Metrics for Linear.Projection:inversePerspective from linear-1.19.1.3, B

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze19.0ms (0.4%)

Memory

14.5MiB live, 14.5MiB 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
25%	25%	74.9%	0.1%	0%	0%	0%	3
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	4
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	5
65.6%	65.6%	34.3%	0.1%	0%	0%	0%	6
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	7
82%	82%	18%	0.1%	0%	0%	0%	8
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	9
90.8%	90.7%	9.2%	0.1%	0%	0%	0%	10
93.8%	93.8%	6.1%	0.1%	0%	0%	0%	11
95.4%	95.3%	4.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample932.0ms (17.6%)

Memory

-11.1MiB live, 1 063.7MiB allocated

Samples

660.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 395.0ms

ival-mult: 228.0ms (57.7% of total)

ival-div: 83.0ms (21% of total)

ival-sub: 71.0ms (18% of total)

ival-true: 5.0ms (1.3% of total)

exact: 5.0ms (1.3% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain102.0ms (1.9%)

Memory

17.5MiB live, 172.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
66	-	3	(7.634998616309228e-215 -5.680015110357973e-97)	`(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`
1	-	0	-	`(.f64 (.f64 x #s(literal 2 binary64)) y)`
0	-	0	-	`(*.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`y`
0	-	0	-	`(-.f64 x y)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`	n/o	32	0
↳	`(*.f64 x #s(literal 2 binary64))`	overflow	1
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	32
`/.f64`	`(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`	n/u	31	0
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	underflow	31
`*.f64`	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	64	3
-	0	189

Precision

1.0

Recall

0.9552238805970149

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	64	0	3
-	0	0	189

Precision?

1.0

Recall?

0.9552238805970149

Freqs

test

number	freq
0	192
1	64

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms

512×

valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

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

ival-mult: 6.0ms (46.9% of total)

ival-sub: 3.0ms (23.4% of total)

ival-div: 3.0ms (23.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess275.0ms (5.2%)

Memory

10.3MiB live, 334.5MiB allocated

Algorithm

1×	egg-herbie

Rules

7 700×	`lower-fma.f64`
7 700×	`lower-fma.f32`
3 752×	`lower-*.f32`
3 748×	`lower-*.f64`
2 616×	`div-sub`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	53
1	71	45
2	303	35
3	1658	35
4	3588	35
5	5120	35
6	5897	35
7	6043	35
8	6091	35
9	6178	35
10	6178	35
11	6640	35
12	7256	35
0	7	9
0	11	9
1	22	9
2	56	7
3	133	7
4	309	7
5	630	7
6	1135	7
7	4009	7
8	7041	7
0	8094	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.7%	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify264.0ms (5%)

Memory

-4.6MiB live, 149.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-64	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	(-.f64 x y)

Rules

7 700×	`lower-fma.f64`
7 700×	`lower-fma.f32`
3 752×	`lower-*.f32`
3 748×	`lower-*.f64`
1 972×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	22	23
2	56	21
3	133	21
4	309	21
5	630	21
6	1135	21
7	4009	21
8	7041	21
0	8094	21

Stop Event

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

Calls

Call 1

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

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

localize18.0ms (0.3%)

Memory

-3.6MiB live, 35.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0.23524516919319446	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	15.337982537549236	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))

Samples

12.0ms

256×

valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

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

ival-mult: 3.0ms (48.6% of total)

ival-div: 2.0ms (32.4% of total)

ival-sub: 1.0ms (16.2% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Memory

16.2MiB live, 16.2MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (- (* 1/2 (/ x y)) 1/2) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (- (* 1/2 (/ x y)) 1/2) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (- (* 1/2 (/ x y)) 1/2) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())

Calls

6 calls:

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

simplify223.0ms (4.2%)

Memory

-18.5MiB live, 169.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 868×	`lower-fma.f64`
16 868×	`lower-fma.f32`
2 616×	`lower-*.f64`
2 616×	`lower-*.f32`
2 482×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	369
1	106	369
2	239	369
3	550	369
4	1455	369
5	2629	369
6	4362	369
7	5581	369
8	6065	369
9	6308	369
10	6428	369
11	7585	369
0	8033	366

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

Calls

Call 1

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

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

rewrite282.0ms (5.3%)

