Metrics for AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze14.0ms (0.6%)

Memory

17.3MiB live, 17.3MiB 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 7 to 6 computations (14.3% saved)

sample570.0ms (23.3%)

Memory

6.2MiB live, 823.7MiB allocated

Samples

335.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-add: 68.0ms (50.2% of total)

ival-div: 59.0ms (43.6% of total)

ival-true: 6.0ms (4.4% of total)

ival-assert: 3.0ms (2.2% of total)

Bogosity

explain39.0ms (1.6%)

Memory

32.1MiB live, 70.8MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

17.0ms

512×

valid

Compiler

Compiled 31 to 16 computations (48.4% saved)

Precisions

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

ival-div: 4.0ms (58.1% of total)

ival-add: 3.0ms (43.6% of total)

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

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

preprocess28.0ms (1.1%)

Memory

-3.4MiB live, 32.5MiB allocated

Algorithm

1×	egg-herbie

Rules

134×	`times-frac`
80×	`associate-l`
70×	`unsub-neg`
70×	`associate-/r*`
58×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	35	25
2	72	25
3	145	25
4	324	25
5	504	25
6	628	25
7	648	25
8	675	25
9	687	25
0	4	5
0	6	5
1	7	5
0	7	5

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 4 computations (42.9% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 x (+.f64 x y))

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify3.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 x y)
cost-diff	0	(/.f64 x (+.f64 x y))

Rules

4×	`lower-+.f32`
2×	`lift-+.f64`
2×	`lift-/.f64`
2×	`lower-+.f64`
2×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	7	10
0	7	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.7%)

Memory

-22.3MiB live, 22.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.00390625	(/.f64 x (+.f64 x y))

Samples

13.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-div: 5.0ms (76.7% of total)

ival-add: 1.0ms (15.3% of total)

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

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

series3.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())
#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())

Outputs
#s(alt (/ x y) (taylor 0 x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 (/ x (pow y 2))) (/ 1 y))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) (taylor inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) (taylor inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor 0 y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (/ y (pow x 2)) (/ 1 x)))) (taylor 0 y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)))) (taylor 0 y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ x (* -1 (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y) (taylor inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (/ (pow x 2) y)) y)) (taylor -inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y))) y)) (taylor -inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 3)) y)) (pow x 2)) y))) y)) (taylor -inf y) (#s(alt (/.f64 x (+.f64 x y)) (patch (/.f64 x (+.f64 x 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 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 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 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 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 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>) () ())) ())

Calls

12 calls:

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

simplify288.0ms (11.8%)

Memory

-20.5MiB live, 297.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 194×	`lower-fma.f64`
10 194×	`lower-fma.f32`
3 612×	`lower-*.f64`
3 612×	`lower-*.f32`
2 202×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	369
1	369	348
2	945	318
3	3738	316
0	8250	303

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

Inputs
(/ x y)
(* x (+ (* -1 (/ x (pow y 2))) (/ 1 y)))
(* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)))
(* x (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)))
1
(+ 1 (* -1 (/ y x)))
(- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x))
(- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))
1
(+ 1 (* -1 (/ y x)))
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x)))
1
(+ 1 (* -1 (/ y x)))
(+ 1 (* y (- (/ y (pow x 2)) (/ 1 x))))
(+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))))
(/ x y)
(/ (+ x (* -1 (/ (pow x 2) y))) y)
(/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y)
(/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y)
(/ x y)
(* -1 (/ (+ (* -1 x) (/ (pow x 2) y)) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y))) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 3)) y)) (pow x 2)) y))) y))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))

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

rewrite290.0ms (11.8%)

Memory

23.3MiB live, 445.0MiB allocated

Rules

5 260×	`lower-/.f32`
5 258×	`lower-/.f64`
4 086×	`lower-fma.f64`
4 086×	`lower-fma.f32`
3 762×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	28	8
2	189	8
3	1838	8
0	8647	8

Stop Event

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

Counts

2 → 316

Calls

Call 1

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

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

eval165.0ms (6.7%)

Memory: -168.2MiB live, 79.8MiB allocated
Compiler: Compiled 10 479 to 1 047 computations (90% saved)

prune51.0ms (2.1%)

Memory

37.9MiB live, 112.3MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	356	2	358
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	356	3	359

