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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze17.0ms (0.5%)

Memory

-14.5MiB live, 22.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
25%	25%	74.9%	0.1%	0%	0%	0%	3
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	4
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	5
65.6%	65.6%	34.3%	0.1%	0%	0%	0%	6
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	7
82%	82%	18%	0.1%	0%	0%	0%	8
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	9
90.8%	90.7%	9.2%	0.1%	0%	0%	0%	10
93.8%	93.8%	6.1%	0.1%	0%	0%	0%	11
95.4%	95.3%	4.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample541.0ms (14.3%)

Memory

12.6MiB live, 726.3MiB allocated

Samples

317.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-add: 78.0ms (51.1% of total)

ival-div: 65.0ms (42.6% of total)

ival-true: 6.0ms (3.9% of total)

ival-assert: 3.0ms (2% of total)

Bogosity

explain43.0ms (1.1%)

Memory

15.6MiB live, 59.5MiB 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

22.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

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

ival-div: 4.0ms (56.4% of total)

ival-add: 3.0ms (42.3% of total)

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

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

preprocess27.0ms (0.7%)

Memory

-14.1MiB live, 24.8MiB 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))
(/.f64 x (+.f64 y x))

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB 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))
(/.f64 x (+.f64 y x))
x
(+.f64 x y)
(+.f64 y x)
y

localize13.0ms (0.3%)

Memory

15.6MiB live, 15.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.0078125	(/.f64 x (+.f64 x y))

Samples

9.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (56.2% of total)

ival-add: 1.0ms (28.1% of total)

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

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

series6.0ms (0.2%)

Memory

-32.1MiB live, 5.9MiB 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 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 (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 (+.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 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 (/ 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 -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 (/ 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 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 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 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 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 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>) () ())) ())

Calls

6 calls:

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

simplify119.0ms (3.1%)

Memory

31.0MiB live, 106.2MiB 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	360
1	369	342
2	945	318
3	3728	316
0	8239	303

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

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

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

rewrite155.0ms (4.1%)

Memory

8.0MiB live, 113.3MiB 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
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eval77.0ms (2%)

Memory: -15.7MiB live, 80.3MiB allocated
Compiler: Compiled 8 228 to 1 058 computations (87.1% saved)

prune8.0ms (0.2%)

Memory

-17.2MiB live, 21.2MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	354	4	358
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	354	5	359

Accuracy

100.0%

Counts

359 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.1%	(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))))
✓	100.0%	(/.f64 x (+.f64 x y))
▶	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
▶	46.1%	#s(approx (/ x (+ x y)) (/.f64 x y))
▶	54.7%	#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Compiler

Compiled 121 to 37 computations (69.4% saved)

simplify187.0ms (4.9%)

Memory

43.8MiB live, 151.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64))
cost-diff	128	(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))
cost-diff	4224	(fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))))
cost-diff	10368	(-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))
cost-diff	0	(neg.f64 x)
cost-diff	0	(+.f64 y x)
cost-diff	0	(/.f64 #s(literal -1 binary64) (+.f64 y x))
cost-diff	448	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
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

12 316×	`lower-fma.f32`
12 314×	`lower-fma.f64`
6 360×	`lower-*.f32`
6 350×	`lower-*.f64`
2 814×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	420
0	48	384
1	109	334
2	435	304
3	2555	279
0	8521	277

