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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze36.0ms (0.6%)

Memory

-9.8MiB live, 29.2MiB 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)

sample1.1s (18.4%)

Memory

4.1MiB live, 1 066.9MiB allocated

Samples

808.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 593.0ms

ival-mult: 424.0ms (71.5% of total)

ival-add: 100.0ms (16.9% of total)

ival-div: 54.0ms (9.1% of total)

ival-true: 6.0ms (1% of total)

exact: 5.0ms (0.8% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain206.0ms (3.3%)

Memory

28.9MiB live, 324.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
61	-	5	(8.163122943675298e-122 1.3308341134803285e-193)	`(/.f64 (+.f64 x y) (.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	-	`(.f64 (.f64 x #s(literal 2 binary64)) 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	35	0
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	35
`/.f64`	`(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`	n/u	21	0
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	underflow	21

Confusion

	Predicted +	Predicted -
+	56	5
-	0	195

Precision

1.0

Recall

0.9180327868852459

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	56	0	5
-	0	0	195

Precision?

1.0

Recall?

0.9180327868852459

Freqs

test

number	freq
0	200
1	56

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

512×

valid

Compiler

Compiled 128 to 58 computations (54.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 9.0ms (48.2% of total)

ival-div: 4.0ms (21.4% of total)

ival-add: 4.0ms (21.4% of total)

ival-true: 1.0ms (5.4% of total)

exact: 0.0ms (0% of total)

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

preprocess45.0ms (0.7%)

Memory

27.8MiB live, 64.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	51
1	62	45
2	206	45
3	853	45
4	2809	37
5	6431	37
0	7	9
0	11	9
1	18	9
2	32	9
3	46	9
4	48	9
0	48	9

Stop Event

1×	iter limit
1×	saturated
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 (/.f64 (+.f64 y x) y) x) #s(literal 2 binary64))

Symmetry

(sort x y)

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.9%	(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify5.0ms (0.1%)

Memory

-28.8MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-768	(/.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)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	18	23
2	32	23
3	46	23
4	48	23
0	48	23

Stop Event

1×	iter limit
1×	saturated
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 (/.f64 (+.f64 y x) y) x) #s(literal 2 binary64))
(+.f64 x y)
(+.f64 y x)
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)

localize29.0ms (0.5%)

Memory

21.8MiB live, 104.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x y)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0.241241431859356	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	13.922839364046034	(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))

Samples

23.0ms

256×

valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-div: 5.0ms (31.2% of total)

ival-add: 5.0ms (31.2% of total)

ival-mult: 5.0ms (31.2% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.2%)

Memory

11.7MiB live, 50.2MiB 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 y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x 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 y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 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 x)) (* 1/2 (/ 1 y))) (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 x)) (* 1/2 (/ 1 y))) (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 x)) (* 1/2 (/ 1 y))) (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 y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ 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 x)) (* 1/2 (/ 1 y))) (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 x)) (* 1/2 (/ 1 y))) (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 x)) (* 1/2 (/ 1 y))) (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 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 (* 1/2 (/ x y))) 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 (* 1/2 (/ x y))) 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 (* 1/2 (/ x y))) 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 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 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 x)) (* 1/2 (/ 1 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 x)) (* 1/2 (/ 1 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 x)) (* 1/2 (/ 1 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 x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ 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 x)) (* 1/2 (/ 1 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 x)) (* 1/2 (/ 1 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 x)) (* 1/2 (/ 1 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>) () ())) ())

Calls

6 calls:

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

simplify156.0ms (2.5%)

Memory

-57.9MiB live, 109.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	372
1	93	372
2	175	372
3	476	372
4	1338	372
5	2520	372
6	4202	372
7	5347	372
8	6256	372
9	6922	372
10	7381	372
11	7982	372
0	8006	366

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite487.0ms (7.9%)

Memory

-24.1MiB live, 172.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	39	20
2	251	20
3	2914	20
0	8839	20

Stop Event

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

Counts

4 → 590

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
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eval144.0ms (2.3%)

Memory: 27.4MiB live, 146.0MiB allocated
Compiler: Compiled 13 607 to 1 678 computations (87.7% saved)

prune47.0ms (0.8%)

Memory

15.5MiB live, 53.1MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	662	6	668
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	662	7	669