Accuracy

100.0%

Counts

359 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (+.f64 x y))
▶	53.5%	#s(approx (/ x (+ x y)) (/.f64 x y))
▶	48.5%	#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify15.0ms (0.6%)

Memory

-37.2MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`lower-+.f64`
4×	`lower-/.f32`
4×	`lower-+.f32`
2×	`lift-/.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
0	9	22
1	12	22
0	12	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.7%)

Memory

21.6MiB live, 21.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x y)
accuracy	29.776789606555315	#s(approx (/ x (+ x y)) (/.f64 x y))
accuracy	32.984117796929276	#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Samples

11.0ms

256×

valid

Compiler

Compiled 18 to 8 computations (55.6% saved)

Precisions

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

ival-div: 3.0ms (58.4% of total)

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

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.2%)

Memory

5.0MiB live, 5.0MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs

#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())

#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())

#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())

Outputs
#s(alt (/ x y) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 (/ x (pow y 2))) (/ 1 y))) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (/ y (pow x 2)) (/ 1 x)))) (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)))) (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ x (* -1 (/ (pow x 2) y))) y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (/ (pow x 2) y)) y)) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y))) y)) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 3)) y)) (pow x 2)) y))) y)) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) #s(literal 1 binary64)) (patch #s(approx (/ x (+ x y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1 (/ x (pow y 2))) (/ 1 y))) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))) (taylor 0 x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) (taylor inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (/ y (pow x 2)) (/ 1 x)))) (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)))) (taylor 0 y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ x (* -1 (/ (pow x 2) y))) y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y) (taylor inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (/ (pow x 2) y)) y)) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y))) y)) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 3)) y)) (pow x 2)) y))) y)) (taylor -inf y) (#s(alt #s(approx (/ x (+ x y)) (/.f64 x y)) (patch #s(approx (/ x (+ x y)) (/.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 (/ x y) (taylor 0 x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#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 (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())

Calls

18 calls:

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

simplify359.0ms (14.7%)

Memory

21.6MiB live, 530.3MiB allocated

Algorithm

1×	egg-herbie

Rules

14 628×	`lower-fma.f64`
14 628×	`lower-fma.f32`
3 568×	`lower-*.f64`
3 568×	`lower-*.f32`
2 460×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	690
1	327	648
2	852	588
3	3179	584
0	8023	552

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(/ x y)
(* x (+ (* -1 (/ x (pow y 2))) (/ 1 y)))
(* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)))
(* x (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)))
1
(+ 1 (* -1 (/ y x)))
(- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x))
(- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))
1
(+ 1 (* -1 (/ y x)))
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x)))
1
(+ 1 (* -1 (/ y x)))
(+ 1 (* y (- (/ y (pow x 2)) (/ 1 x))))
(+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))))
(/ x y)
(/ (+ x (* -1 (/ (pow x 2) y))) y)
(/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y)
(/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y)
(/ x y)
(* -1 (/ (+ (* -1 x) (/ (pow x 2) y)) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y))) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 3)) y)) (pow x 2)) y))) y))
(/ x y)
(* x (+ (* -1 (/ x (pow y 2))) (/ 1 y)))
(* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)))
(* x (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)))
1
(+ 1 (* -1 (/ y x)))
(- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x))
(- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))
1
(+ 1 (* -1 (/ y x)))
(+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x)))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x)))
1
(+ 1 (* -1 (/ y x)))
(+ 1 (* y (- (/ y (pow x 2)) (/ 1 x))))
(+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))))
(/ x y)
(/ (+ x (* -1 (/ (pow x 2) y))) y)
(/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y)
(/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y)
(/ x y)
(* -1 (/ (+ (* -1 x) (/ (pow x 2) y)) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y))) y))
(* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 3)) y)) (pow x 2)) y))) y))
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)

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

rewrite307.0ms (12.6%)

Memory

17.2MiB live, 462.2MiB allocated

Rules

5 344×	`lower-/.f32`
5 342×	`lower-/.f64`
4 270×	`lower-fma.f64`
4 270×	`lower-fma.f32`
3 410×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
0	9	19
1	38	19
2	222	19
3	1987	19
0	8765	19

Stop Event

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

Counts

3 → 43

Calls

Call 1

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

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

eval17.0ms (0.7%)