Stop Event

1×	iter limit
1×	node limit
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
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (+.f64 y x))
#s(literal -1 binary64)
(+.f64 y x)
y
x
(neg.f64 x)
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))))
(+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64)))
(pow.f64 (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64))
(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x)
(/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y))
(/.f64 x (+.f64 y x))
x
(+.f64 y x)
y
(-.f64 x y)
#s(literal 3 binary64)
(pow.f64 (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))
(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))
(neg.f64 y)
(fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))))
(-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))
(.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))
(.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 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
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
(/.f64 x (+.f64 y x))
(/.f64 #s(literal -1 binary64) (+.f64 y x))
#s(literal -1 binary64)
(+.f64 y x)
y
x
(neg.f64 x)
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x))) (/.f64 (pow.f64 (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x)) #s(literal 3 binary64)) (.f64 (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x)) (fma.f64 x x (*.f64 y (+.f64 y x))))))
(+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x)) #s(literal 3 binary64)))
(pow.f64 (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64))
(pow.f64 (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (+.f64 y x))) #s(literal 3 binary64))
(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x)
(*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (+.f64 y x)))
(/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y))
(/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x))
(/.f64 x (+.f64 y x))
x
(+.f64 y x)
y
(-.f64 x y)
#s(literal 3 binary64)
(pow.f64 (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))
(pow.f64 (*.f64 (/.f64 x (-.f64 y x)) (/.f64 y (+.f64 y x))) #s(literal 3 binary64))
(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))
(*.f64 (/.f64 x (-.f64 y x)) (/.f64 y (+.f64 y x)))
(neg.f64 y)
(fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))))
(.f64 (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x)) (.f64 (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x)) (fma.f64 x x (*.f64 y (+.f64 y x)))))
(-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))
(.f64 (.f64 (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x)) (+.f64 y x)) (*.f64 (/.f64 y (+.f64 y x)) (/.f64 x (-.f64 x y))))
(.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))
(.f64 (/.f64 (.f64 (*.f64 y y) x) (-.f64 x y)) (/.f64 (/.f64 (/.f64 x (-.f64 x y)) (+.f64 y x)) (+.f64 y x)))
(.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))
(*.f64 (/.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 y x)) (-.f64 y x)) (+.f64 y x)) (/.f64 y (-.f64 x y)))

localize104.0ms (2.8%)

Memory

-15.5MiB live, 113.0MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.221035009768442	(.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))
accuracy	1.292972607530881	(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x)
accuracy	6.483270789488536	(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))
accuracy	16.724803229386175	(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))))
accuracy	0	(+.f64 y x)
accuracy	0	(neg.f64 x)
accuracy	0.015625	(/.f64 #s(literal -1 binary64) (+.f64 y x))
accuracy	0.16796875	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
accuracy	0	(/.f64 x y)
accuracy	34.525622063349495	#s(approx (/ x (+ x y)) (/.f64 x y))
accuracy	28.99339596456294	#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Samples

85.0ms

256×

valid

Compiler

Compiled 418 to 29 computations (93.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-sub: 30.0ms (42% of total)

ival-mult: 15.0ms (21% of total)

ival-div: 11.0ms (15.4% of total)

ival-pow: 7.0ms (9.8% of total)

ival-add: 5.0ms (7% of total)

ival-neg: 2.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

series90.0ms (2.4%)