Memory

23.7MiB live, 353.2MiB allocated

Rules

5 688×	`lower-/.f32`
5 686×	`lower-/.f64`
4 398×	`lower-*.f32`
4 394×	`lower-*.f64`
2 466×	`lower-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	43	20
2	301	18
3	4219	18
0	10118	18

Stop Event

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

Counts

4 → 623

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (+.f64 y x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 y x (hypot.f64 y x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 y x (hypot.f64 y x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 y x (hypot.f64 y x)) (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3/2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (hypot.f64 y x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y x) y) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (+.f64 y x) y)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 y x) y) (-.f64 (.f64 (+.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (fma.f64 (neg.f64 y) y (*.f64 x x))) (-.f64 x y))
(.f64 (/.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (-.f64 (hypot.f64 y x) (*.f64 y x)))
(.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x)))
(*.f64 (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(.f64 (.f64 (+.f64 y x) (-.f64 y x)) (pow.f64 (neg.f64 (+.f64 y x)) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (neg.f64 (fma.f64 y x (hypot.f64 y x))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 y x))
(.f64 (+.f64 y x) (.f64 (-.f64 x y) (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
(*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))
(.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 x y))
(.f64 (fma.f64 y x (hypot.f64 y x)) (.f64 (-.f64 x y) (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64))))
(*.f64 (fma.f64 y x (hypot.f64 y x)) (/.f64 (-.f64 x y) (fma.f64 y x (hypot.f64 y x))))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64)))
(*.f64 (-.f64 x y) #s(literal 1 binary64))
(pow.f64 (/.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (-.f64 x y) #s(literal 1 binary64))
(/.f64 (-.f64 (neg.f64 (.f64 x x)) (.f64 (neg.f64 y) y)) (neg.f64 (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 y x (hypot.f64 y x))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (+.f64 y x) #s(literal -1 binary64))) (hypot.f64 y x))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (+.f64 y x) #s(literal -1 binary64))) (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))))
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(exp.f64 (*.f64 (neg.f64 (log.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) #s(literal -1 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (neg.f64 y)) (/.f64 #s(literal 1/2 binary64) y))
(+.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/2 binary64) y))
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (neg.f64 y)))
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1/2 binary64) x))))
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 (/.f64 #s(literal 1/2 binary64) x)))

eval206.0ms (3.9%)

Memory: -14.0MiB live, 231.4MiB allocated
Compiler: Compiled 13 960 to 1 727 computations (87.6% saved)

prune17.0ms (0.3%)

Memory

-18.2MiB live, 57.0MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	698	6	704
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	698	7	705

Accuracy

100.0%

Counts

705 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	88.2%	(/.f64 (/.f64 (-.f64 y x) y) (*.f64 #s(literal -2 binary64) x))
✓	75.7%	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
▶	42.6%	(/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
▶	100.0%	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
▶	89.2%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))
▶	47.2%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
▶	54.1%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))

Compiler

Compiled 93 to 85 computations (8.6% saved)

simplify172.0ms (3.2%)

Memory

25.2MiB live, 142.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 y x)
cost-diff	0	(fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))
cost-diff	192	(/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	(neg.f64 y)
cost-diff	0	#s(approx (- x y) (neg.f64 y))
cost-diff	0	(/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))

Rules

4 160×	`lower-fma.f32`
4 158×	`lower-fma.f64`
3 728×	`lower-*.f32`
3 724×	`lower-*.f64`
1 854×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	122
0	36	121
1	58	121
2	108	115
3	223	114
4	503	114
5	1200	114
6	3148	114
7	4676	114
8	6956	114
9	7985	114
0	8062	114

Stop Event

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

Calls

Call 1

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

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

localize76.0ms (1.4%)

Memory

-22.8MiB live, 99.8MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
accuracy	0	(/.f64 y x)
accuracy	0	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))
accuracy	6.927180374427969	(/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)
accuracy	0	(neg.f64 y)
accuracy	0.23524516919319446	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	15.337982537549236	(/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
accuracy	29.33602809534896	#s(approx (- x y) (neg.f64 y))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	33.82202525441855	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	29.37043488715363	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.0234375	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))

Samples

46.0ms

256×

valid

Compiler

Compiled 103 to 20 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 17.0ms (50.3% of total)

ival-div: 12.0ms (35.5% of total)

ival-sub: 2.0ms (5.9% of total)

ival-add: 1.0ms (3% of total)

ival-neg: 1.0ms (3% of total)