Accuracy

100.0%

Counts

669 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.9%	(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
	38.2%	(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64)) (pow.f64 (/.f64 y (pow.f64 (-.f64 x y) #s(literal -1 binary64))) #s(literal -1 binary64)))
▶	77.3%	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
▶	85.5%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y))
▶	50.3%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
▶	50.4%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) x))
▶	100.0%	#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))

Compiler

Compiled 123 to 99 computations (19.5% saved)

simplify127.0ms (2.1%)

Memory

-3.4MiB live, 187.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 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	-384	(/.f64 #s(literal 1/2 binary64) (*.f64 y x))
cost-diff	0	(+.f64 y x)
cost-diff	0	(*.f64 y x)
cost-diff	320	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
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))
cost-diff	0	#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	131
0	36	127
1	64	127
2	129	127
3	215	127
4	437	127
5	1615	127
6	4766	127
0	8115	127

Stop Event

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

Calls

Call 1

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

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

localize114.0ms (1.8%)

Memory

-11.1MiB live, 117.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
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	0.00390625	(fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	9.251042159337269	(/.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y)
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 y x)
accuracy	0.34175941986591063	(/.f64 #s(literal 1/2 binary64) (*.f64 y x))
accuracy	14.199112699055524	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	31.803837543265782	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	31.727028402198016	#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	#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))
accuracy	0.01171875	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x))

Samples

98.0ms

256×

valid

Compiler

Compiled 205 to 42 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-div: 71.0ms (83.8% of total)

ival-mult: 8.0ms (9.4% of total)

ival-add: 4.0ms (4.7% of total)

ival-sub: 1.0ms (1.2% of total)

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

exact: 0.0ms (0% of total)

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

series24.0ms (0.4%)

Memory

10.3MiB live, 45.9MiB allocated

Counts

15 → 324

Calls

Call 1

Inputs
#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())
#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 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())
#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())
#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 y x)) #<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 #s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (/ (+ x y) (* (* x 2) y)) (-.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 #s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (/ (+ x y) (* (* x 2) y)) (-.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 #s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (/ (+ x y) (* (* x 2) y)) (-.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 #s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (/ (+ x y) (* (* x 2) y)) (-.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 (/.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 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/2 (/ y x))) y) (taylor 0 y) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/2 (/ y x))) y) (taylor 0 y) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 y) (taylor -inf x) (#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 (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#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 1/2 (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 (+ 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
4.0ms	x	@	0	((/ (+ x y) (* (* x 2) y)) (- (/ 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)) (* (/ 1/2 (* y x)) (+ y x)) (* y x) (+ y x) (/ 1/2 (* y x)) (/ (+ (* (/ y x) 1/2) 1/2) y) (/ (+ x y) (* (* x 2) y)) (+ (* (/ y x) 1/2) 1/2) (/ y x))
3.0ms	y	@	-inf	((/ (+ x y) (* (* x 2) y)) (- (/ 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)) (* (/ 1/2 (* y x)) (+ y x)) (* y x) (+ y x) (/ 1/2 (* y x)) (/ (+ (* (/ y x) 1/2) 1/2) y) (/ (+ x y) (* (* x 2) y)) (+ (* (/ y x) 1/2) 1/2) (/ y x))
2.0ms	x	@	-inf	((/ (+ x y) (* (* x 2) y)) (- (/ 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)) (* (/ 1/2 (* y x)) (+ y x)) (* y x) (+ y x) (/ 1/2 (* y x)) (/ (+ (* (/ y x) 1/2) 1/2) y) (/ (+ x y) (* (* x 2) y)) (+ (* (/ y x) 1/2) 1/2) (/ y x))
2.0ms	y	@	0	((/ (+ x y) (* (* x 2) y)) (- (/ 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)) (* (/ 1/2 (* y x)) (+ y x)) (* y x) (+ y x) (/ 1/2 (* y x)) (/ (+ (* (/ y x) 1/2) 1/2) y) (/ (+ x y) (* (* x 2) y)) (+ (* (/ y x) 1/2) 1/2) (/ y x))
2.0ms	x	@	inf	((/ (+ x y) (* (* x 2) y)) (- (/ 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)) (* (/ 1/2 (* y x)) (+ y x)) (* y x) (+ y x) (/ 1/2 (* y x)) (/ (+ (* (/ y x) 1/2) 1/2) y) (/ (+ x y) (* (* x 2) y)) (+ (* (/ y x) 1/2) 1/2) (/ y x))

simplify104.0ms (1.7%)