Memory

-17.5MiB live, 134.3MiB allocated

Counts

14 → 324

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>) () ())
#s(alt (.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x)) (patch (.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (+.f64 y x)) (patch (/.f64 #s(literal -1 binary64) (+.f64 y x)) #<representation binary64>) () ())
#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))) (patch (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))) (patch (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (patch (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (patch (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))))) (patch (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))))) #<representation binary64>) () ())
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Outputs
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#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>) () ())) ())
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#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
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#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
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#s(alt (* y (- (* (pow y 2) (- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow x 7))) (/ 1 (pow x 5)))) (/ 1 (pow x 3)))) (/ 1 x))) (taylor 0 y) (#s(alt (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (patch (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (patch (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	x	@	0	((/ x (+ x y)) (/ x (+ x y)) (/ x y) (* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y))))) (* (/ (/ x (+ y x)) (- x y)) (neg y)) (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (/ (+ (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (pow (* (/ (/ x (+ y x)) (- x y)) (neg y)) 3)) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))))) (* (/ (/ x (+ y x)) (- x y)) x) (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))))
12.0ms	x	@	inf	((/ x (+ x y)) (/ x (+ x y)) (/ x y) (* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y))))) (* (/ (/ x (+ y x)) (- x y)) (neg y)) (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (/ (+ (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (pow (* (/ (/ x (+ y x)) (- x y)) (neg y)) 3)) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))))) (* (/ (/ x (+ y x)) (- x y)) x) (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))))
12.0ms	y	@	inf	((/ x (+ x y)) (/ x (+ x y)) (/ x y) (* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y))))) (* (/ (/ x (+ y x)) (- x y)) (neg y)) (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (/ (+ (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (pow (* (/ (/ x (+ y x)) (- x y)) (neg y)) 3)) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))))) (* (/ (/ x (+ y x)) (- x y)) x) (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))))
11.0ms	y	@	0	((/ x (+ x y)) (/ x (+ x y)) (/ x y) (* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y))))) (* (/ (/ x (+ y x)) (- x y)) (neg y)) (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (/ (+ (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (pow (* (/ (/ x (+ y x)) (- x y)) (neg y)) 3)) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))))) (* (/ (/ x (+ y x)) (- x y)) x) (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))))
10.0ms	x	@	-inf	((/ x (+ x y)) (/ x (+ x y)) (/ x y) (* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y))))) (* (/ (/ x (+ y x)) (- x y)) (neg y)) (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (/ (+ (pow (* (/ (/ x (+ y x)) (- x y)) x) 3) (pow (* (/ (/ x (+ y x)) (- x y)) (neg y)) 3)) (+ (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) x)) (- (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))) (* (* (/ (/ x (+ y x)) (- x y)) x) (* (/ (/ x (+ y x)) (- x y)) (neg y)))))) (* (/ (/ x (+ y x)) (- x y)) x) (* (* (/ (/ x (+ y x)) (- x y)) (neg y)) (* (/ (/ x (+ y x)) (- x y)) (neg y))))

simplify234.0ms (6.2%)

Memory

53.9MiB live, 315.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 728×	`lower-fma.f64`
7 728×	`lower-fma.f32`
4 382×	`lower-*.f64`
4 382×	`lower-*.f32`
4 286×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1527	11148
1	5389	8828
0	9049	8349

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 318

Calls

Call 1

Inputs
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))))
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 y)
(/ x y)
(/ x y)
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))))
(/ -1 x)
(- (/ y (pow x 2)) (/ 1 x))
(- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(- (* y (+ (* y (- (/ y (pow x 4)) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
x
(+ x y)
(+ x y)
(+ x y)
(/ y x)
(* y (+ (/ 1 x) (/ y (pow x 2))))
(* y (+ (* y (+ (* 2 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)))
(* y (+ (* y (+ (* y (+ (* y (- (* 2 (/ 1 (pow x 4))) (* 2 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow x 7))))) (* 2 (/ 1 (pow x 3))))) (/ 1 (pow x 2)))) (/ 1 x)))
1
(+ 1 (/ y x))
(+ 1 (* y (+ (* 3 (/ y (pow x 2))) (/ 1 x))))
(+ 1 (* y (+ (* y (+ (* y (- (* 2 (/ 1 (pow x 3))) (* 2 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow x 6))))) (* 3 (/ 1 (pow x 2))))) (/ 1 x))))
(* -1 (/ y x))
(* y (- (* -1 (/ (pow y 2) (pow x 3))) (/ 1 x)))
(* y (- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow x 5))) (/ 1 (pow x 3)))) (/ 1 x)))
(* y (- (* (pow y 2) (- (* (pow y 2) (- (* -1 (/ (pow y 2) (pow x 7))) (/ 1 (pow x 5)))) (/ 1 (pow x 3)))) (/ 1 x)))
1
(+ 1 (* -1 (* (pow y 2) (+ (* 2 (/ (+ x (* 2 x)) (pow x 3))) (/ (* (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* 2 (pow x 2)) (pow x 2))) (pow x 6))))))
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(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (+ (* -2 y) (* 2 y)) (+ (* -1 (* (pow y 2) (pow (+ (* -2 y) (* 2 y)) 2))) (* (pow y 2) (+ (* -4 (pow y 2)) (* 2 (pow y 2)))))) x)) (+ (* -1 (/ (* (pow y 2) (* (+ (* -4 (pow y 2)) (* 2 (pow y 2))) (+ (* -2 y) (* 2 y)))) x)) (/ (* (pow y 2) (+ (* -2 (pow y 3)) (* 2 (pow y 3)))) x))) (+ (* -1 (* (pow y 2) (pow (+ (* -2 y) (* 2 y)) 2))) (* (pow y 2) (+ (* -4 (pow y 2)) (* 2 (pow y 2)))))) x)) (* (pow y 2) (+ (* -2 y) (* 2 y)))) x)) (pow y 2)) (pow x 2))
(/.f64 (-.f64 (.f64 y y) (/.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 (.f64 y y) (/.f64 (.f64 #s(literal 0 binary64) (.f64 (.f64 y y) #s(literal -2 binary64))) x) (fma.f64 (.f64 y y) (/.f64 (.f64 #s(literal 0 binary64) (.f64 (.f64 y y) #s(literal -2 binary64))) x) (/.f64 #s(literal 0 binary64) x))) (fma.f64 (.f64 (.f64 y y) #s(literal -2 binary64)) (.f64 y y) #s(literal 0 binary64))) x) #s(literal -1 binary64) #s(literal 0 binary64)) x)) (*.f64 x x))

