live, 16.0MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	45
1	21	45

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
(/.f64 (+.f64 x y) (+.f64 y y))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -5 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)))
#s(literal 1/2 binary64)

Outputs
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
(/.f64 (+.f64 x y) (+.f64 y y))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -5 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)))
#s(literal 1/2 binary64)

soundness424.0ms (13%)

Memory

-14.7MiB live, 158.4MiB allocated

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 672×	`lower-*.f64`
2 672×	`lower-*.f32`
1 714×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 68 to 32 computations (52.9% saved)

preprocess90.0ms (2.7%)

Memory: 7.6MiB live, 89.0MiB allocated
Compiler: Compiled 130 to 54 computations (58.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze119.0ms (3.7%)

sample710.0ms (21.8%)

preprocess147.0ms (4.5%)

explain115.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.2%)

localize18.0ms (0.5%)

series5.0ms (0.1%)

rewrite54.0ms (1.6%)

simplify181.0ms (5.5%)

eval15.0ms (0.5%)

prune10.0ms (0.3%)

simplify9.0ms (0.3%)

localize42.0ms (1.3%)

series9.0ms (0.3%)

rewrite81.0ms (2.5%)

simplify204.0ms (6.3%)

eval28.0ms (0.9%)

prune19.0ms (0.6%)

simplify11.0ms (0.4%)

localize31.0ms (0.9%)

series4.0ms (0.1%)

rewrite61.0ms (1.9%)

simplify250.0ms (7.7%)

eval48.0ms (1.5%)

prune19.0ms (0.6%)

simplify12.0ms (0.4%)

localize31.0ms (0.9%)

series6.0ms (0.2%)

rewrite72.0ms (2.2%)

simplify234.0ms (7.2%)

eval29.0ms (0.9%)

prune45.0ms (1.4%)

regimes31.0ms (1%)

regimes14.0ms (0.4%)

regimes48.0ms (1.5%)

regimes12.0ms (0.4%)

bsearch0.0ms (0%)

simplify14.0ms (0.4%)

soundness424.0ms (13%)

preprocess90.0ms (2.7%)

end0.0ms (0%)

Profiling