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

exact: 0.0ms (0% of total)

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

series23.0ms (0.4%)

Memory

19.1MiB live, 54.2MiB allocated

Counts

14 → 288

Calls

Call 1

Inputs
#s(alt (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation:binary64>) () ())
#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation:binary64>) () ())
#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) #<representation:binary64>) () ())
#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())
#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation:binary64>) () ())
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())
#s(alt (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) (patch (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) #<representation:binary64>) () ())
#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)) #<representation:binary64>) () ())
#s(alt (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation:binary64>) () ())

Outputs
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 1/2 binary64) y) (patch (/.f64 #s(literal 1/2 binary64) y) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (patch #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) y) (patch (.f64 (.f64 x #s(literal 2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) (patch (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) (patch (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) (patch (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y) #<representation:binary64>) () ())) ())
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#s(alt (+ 1/2 (* -1/2 (/ y x))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (/ y x))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (/ y x))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation:binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((- (/ 1/2 y) (/ 1/2 x)) (/ 1/2 y) (/ 1/2 x) (/ (- x y) (* (* x 2) y)) (/ -1/2 x) (/ (- x y) (* (* x 2) y)) (/ (- x y) (* (* x 2) y)) (- x y) (neg y) (* (* x 2) y) (/ (+ (* (/ y x) -1/2) 1/2) y) (/ (- x y) (* (* x 2) y)) (+ (* (/ y x) -1/2) 1/2) (/ y x))
2.0ms	y	@	-inf	((- (/ 1/2 y) (/ 1/2 x)) (/ 1/2 y) (/ 1/2 x) (/ (- x y) (* (* x 2) y)) (/ -1/2 x) (/ (- x y) (* (* x 2) y)) (/ (- x y) (* (* x 2) y)) (- x y) (neg y) (* (* x 2) y) (/ (+ (* (/ y x) -1/2) 1/2) y) (/ (- x y) (* (* x 2) y)) (+ (* (/ y x) -1/2) 1/2) (/ y x))
2.0ms	y	@	0	((- (/ 1/2 y) (/ 1/2 x)) (/ 1/2 y) (/ 1/2 x) (/ (- x y) (* (* x 2) y)) (/ -1/2 x) (/ (- x y) (* (* x 2) y)) (/ (- x y) (* (* x 2) y)) (- x y) (neg y) (* (* x 2) y) (/ (+ (* (/ y x) -1/2) 1/2) y) (/ (- x y) (* (* x 2) y)) (+ (* (/ y x) -1/2) 1/2) (/ y x))
2.0ms	x	@	0	((- (/ 1/2 y) (/ 1/2 x)) (/ 1/2 y) (/ 1/2 x) (/ (- x y) (* (* x 2) y)) (/ -1/2 x) (/ (- x y) (* (* x 2) y)) (/ (- x y) (* (* x 2) y)) (- x y) (neg y) (* (* x 2) y) (/ (+ (* (/ y x) -1/2) 1/2) y) (/ (- x y) (* (* x 2) y)) (+ (* (/ y x) -1/2) 1/2) (/ y x))
2.0ms	y	@	inf	((- (/ 1/2 y) (/ 1/2 x)) (/ 1/2 y) (/ 1/2 x) (/ (- x y) (* (* x 2) y)) (/ -1/2 x) (/ (- x y) (* (* x 2) y)) (/ (- x y) (* (* x 2) y)) (- x y) (neg y) (* (* x 2) y) (/ (+ (* (/ y x) -1/2) 1/2) y) (/ (- x y) (* (* x 2) y)) (+ (* (/ y x) -1/2) 1/2) (/ y x))

simplify176.0ms (3.3%)

Memory

5.9MiB live, 165.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4 148×	`lower-fma.f64`
4 148×	`lower-fma.f32`
2 444×	`lower-*.f64`
2 444×	`lower-*.f32`
1 436×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	1431
1	125	1431
2	306	1431
3	878	1431
4	2027	1431
5	3167	1431
6	4931	1431
7	5459	1431
8	5686	1431
9	5832	1431
10	5874	1431
11	6948	1431
12	7692	1431
0	8090	1395

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 285

Calls

Call 1

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

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

rewrite344.0ms (6.5%)

Memory

-18.2MiB live, 258.3MiB allocated

Rules

5 356×	`lower-/.f32`
5 344×	`lower-/.f64`
4 606×	`lower-*.f32`
4 602×	`lower-*.f64`
3 242×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	102
0	36	102
1	141	102
2	1078	96
0	8119	96