rewrite263.0ms (6.9%)

Memory

-29.3MiB live, 284.2MiB allocated

Rules

5 268×	`lower-fma.f32`
5 266×	`lower-fma.f64`
5 208×	`lower-*.f32`
5 198×	`lower-*.f64`
5 094×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	323
0	48	183
1	221	152
2	2073	151
0	9912	150

Stop Event

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

Counts

14 → 1 289

Calls

Call 1

Inputs
#s(approx (/ x (+ x y)) #s(literal 1 binary64))
#s(approx (/ x (+ x y)) (/.f64 x y))
(/.f64 x y)
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (+.f64 y x))
(+.f64 y x)
(neg.f64 x)
(-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))
(fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))))
(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))
(pow.f64 (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))))
(*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x)
(.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (*.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)))

Outputs
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eval495.0ms (13.1%)

Memory: 37.4MiB live, 625.4MiB allocated
Compiler: Compiled 188 374 to 7 051 computations (96.3% saved)

prune82.0ms (2.2%)

Memory

-21.3MiB live, 135.8MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	2 325	1	2 326
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	2 326	5	2 331

Accuracy

100.0%

Counts

2 331 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (+.f64 x y))
✓	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
▶	45.7%	(*.f64 #s(approx (/ -1 (+ y x)) (/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (neg.f64 x))
✓	46.1%	#s(approx (/ x (+ x y)) (/.f64 x y))
✓	54.7%	#s(approx (/ x (+ x y)) #s(literal 1 binary64))

Compiler

Compiled 30 to 28 computations (6.7% saved)

simplify41.0ms (1.1%)

Memory

20.5MiB live, 55.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

432×	`lower-fma.f64`
432×	`lower-fma.f32`
304×	`lower-*.f32`
302×	`lower-*.f64`
230×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
0	17	49
1	30	49
2	46	49
3	64	49
4	79	49
5	102	49
6	150	49
7	254	49
8	444	49
9	803	49
10	1036	49
11	1075	49
12	1131	49
13	1142	49
14	1147	49
15	1148	49
0	1148	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize58.0ms (1.5%)

Memory

-56.8MiB live, 27.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.0625	(/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
accuracy	0.16796875	(*.f64 #s(approx (/ -1 (+ y x)) (/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (neg.f64 x))
accuracy	34.508024330091224	#s(approx (/ -1 (+ y x)) (/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))

Samples

50.0ms

256×

valid

Compiler

Compiled 35 to 13 computations (62.9% saved)