Memory

5.7MiB live, 123.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	1836
1	105	1836
2	207	1836
3	585	1584
4	2827	1584
5	5657	1584
6	7332	1584
0	8044	1566

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 318

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

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

rewrite178.0ms (2.9%)

Memory

5.7MiB live, 266.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	114
0	36	114
1	155	114
2	1316	114
0	8165	114

Stop Event

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

Counts

15 → 737

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))
(-.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 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
(*.f64 y x)
(+.f64 y x)
(/.f64 #s(literal 1/2 binary64) (*.f64 y x))
(/.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
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eval239.0ms (3.9%)

Memory: -18.9MiB live, 343.8MiB allocated
Compiler: Compiled 16 213 to 2 123 computations (86.9% saved)

prune31.0ms (0.5%)

Memory

-0.2MiB live, 87.2MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	1 082	1	1 083
Fresh	1	0	1
Picked	0	5	5
Done	0	1	1
Total	1 083	7	1 090

Accuracy

100.0%

Counts

1 090 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.9%	(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
✓	77.3%	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
✓	85.5%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y))
▶	60.1%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
✓	50.3%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
✓	50.4%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) x))
✓	100.0%	#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))

Compiler

Compiled 63 to 53 computations (15.9% saved)

simplify225.0ms (3.6%)

Memory

22.2MiB live, 97.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	18	90
0	26	90
1	42	90
2	77	90
3	123	90
4	188	90
5	372	90
6	873	90
7	2096	90
8	3083	90
9	4457	90
10	5356	90
11	6069	90
12	6301	88
13	6912	88
14	7304	88
15	7484	88
16	7728	88
17	7760	88
18	7764	88
19	7764	88
20	7764	88
0	8964	88

Stop Event

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

Calls

Call 1

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

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

localize51.0ms (0.8%)

Memory

-6.0MiB live, 32.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.29134750976844204	(pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64))
accuracy	2.953110550811441	(-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)))
accuracy	25.424979486865663	(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))

Samples

40.0ms

256×

valid

Compiler

Compiled 153 to 33 computations (78.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-pow2: 11.0ms (35.9% of total)

ival-div: 6.0ms (19.6% of total)

ival-mult: 4.0ms (13% of total)

ival-pow: 4.0ms (13% of total)

ival-add: 2.0ms (6.5% of total)

ival-sub: 2.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

series37.0ms (0.6%)

Memory

3.2MiB live, 44.7MiB allocated

Counts

5 → 108

Calls

Call 1

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

Outputs
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor inf x) (#s(alt (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1/4 (pow y 2)) (taylor inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (pow y 2))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (pow y 2))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (pow y 2))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor inf x) (#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 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#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 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#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 y)) (* 1/2 (/ 1 x))) (taylor inf x) (#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 -inf x) (#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor -inf x) (#s(alt (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1/4 (pow y 2)) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (pow y 2))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (pow y 2))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (pow y 2))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (patch (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 y) (taylor -inf x) (#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 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#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 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#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 y)) (* 1/2 (/ 1 x))) (taylor -inf x) (#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>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	0	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (pow (/ 1/2 y) 2) (- (/ 1/2 y) (/ 1/2 x)))
2.0ms	y	@	inf	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (pow (/ 1/2 y) 2) (- (/ 1/2 y) (/ 1/2 x)))
2.0ms	x	@	0	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (pow (/ 1/2 y) 2) (- (/ 1/2 y) (/ 1/2 x)))
1.0ms	y	@	-inf	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (pow (/ 1/2 y) 2) (- (/ 1/2 y) (/ 1/2 x)))
1.0ms	x	@	inf	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (pow (/ 1/2 y) 2) (- (/ 1/2 y) (/ 1/2 x)))

simplify236.0ms (3.8%)

Memory

-23.8MiB live, 163.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	750
1	102	750
2	203	750
3	416	750
4	1048	750
5	3378	750
6	7206	750
0	8050	738