Stop Event

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

Counts

14 → 557

Calls

Call 1

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

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

eval327.0ms (6.2%)

Memory: 11.1MiB live, 181.6MiB allocated
Compiler: Compiled 11 998 to 1 757 computations (85.4% saved)

prune220.0ms (4.2%)

Memory

-11.7MiB live, 62.9MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	871	0	871
Fresh	0	1	1
Picked	0	5	5
Done	0	1	1
Total	871	7	878

Accuracy

100.0%

Counts

878 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	88.2%	(/.f64 (/.f64 (-.f64 y x) y) (*.f64 #s(literal -2 binary64) x))
✓	75.7%	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
✓	42.6%	(/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
✓	100.0%	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
✓	89.2%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))
✓	47.2%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
✓	54.1%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify174.0ms (3.3%)

Memory

-14.3MiB live, 228.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -2 binary64) x)
cost-diff	0	(-.f64 y x)
cost-diff	0	(/.f64 (-.f64 y x) y)
cost-diff	320	(/.f64 (/.f64 (-.f64 y x) y) (*.f64 #s(literal -2 binary64) x))

Rules

8 990×	`lower-fma.f64`
8 990×	`lower-fma.f32`
2 632×	`lower-*.f32`
2 630×	`lower-*.f64`
1 892×	`unsub-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	21	23
2	49	23
3	107	21
4	233	21
5	460	21
6	907	21
7	2368	21
8	5504	21
0	8032	21

Stop Event

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

Calls

Call 1

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

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

localize19.0ms (0.4%)

Memory

13.8MiB live, 52.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 y x)
accuracy	0	(*.f64 #s(literal -2 binary64) x)
accuracy	0.01171875	(/.f64 (-.f64 y x) y)
accuracy	7.553823180297353	(/.f64 (/.f64 (-.f64 y x) y) (*.f64 #s(literal -2 binary64) x))

Samples

14.0ms

256×

valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

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

ival-div: 3.0ms (40.6% of total)

ival-mult: 2.0ms (27.1% of total)

ival-sub: 1.0ms (13.5% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ y x))) y) (taylor 0 y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (/ x y)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ y (* -1 x)) y) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ y (* -1 x)) y) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ y (* -1 x)) y) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf y) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor -inf y) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (- (* 1/2 (/ x y)) 1/2) x) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (- (* 1/2 (/ x y)) 1/2) x) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (- (* 1/2 (/ x y)) 1/2) x) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ x y))) (taylor 0 x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor 0 x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (/ x y)) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) (/ 1 y))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) (/ 1 y))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) (/ 1 y))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) (patch (/.f64 (/.f64 (-.f64 y x) y) (.f64 #s(literal -2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (/ x y)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 y) (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 y) (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 y) (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) y) (patch (/.f64 (-.f64 y x) y) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -2 binary64) x) (patch (.f64 #s(literal -2 binary64) x) #<representation:binary64>) () ())) ())

Calls

6 calls:

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

simplify252.0ms (4.8%)

Memory

-22.0MiB live, 175.7MiB allocated

Algorithm

1×	egg-herbie

Rules

5 504×	`lower-fma.f64`
5 504×	`lower-fma.f32`
4 256×	`lower-*.f64`
4 256×	`lower-*.f32`
1 424×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	354
1	115	354
2	280	354
3	702	354
4	1798	354
5	3629	354
6	5197	354
7	5815	354
8	6314	354
9	6677	354
10	6840	354
11	7308	354
0	8005	351

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

Calls

Call 1

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

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

rewrite268.0ms (5.1%)

Memory

13.8MiB live, 331.5MiB allocated

Rules

6 020×	`lower-*.f32`
6 018×	`lower-*.f64`
4 034×	`lower-/.f32`
4 030×	`lower-/.f64`
3 046×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	49	20
2	385	20
3	4620	20
0	9823	20