Memory: -2.6MiB live, 30.3MiB allocated
Compiler: Compiled 1 059 to 127 computations (88% saved)

prune9.0ms (0.4%)

Memory

22.7MiB live, 22.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	115	3	118

Accuracy

100.0%

Counts

118 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (+.f64 x y))
✓	53.5%	#s(approx (/ x (+ x y)) (/.f64 x y))
✓	48.5%	#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Compiler

Compiled 30 to 16 computations (46.7% saved)

regimes6.0ms (0.2%)

Memory

-25.2MiB live, 14.5MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	(/.f64 x (+.f64 x y))
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(/.f64 x (+.f64 x y))`

Compiler

Compiled 13 to 8 computations (38.5% saved)

regimes5.0ms (0.2%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
1.0ms	y
1.0ms	(/.f64 x (+.f64 x y))

Results

Accuracy	Segments	Branch
76.1%	3	`x`
82.7%	3	`y`
98.6%	2	`(/.f64 x (+.f64 x y))`

Compiler

Compiled 13 to 8 computations (38.5% saved)

regimes4.0ms (0.2%)

Memory

11.4MiB live, 11.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Outputs
#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Calls

3 calls:

1.0ms	x
1.0ms	y
1.0ms	(/.f64 x (+.f64 x y))

Results

Accuracy	Segments	Branch
48.5%	1	`x`
48.5%	1	`y`
48.5%	1	`(/.f64 x (+.f64 x y))`

Compiler

Compiled 13 to 8 computations (38.5% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.813419823118008e-17	0.9916503704888738

Compiler

Compiled 10 to 9 computations (10% saved)

simplify16.0ms (0.7%)

Memory

-29.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	17	36

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (/.f64 x (+.f64 x y)) #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) #s(approx (/ x (+ x y)) (/.f64 x y)) #s(approx (/ x (+ x y)) #s(literal 1 binary64)))

#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Outputs

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

(if (<=.f64 (/.f64 x (+.f64 x y)) #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) #s(approx (/ x (+ x y)) (/.f64 x y)) #s(approx (/ x (+ x y)) #s(literal 1 binary64)))

#s(approx (/ x (+ x y)) #s(literal 1 binary64))

soundness196.0ms (8%)

Memory

-21.3MiB live, 158.5MiB allocated

Rules

10 194×	`lower-fma.f64`
10 194×	`lower-fma.f32`
3 612×	`lower-*.f64`
3 612×	`lower-*.f32`
2 202×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	369
1	369	348
2	945	318
3	3738	316
0	8250	303

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 34 to 18 computations (47.1% saved)

preprocess21.0ms (0.9%)

Memory: 11.6MiB live, 51.0MiB allocated
Compiler: Compiled 60 to 26 computations (56.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	35
1	35	25
2	72	25
3	145	25
4	324	25
5	504	25
6	628	25
7	648	25
8	675	25
9	687	25
0	4	5
0	6	5
1	7	5
0	7	5

Iter	Nodes	Cost
0	12	35
1	35	25
2	72	25
3	145	25
4	324	25
5	504	25
6	628	25
7	648	25
8	675	25
9	687	25
0	4	5
0	6	5
1	7	5
0	7	5

start0.0ms (0%)

analyze14.0ms (0.6%)

sample570.0ms (23.3%)

explain39.0ms (1.6%)

preprocess28.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize17.0ms (0.7%)

series3.0ms (0.1%)

simplify288.0ms (11.8%)

rewrite290.0ms (11.8%)

eval165.0ms (6.7%)

prune51.0ms (2.1%)

simplify15.0ms (0.6%)

localize17.0ms (0.7%)

series4.0ms (0.2%)

simplify359.0ms (14.7%)

rewrite307.0ms (12.6%)

eval17.0ms (0.7%)

prune9.0ms (0.4%)

regimes6.0ms (0.2%)

regimes5.0ms (0.2%)

regimes4.0ms (0.2%)

bsearch0.0ms (0%)

simplify16.0ms (0.7%)

soundness196.0ms (8%)

preprocess21.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	35
1	35	25
2	72	25
3	145	25
4	324	25
5	504	25
6	628	25
7	648	25
8	675	25
9	687	25
0	4	5
0	6	5
1	7	5
0	7	5