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

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

rewrite148.0ms (2.4%)

Memory

11.4MiB live, 240.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	71
0	26	71
1	129	47
2	1113	47
0	8161	46

Stop Event

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

Counts

5 → 686

Calls

Call 1

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

Outputs
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eval169.0ms (2.7%)

Memory: -1.9MiB live, 228.8MiB allocated
Compiler: Compiled 24 088 to 3 236 computations (86.6% saved)

prune39.0ms (0.6%)

Memory

8.6MiB live, 46.8MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	793	1	794
Fresh	0	0	0
Picked	1	0	1
Done	0	6	6
Total	794	7	801

Accuracy

100.0%

Counts

801 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.9%	(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
✓	77.3%	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
✓	85.5%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y))
▶	31.2%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
✓	50.3%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
✓	50.4%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) x))
✓	100.0%	#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))

Compiler

Compiled 58 to 51 computations (12.1% saved)

simplify217.0ms (3.5%)

Memory

-6.1MiB live, 132.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
cost-diff	0	#s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
cost-diff	0	(/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	23	102
0	29	102
1	43	102
2	74	102
3	108	102
4	138	102
5	208	102
6	329	102
7	457	102
8	859	102
9	1562	100
10	3299	100
11	5393	100
12	6507	100
13	6837	100
14	7034	100
15	7196	100
16	7666	100
0	8094	100

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
#s(literal -1/4 binary64)
(*.f64 x x)
x
(-.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)

Outputs
#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) y))))
(/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1/2 binary64) y)))
#s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
#s(literal -1/4 binary64)
(*.f64 x x)
x
(-.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)

localize254.0ms (4.1%)

Memory

7.0MiB live, 43.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.23284711409646108	(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
accuracy	25.424979486865663	(/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))
accuracy	30.044709394816245	#s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))

Samples

243.0ms

256×

valid

Compiler

Compiled 126 to 34 computations (73% saved)

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-mult: 215.0ms (91.9% of total)

ival-div: 8.0ms (3.4% of total)

ival-pow: 4.0ms (1.7% of total)

ival-pow2: 3.0ms (1.3% of total)

ival-add: 2.0ms (0.9% of total)

ival-sub: 2.0ms (0.9% of total)

exact: 1.0ms (0.4% of total)

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

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

series31.0ms (0.5%)

Memory

-17.6MiB live, 20.2MiB allocated

Counts

5 → 108

Calls

Call 1

Inputs
#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (patch #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (patch (/.f64 #s(literal -1/4 binary64) (.f64 x x)) #<representation binary64>) () ())
#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>) () ())

Outputs
#s(alt (/ 1/2 y) (taylor 0 y) (#s(alt #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.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 #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.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 #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.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 #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (+ x y) ( (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.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(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.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 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.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 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.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 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1/4 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (patch #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/4 (* -1/4 (/ (pow y 2) (pow x 2)))) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (patch #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/4 (* -1/4 (/ (pow y 2) (pow x 2)))) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (patch #s(approx (- (pow (/ 1/2 y) 2) (pow ( 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
21.0ms	y	@	inf	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/ -1/4 (* x x)) (- (/ 1/2 y) (/ 1/2 x)))
1.0ms	x	@	0	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/ -1/4 (* x x)) (- (/ 1/2 y) (/ 1/2 x)))
1.0ms	x	@	inf	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/ -1/4 (* x x)) (- (/ 1/2 y) (/ 1/2 x)))
1.0ms	y	@	0	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/ -1/4 (* x x)) (- (/ 1/2 y) (/ 1/2 x)))
1.0ms	x	@	-inf	((/ (+ x y) (* (* x 2) y)) (/ (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (- (/ 1/2 y) (/ 1/2 x))) (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/ -1/4 (* x x)) (- (/ 1/2 y) (/ 1/2 x)))

simplify244.0ms (3.9%)

Memory

0.3MiB live, 122.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	750
1	102	750
2	203	750
3	416	750
4	1048	750
5	3378	750
6	7206	750
0	8050	738

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

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

rewrite222.0ms (3.6%)

Memory

19.8MiB live, 94.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	89
0	29	89
1	139	89
2	1087	89
0	8397	86

Stop Event

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

Counts

5 → 229

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))