Precisions

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

ival-div: 5.0ms (44.5% of total)

ival-add: 2.0ms (17.8% of total)

ival-mult: 2.0ms (17.8% of total)

ival-sub: 1.0ms (8.9% of total)

ival-neg: 1.0ms (8.9% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

5 → 108

Calls

Call 1

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

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

6 calls:

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

simplify179.0ms (4.7%)

Memory

22.7MiB live, 176.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 818×	`lower-fma.f64`
11 818×	`lower-fma.f32`
3 602×	`lower-*.f64`
3 602×	`lower-*.f32`
2 008×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	192	930
1	571	822
2	1500	788
3	5494	786
0	8336	755

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite128.0ms (3.4%)

Memory

15.5MiB live, 171.2MiB allocated

Rules

3 498×	`lower-fma.f64`
3 498×	`lower-fma.f32`
3 370×	`lower-*.f32`
3 368×	`lower-*.f64`
3 206×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
0	17	43
1	72	43
2	489	43
3	7818	43
0	8220	43

Stop Event

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

Counts

5 → 327

Calls

Call 1

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

Outputs
#<batchref>
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eval54.0ms (1.4%)

Memory: 7.7MiB live, 112.9MiB allocated
Compiler: Compiled 8 720 to 1 451 computations (83.4% saved)

prune16.0ms (0.4%)

Memory

-11.8MiB live, 28.7MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	435	5	440

Accuracy

100.0%

Counts

440 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (+.f64 x y))
✓	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
✓	46.1%	#s(approx (/ x (+ x y)) (/.f64 x y))
✓	54.7%	#s(approx (/ x (+ x y)) #s(literal 1 binary64))
▶	45.7%	#s(approx (* (/ -1 (+ y x)) (neg x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) x))

Compiler

Compiled 29 to 27 computations (6.9% saved)

simplify54.0ms (1.4%)

Memory

4.5MiB live, 40.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

824×	`lower-fma.f64`
824×	`lower-fma.f32`
528×	`lower-*.f32`
526×	`lower-*.f64`
322×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	45
0	17	45
1	35	44
2	65	42
3	127	42
4	449	42
5	1389	42
6	1653	42
7	1805	42
8	1811	42
9	1811	42
10	1811	42
0	1811	42

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize32.0ms (0.8%)

Memory

21.9MiB live, 57.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 #s(literal 1 binary64) (/.f64 x y))
accuracy	0.0625	(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
accuracy	2.7380312437415046	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) x)
accuracy	34.643681255860855	#s(approx (* (/ -1 (+ y x)) (neg x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) x))

Samples

24.0ms

256×

valid

Compiler

Compiled 37 to 14 computations (62.2% saved)

Precisions

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

ival-div: 7.0ms (40.8% of total)

ival-sub: 3.0ms (17.5% of total)

ival-mult: 3.0ms (17.5% of total)

ival-add: 2.0ms (11.7% of total)

ival-neg: 1.0ms (5.8% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

-21.2MiB live, 14.0MiB allocated

Counts

4 → 96

Calls

Call 1

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

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

Calls

6 calls:

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

simplify179.0ms (4.7%)

Memory

24.1MiB live, 279.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 766×	`lower-fma.f64`
12 766×	`lower-fma.f32`
3 962×	`lower-*.f64`
3 962×	`lower-*.f32`
2 188×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	140	777
1	396	741
2	1027	707
3	3692	705
0	8258	693

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite192.0ms (5.1%)

Memory

28.9MiB live, 224.1MiB allocated

Rules

3 444×	`lower-fma.f64`
3 444×	`lower-fma.f32`
3 306×	`lower-*.f32`
3 304×	`lower-*.f64`
2 982×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	39
0	17	39
1	77	38
2	559	36
3	6911	36
0	8145	36

Stop Event

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

Counts

4 → 293

Calls

Call 1

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

Outputs
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eval56.0ms (1.5%)