Stop Event

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

Counts

4 → 597

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (.f64 (.f64 x y) #s(literal -2 binary64)) (.f64 (+.f64 x y) (-.f64 x y))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (+.f64 x y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (*.f64 x y) #s(literal -2 binary64)) (fma.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 x y (hypot.f64 x y))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (/.f64 x (-.f64 y x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) y))
(.f64 (pow.f64 (pow.f64 (.f64 (/.f64 (-.f64 y x) y) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) y)) #s(literal -1 binary64)) (pow.f64 (+.f64 x y) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) y)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x y (hypot.f64 x y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (/.f64 x y) (+.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (*.f64 y (-.f64 y x))) #s(literal -1 binary64)) (pow.f64 y #s(literal -2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 x y) y))
(.f64 (pow.f64 (/.f64 (.f64 (.f64 x y) #s(literal -2 binary64)) (fma.f64 (neg.f64 x) x (.f64 y y))) #s(literal -1 binary64)) (pow.f64 (+.f64 x y) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (*.f64 x y) #s(literal -2 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x y (hypot.f64 x y)) #s(literal -1 binary64)))
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(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (neg.f64 y))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) y)) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) x) (.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 (neg.f64 x) x))) (*.f64 (pow.f64 y #s(literal -1 binary64)) (+.f64 #s(literal 0 binary64) x)))
(/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (pow.f64 y #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (pow.f64 y #s(literal -1 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))
(/.f64 (fma.f64 (neg.f64 y) (+.f64 #s(literal 0 binary64) x) (.f64 x x)) (.f64 #s(literal -1 binary64) (+.f64 #s(literal 0 binary64) x)))
(/.f64 (fma.f64 (neg.f64 y) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal -1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (fma.f64 y (+.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) x))) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) x)))
(/.f64 (fma.f64 y (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x)) (neg.f64 (+.f64 x y)))
(/.f64 (-.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 x y (hypot.f64 x y))))
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 x y) #s(literal -1 binary64))) (hypot.f64 x y))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 x y) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (hypot.f64 x y) (pow.f64 y #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 x y (hypot.f64 x y)) #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 x y (hypot.f64 x y)) #s(literal -1 binary64))) (hypot.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 x y) #s(literal 3/2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 y (/.f64 y (+.f64 x y))) #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 x (+.f64 x y))) #s(literal 2 binary64))) (fma.f64 y (/.f64 y (+.f64 x y)) (*.f64 x (/.f64 x (+.f64 x y)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (-.f64 (neg.f64 x) y))
(/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (+.f64 x y) #s(literal 3 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 x y) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 y (/.f64 y (+.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 x (+.f64 x y))) #s(literal 2 binary64)) (.f64 (.f64 y (/.f64 y (+.f64 x y))) (*.f64 x (/.f64 x (+.f64 x y)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (neg.f64 (neg.f64 (+.f64 x y))))
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (+.f64 x y))
(/.f64 (neg.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 x y (hypot.f64 x y)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x y (hypot.f64 x y)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (hypot.f64 x y) (+.f64 x y)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (*.f64 x x) (hypot.f64 x y) (pow.f64 y #s(literal 4 binary64))) (+.f64 x y)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x y (hypot.f64 x y))))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (hypot.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (*.f64 x y) #s(literal 3/2 binary64))) (fma.f64 x y (hypot.f64 x y))))
(/.f64 (.f64 (.f64 (+.f64 x y) (-.f64 x y)) #s(literal 1 binary64)) (neg.f64 (+.f64 x y)))
(/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (neg.f64 (fma.f64 x y (hypot.f64 x y))))
(/.f64 (-.f64 (.f64 (.f64 y y) (+.f64 x y)) (.f64 (+.f64 x y) (.f64 x x))) (pow.f64 (+.f64 x y) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) (.f64 (fma.f64 x y (hypot.f64 x y)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 x y (hypot.f64 x y)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (+.f64 x y) (hypot.f64 x y)))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (+.f64 x y) (fma.f64 (.f64 x x) (hypot.f64 x y) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 (fma.f64 x y (hypot.f64 x y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 x y (hypot.f64 x y)) (hypot.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 x y) #s(literal 3/2 binary64)))))
(/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (neg.f64 (+.f64 x y)))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 x y (hypot.f64 x y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64))))
(/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (neg.f64 (neg.f64 (+.f64 x y))))
(/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (+.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 y y) (.f64 (neg.f64 x) y))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (neg.f64 (fma.f64 x y (hypot.f64 x y)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x y (hypot.f64 x y)))
(neg.f64 (-.f64 x y))
(fma.f64 (/.f64 (.f64 y y) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (hypot.f64 x y) (.f64 x y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 (/.f64 (.f64 y y) (fma.f64 (neg.f64 x) x (.f64 y y))) (-.f64 y x) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 x y) x) #s(literal 2 binary64)))) (-.f64 (.f64 y (-.f64 y x)) (*.f64 x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (+.f64 x y) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 x y) x) (-.f64 (.f64 (+.f64 x y) x) (.f64 y y)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(fma.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 (pow.f64 y #s(literal 3/2 binary64)) (fma.f64 x y (hypot.f64 x y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(fma.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 y) #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) (neg.f64 y) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) x y)
(fma.f64 #s(literal 1 binary64) y (neg.f64 x))
(fma.f64 (*.f64 y y) (/.f64 y (fma.f64 x y (hypot.f64 x y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(fma.f64 (.f64 y y) (pow.f64 (+.f64 x y) #s(literal -1 binary64)) (neg.f64 (.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x y (hypot.f64 x y)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(fma.f64 x #s(literal -1 binary64) y)
(fma.f64 y (/.f64 (*.f64 y y) (fma.f64 x y (hypot.f64 x y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(fma.f64 y (/.f64 y (+.f64 x y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x y)))))
(fma.f64 y #s(literal 1 binary64) (neg.f64 x))
(-.f64 (+.f64 y #s(literal 0 binary64)) x)
(-.f64 (.f64 y (/.f64 y (+.f64 x y))) (.f64 x (/.f64 x (+.f64 x y))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))))
(-.f64 #s(literal 0 binary64) (-.f64 x y))
(-.f64 y x)
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 y (/.f64 y (+.f64 x y))) (neg.f64 (.f64 x (/.f64 x (+.f64 x y)))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x y (hypot.f64 x y)))))
(+.f64 (neg.f64 x) y)
(+.f64 y (neg.f64 x))
(*.f64 #s(literal 2 binary64) (neg.f64 x))
(.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) x))
(*.f64 (neg.f64 x) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) x))
(.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -2 binary64) (/.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal -2 binary64) x)
(*.f64 x #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 1 binary64))
(neg.f64 (*.f64 #s(literal 2 binary64) x))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) x))
(exp.f64 (neg.f64 (.f64 (log.f64 (.f64 #s(literal -2 binary64) x)) #s(literal -1 binary64))))