Outputs
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eval232.0ms (3.7%)

Memory: 1.1MiB live, 83.6MiB allocated
Compiler: Compiled 7 437 to 1 088 computations (85.4% saved)

prune33.0ms (0.5%)

Memory

-15.0MiB live, 21.3MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	336	1	337
Fresh	0	0	0
Picked	1	0	1
Done	0	6	6
Total	337	7	344

Accuracy

100.0%

Counts

344 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.9%	(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
✓	77.3%	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
✓	85.5%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y))
	31.3%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(approx (- (/ 1/2 y) (/ 1/2 x)) (/.f64 #s(literal -1/2 binary64) x))))
✓	50.3%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y))
✓	50.4%	#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) x))
✓	100.0%	#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))

Compiler

Compiled 168 to 100 computations (40.5% saved)

regimes12.0ms (0.2%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

10 → 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 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x))
(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))
#s(approx (/ (+ x y) (* (* x 2) 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))
#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(approx (- (/ 1/2 y) (/ 1/2 x)) (/.f64 #s(literal -1/2 binary64) x))))
#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(approx (- (pow (/ 1/2 y) 2) (pow (* 2 x) -2)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) x))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64)) (pow.f64 (/.f64 y (pow.f64 (-.f64 x y) #s(literal -1 binary64))) #s(literal -1 binary64)))

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

Calls

3 calls:

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

regimes37.0ms (0.6%)

Memory

-29.2MiB live, 9.8MiB allocated

Counts

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

Calls

3 calls:

32.0ms	x
2.0ms	y
2.0ms	(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))

Results

Accuracy	Segments	Branch
91.3%	3	`x`
91.5%	3	`y`
87.5%	4	`(/.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

7.9MiB live, 7.9MiB 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 (/.f64 #s(literal 1/2 binary64) (*.f64 y x)) (+.f64 y x))

Outputs

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

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
91.0%	3	`x`
90.8%	3	`y`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes5.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

2 → 2

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))

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))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
58.9%	5	`(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`
83.9%	2	`y`
84.0%	2	`x`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB 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
50.4%	1	`(/.f64 (+.f64 x y) (.f64 (.f64 x #s(literal 2 binary64)) y))`
50.4%	1	`y`
50.4%	1	`x`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch106.0ms (1.7%)

Memory

-16.6MiB live, 29.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	1.5830247112013138e+121	2.394168560497389e+127
91.0ms	3.497925133783223e-195	2.7791863576062066e-193

Samples

12.0ms

256×

valid

Compiler

Compiled 220 to 236 computations (-7.3% saved)

Precisions

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

ival-mult: 3.0ms (45.2% of total)

ival-div: 2.0ms (30.1% of total)

ival-add: 1.0ms (15.1% of total)

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

exact: 0.0ms (0% of total)

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

bsearch36.0ms (0.6%)

Memory

3.9MiB live, 42.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
24.0ms	-3.8628143017422914e-227	-2.621640970647873e-228
10.0ms	-3.5157262001385736e+144	-1.3620437033691969e+143

Samples

26.0ms

208×

valid

Compiler

Compiled 181 to 194 computations (-7.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 18.0ms (85.4% of total)

ival-div: 1.0ms (4.7% of total)

ival-add: 1.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	-3.019474265408887e-8	-2.999809341753491e-8

Compiler

Compiled 12 to 12 computations (0% saved)

simplify30.0ms (0.5%)

Memory

-0.3MiB live, 72.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	146
1	46	146
2	55	146
3	61	146
4	66	146
5	68	146

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal 4725903349047367/20547405865423334012660116730000502599806014854778022888665159777612234977722971961381509907334329887605402222094446162941482157227280483840343026447858909570137592465345486711686186554235635614340989264592896 binary64)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 y #s(literal 15500000000000001165204547206032233725807150497462327308985091086545371841257435672300387067015249549138122303102214158063501312 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 -3499999999999999823171229431452475665453972983986290458991151643863027081164611321367874091978889369455110319705354959634850918463030426540703744 binary64)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal -8108305550381903/213376461852155336770555257303080249508632266314109061132680249976449191610164226288685830427889737303773757138989863694268441652931819682571627393674586561475045042544448465870818505149178048791326880516348371263414103937199246761317244076032 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) x))))
(if (<=.f64 x #s(literal -4533471823554859/151115727451828646838272 binary64)) #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) x))