Memory: -13.7MiB live, 105.8MiB allocated
Compiler: Compiled 7 121 to 1 241 computations (82.6% saved)

prune9.0ms (0.2%)

Memory

-16.0MiB live, 23.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	389	0	389
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	389	5	394

Accuracy

100.0%

Counts

394 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (+.f64 x y))
✓	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
✓	46.1%	#s(approx (/ x (+ x y)) (/.f64 x y))
✓	54.7%	#s(approx (/ x (+ x y)) #s(literal 1 binary64))
✓	45.7%	#s(approx (* (/ -1 (+ y x)) (neg x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) x))

Compiler

Compiled 171 to 63 computations (63.2% saved)

regimes8.0ms (0.2%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

7 → 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))
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
#s(approx (* (/ -1 (+ y x)) (neg x)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y) x))
(*.f64 #s(approx (/ -1 (+ y x)) (/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (neg.f64 x))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (-.f64 (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y)) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))) (.f64 (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) x) (.f64 (/.f64 (/.f64 x (+.f64 y x)) (-.f64 x y)) (neg.f64 y))))))

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

Calls

3 calls:

3.0ms	x
3.0ms	y
2.0ms	(/.f64 x (+.f64 x y))

Results

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

Compiler

Compiled 7 to 8 computations (-14.3% saved)

regimes5.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB 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
73.9%	3	`x`
82.3%	3	`y`
97.3%	2	`(/.f64 x (+.f64 x y))`

Compiler

Compiled 7 to 8 computations (-14.3% saved)

regimes4.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB 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	y
1.0ms	x
1.0ms	(/.f64 x (+.f64 x y))

Results

Accuracy	Segments	Branch
54.7%	1	`x`
54.7%	1	`y`
54.7%	1	`(/.f64 x (+.f64 x y))`

Compiler

Compiled 7 to 8 computations (-14.3% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.014670063033474151	1.0

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify49.0ms (1.3%)

Memory

-56.7MiB live, 69.9MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

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 5764607523034235/288230376151711744 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))
(/.f64 x (+.f64 y x))
(if (<=.f64 (/.f64 x (+.f64 x y)) #s(literal 5764607523034235/288230376151711744 binary64)) #s(approx (/ x (+ x y)) (/.f64 x y)) #s(approx (/ x (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 y x)) #s(literal 5764607523034235/288230376151711744 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))

soundness220.0ms (5.8%)

Memory

-15.9MiB live, 138.6MiB 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	360
1	369	342
2	945	318
3	3728	316
0	8239	303

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 26 to 20 computations (23.1% saved)

preprocess21.0ms (0.6%)

Memory: 5.9MiB live, 44.2MiB allocated
Compiler: Compiled 52 to 30 computations (42.3% 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%)

analyze17.0ms (0.5%)

sample541.0ms (14.3%)

explain43.0ms (1.1%)

preprocess27.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize13.0ms (0.3%)

series6.0ms (0.2%)

simplify119.0ms (3.1%)

rewrite155.0ms (4.1%)

eval77.0ms (2%)

prune8.0ms (0.2%)

simplify187.0ms (4.9%)

localize104.0ms (2.8%)

series90.0ms (2.4%)

simplify234.0ms (6.2%)

rewrite263.0ms (6.9%)

eval495.0ms (13.1%)

prune82.0ms (2.2%)

simplify41.0ms (1.1%)

localize58.0ms (1.5%)

series6.0ms (0.2%)

simplify179.0ms (4.7%)

rewrite128.0ms (3.4%)

eval54.0ms (1.4%)

prune16.0ms (0.4%)

simplify54.0ms (1.4%)

localize32.0ms (0.8%)

series9.0ms (0.2%)

simplify179.0ms (4.7%)

rewrite192.0ms (5.1%)

eval56.0ms (1.5%)

prune9.0ms (0.2%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify49.0ms (1.3%)

soundness220.0ms (5.8%)

preprocess21.0ms (0.6%)

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