eval113.0ms (2.1%)

Memory: -4.1MiB live, 147.0MiB allocated
Compiler: Compiled 11 646 to 1 733 computations (85.1% saved)

prune18.0ms (0.3%)

Memory

-8.6MiB live, 41.6MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	678	0	678
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	678	7	685

Accuracy

100.0%

Counts

685 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	88.2%	(/.f64 (/.f64 (-.f64 y x) y) (*.f64 #s(literal -2 binary64) x))
✓	75.7%	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
✓	42.6%	(/.f64 #s(approx (- x y) (neg.f64 y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
✓	100.0%	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
✓	89.2%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))
✓	47.2%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
✓	54.1%	#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))

Compiler

Compiled 102 to 73 computations (28.4% saved)

regimes9.0ms (0.2%)

Memory

16.9MiB live, 16.9MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	y
3.0ms	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
3.0ms	x

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
88.2%	5	`x`
86.5%	5	`y`
89.3%	5	`(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes10.0ms (0.2%)

Memory

-21.4MiB live, 13.6MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

Calls

3 calls:

6.0ms	(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
75.4%	3	`y`
77.0%	3	`x`
63.2%	6	`(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
54.1%	1	`(/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`
54.1%	1	`y`
54.1%	1	`x`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	6.034731558231778e+297	+inf
0.0ms	-0.0	3.227407602212155e-123
0.0ms	-6.5707353278054894e-108	-4.364247020342729e-109
0.0ms	-inf	-5.975963216819053e+292

Compiler

Compiled 12 to 12 computations (0% saved)

bsearch23.0ms (0.4%)

Memory

-6.2MiB live, 31.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	4.800729823626441e+37	4.684988386653524e+38
9.0ms	-2.2007041320094645e+57	-1.1556857270813027e+55

Samples

10.0ms

208×

valid

Compiler

Compiled 116 to 168 computations (-44.8% saved)

Precisions

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

ival-mult: 3.0ms (57.3% of total)

ival-sub: 1.0ms (19.1% of total)

ival-div: 1.0ms (19.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify30.0ms (0.6%)