Outputs
#s(approx (/ (+ x y) (* (* x 2) y)) (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal 4725903349047367/20547405865423334012660116730000502599806014854778022888665159777612234977722971961381509907334329887605402222094446162941482157227280483840343026447858909570137592465345486711686186554235635614340989264592896 binary64)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 y #s(literal 15500000000000001165204547206032233725807150497462327308985091086545371841257435672300387067015249549138122303102214158063501312 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 y #s(literal 4725903349047367/20547405865423334012660116730000502599806014854778022888665159777612234977722971961381509907334329887605402222094446162941482157227280483840343026447858909570137592465345486711686186554235635614340989264592896 binary64)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 y #s(literal 15500000000000001165204547206032233725807150497462327308985091086545371841257435672300387067015249549138122303102214158063501312 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 -3499999999999999823171229431452475665453972983986290458991151643863027081164611321367874091978889369455110319705354959634850918463030426540703744 binary64)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal -8108305550381903/213376461852155336770555257303080249508632266314109061132680249976449191610164226288685830427889737303773757138989863694268441652931819682571627393674586561475045042544448465870818505149178048791326880516348371263414103937199246761317244076032 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y x)) (+.f64 y x)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) x))))
(if (<=.f64 x #s(literal -3499999999999999823171229431452475665453972983986290458991151643863027081164611321367874091978889369455110319705354959634850918463030426540703744 binary64)) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 x #s(literal -8108305550381903/213376461852155336770555257303080249508632266314109061132680249976449191610164226288685830427889737303773757138989863694268441652931819682571627393674586561475045042544448465870818505149178048791326880516348371263414103937199246761317244076032 binary64)) (.f64 (+.f64 x y) (/.f64 #s(literal 1/2 binary64) (.f64 x y))) #s(approx (/ (+ x y) (* (* x 2) y)) (/.f64 #s(literal 1/2 binary64) x))))
(if (<=.f64 x #s(literal -4533471823554859/151115727451828646838272 binary64)) #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) x))

soundness613.0ms (9.9%)

Memory

6.4MiB live, 313.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	372
1	93	372
2	175	372
3	476	372
4	1338	372
5	2520	372
6	4202	372
7	5347	372
8	6256	372
9	6922	372
10	7381	372
11	7982	372
0	8006	366
0	7	20
0	11	20
1	39	20
2	251	20
3	2914	20
0	8839	20

Stop Event

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

Compiler

Compiled 129 to 82 computations (36.4% saved)

preprocess68.0ms (1.1%)

Memory: 9.6MiB live, 210.0MiB allocated
Remove: (sort x y)
Compiler: Compiled 196 to 110 computations (43.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze36.0ms (0.6%)

sample1.1s (18.4%)

explain206.0ms (3.3%)

preprocess45.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize29.0ms (0.5%)

series13.0ms (0.2%)

simplify156.0ms (2.5%)

rewrite487.0ms (7.9%)

eval144.0ms (2.3%)

prune47.0ms (0.8%)

simplify127.0ms (2.1%)

localize114.0ms (1.8%)

series24.0ms (0.4%)

simplify104.0ms (1.7%)

rewrite178.0ms (2.9%)

eval239.0ms (3.9%)

prune31.0ms (0.5%)

simplify225.0ms (3.6%)

localize51.0ms (0.8%)

series37.0ms (0.6%)

simplify236.0ms (3.8%)

rewrite148.0ms (2.4%)

eval169.0ms (2.7%)

prune39.0ms (0.6%)

simplify217.0ms (3.5%)

localize254.0ms (4.1%)

series31.0ms (0.5%)

simplify244.0ms (3.9%)

rewrite222.0ms (3.6%)

eval232.0ms (3.7%)

prune33.0ms (0.5%)

regimes12.0ms (0.2%)

regimes37.0ms (0.6%)

regimes4.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch106.0ms (1.7%)

bsearch36.0ms (0.6%)

bsearch0.0ms (0%)

simplify30.0ms (0.5%)

soundness613.0ms (9.9%)

preprocess68.0ms (1.1%)

end0.0ms (0%)

Profiling