Memory

17.5MiB live, 54.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`-commutative-binary64-.f64`
12×	`+-commutative-binary64-+.f64`
12×	`sub-neg-binary64-neg.f64-+.f64--.f64`
8×	`neg-sub0-binary64--.f64-neg.f64`
8×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	172
1	43	172
2	54	172
3	62	172
4	68	172
5	70	172

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal -inf.0 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal -3305279843951243/661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256 binary64)) (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal 0 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal 9999999999999999595662034753429788238255624467393741467120915117996487670031669885400803025551745174706847878231119663145222863482996149222332143382301002459214758820269116923021527058285459686414683385913622455551313826420028155008403585629126369847605750170289266545852965785882018353801250996224 binary64)) (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 x #s(literal -11999999999999999578369017171401072254165893871560556544 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal 75000000000000003033973850461670735872 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))))
#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))

Outputs
(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal -inf.0 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal -3305279843951243/661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256 binary64)) (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal 0 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(literal 9999999999999999595662034753429788238255624467393741467120915117996487670031669885400803025551745174706847878231119663145222863482996149222332143382301002459214758820269116923021527058285459686414683385913622455551313826420028155008403585629126369847605750170289266545852965785882018353801250996224 binary64)) (/.f64 (-.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 #s(literal 2 binary64) x) y)) #s(literal -inf.0 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 #s(literal 2 binary64) x) y)) #s(literal -3305279843951243/661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256 binary64)) (/.f64 (-.f64 x y) (.f64 (.f64 #s(literal 2 binary64) x) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 #s(literal 2 binary64) x) y)) #s(literal 0 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 x y) (.f64 (.f64 #s(literal 2 binary64) x) y)) #s(literal 9999999999999999595662034753429788238255624467393741467120915117996487670031669885400803025551745174706847878231119663145222863482996149222332143382301002459214758820269116923021527058285459686414683385913622455551313826420028155008403585629126369847605750170289266545852965785882018353801250996224 binary64)) (/.f64 (-.f64 x y) (.f64 (.f64 #s(literal 2 binary64) x) y)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 x #s(literal -11999999999999999578369017171401072254165893871560556544 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal 75000000000000003033973850461670735872 binary64)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x)) #s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))))
#s(approx (/ (- x y) (* (* x 2) y)) (/.f64 #s(literal -1/2 binary64) x))

soundness610.0ms (11.5%)

Memory

-36.4MiB live, 297.3MiB allocated

Rules

16 868×	`lower-fma.f64`
16 868×	`lower-fma.f32`
5 688×	`lower-/.f32`
5 686×	`lower-/.f64`
4 398×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	369
1	106	369
2	239	369
3	550	369
4	1455	369
5	2629	369
6	4362	369
7	5581	369
8	6065	369
9	6308	369
10	6428	369
11	7585	369
0	8033	366
0	7	20
0	11	20
1	43	20
2	301	18
3	4219	18
0	10118	18

Stop Event

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

Compiler

Compiled 140 to 64 computations (54.3% saved)

preprocess57.0ms (1.1%)

Memory: 29.3MiB live, 110.2MiB allocated
Compiler: Compiled 250 to 92 computations (63.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze19.0ms (0.4%)

sample932.0ms (17.6%)

explain102.0ms (1.9%)

preprocess275.0ms (5.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify264.0ms (5%)

localize18.0ms (0.3%)

series11.0ms (0.2%)

simplify223.0ms (4.2%)

rewrite282.0ms (5.3%)

eval206.0ms (3.9%)

prune17.0ms (0.3%)

simplify172.0ms (3.2%)

localize76.0ms (1.4%)

series23.0ms (0.4%)

simplify176.0ms (3.3%)

rewrite344.0ms (6.5%)

eval327.0ms (6.2%)

prune220.0ms (4.2%)

simplify174.0ms (3.3%)

localize19.0ms (0.4%)

series8.0ms (0.2%)

simplify252.0ms (4.8%)

rewrite268.0ms (5.1%)

eval113.0ms (2.1%)

prune18.0ms (0.3%)

regimes9.0ms (0.2%)

regimes7.0ms (0.1%)

regimes10.0ms (0.2%)

regimes4.0ms (0.1%)

bsearch1.0ms (0%)

bsearch23.0ms (0.4%)

simplify30.0ms (0.6%)

soundness610.0ms (11.5%)

preprocess57.0ms (1.1%)

end0.0ms (0%)

Profiling