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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze15.0ms (0.4%)

Memory

7.5MiB live, 46.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
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)

sample613.0ms (14.7%)

Memory

-0.9MiB live, 552.2MiB allocated

Samples

389.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 209.0ms

ival-add: 127.0ms (60.9% of total)

ival-div: 73.0ms (35% of total)

ival-true: 6.0ms (2.9% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

explain84.0ms (2%)

Memory

8.8MiB live, 46.5MiB allocated

FPErrors

Click to see full error table

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

64.0ms

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: 3.0ms (43.8% of total)

ival-add: 3.0ms (43.8% of total)

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

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

preprocess56.0ms (1.3%)

Memory

-23.8MiB live, 15.0MiB 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	31
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 y x))

Outputs
(/.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

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

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

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

localize12.0ms (0.3%)

Memory

13.8MiB live, 13.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 y x)
accuracy	0.01171875	(/.f64 x (+.f64 y x))

Samples

8.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 2.0ms (59.9% of total)

ival-add: 1.0ms (30% of total)

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

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

series3.0ms (0.1%)

Memory

3.8MiB live, 3.8MiB allocated

Counts

2 → 48

Calls

Call 1

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

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

Calls

6 calls:

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

simplify181.0ms (4.3%)

Memory

-15.2MiB live, 99.8MiB 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)

rewrite353.0ms (8.5%)

Memory

-131.2MiB live, 156.4MiB allocated

Rules

5 282×	`lower-/.f32`
5 280×	`lower-/.f64`
3 946×	`lower-fma.f64`
3 946×	`lower-fma.f32`
3 770×	`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	8683	8

Stop Event

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

Counts

2 → 315

Calls

Call 1

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

Outputs
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eval60.0ms (1.4%)

Memory: 31.6MiB live, 68.1MiB allocated
Compiler: Compiled 8 205 to 1 057 computations (87.1% saved)

prune25.0ms (0.6%)

Memory

-10.1MiB live, 25.7MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	352	5	357
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	352	6	358

Accuracy

100.0%

Counts

358 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.9%	(/.f64 x (/.f64 (-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x)) (fma.f64 #s(literal -1 binary64) y x)))
✓	100.0%	(/.f64 x (+.f64 y x))
▶	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
▶	51.2%	#s(approx (/ x (+ y x)) (/.f64 x y))
▶	49.0%	#s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x)))
▶	49.8%	#s(approx (/ x (+ y x)) #s(literal 1 binary64))

Compiler

Compiled 77 to 68 computations (11.7% saved)

simplify179.0ms (4.3%)

Memory

-12.6MiB live, 108.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 x (/.f64 (-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x)) (fma.f64 #s(literal -1 binary64) y x)))
cost-diff	192	(fma.f64 #s(literal -1 binary64) y x)
cost-diff	384	(-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x))
cost-diff	1408	(/.f64 (-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x)) (fma.f64 #s(literal -1 binary64) y x))
cost-diff	0	(/.f64 y x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (/.f64 y x))
cost-diff	0	#s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x)))
cost-diff	0	(/.f64 x y)
cost-diff	0	#s(approx (/ x (+ y x)) (/.f64 x y))
cost-diff	0	#s(approx (/ x (+ y x)) #s(literal 1 binary64))
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))

Rules

8 566×	`lower-fma.f32`
8 564×	`lower-fma.f64`
2 494×	`lower-*.f32`
2 488×	`lower-*.f64`
1 472×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	124
0	38	104
1	71	97
2	139	96
3	417	96
4	1432	96
5	4112	96
6	5450	96
7	7147	96
0	8143	96

Stop Event

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

Calls

Call 1

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

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

localize110.0ms (2.6%)

Memory

10.5MiB live, 99.2MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.01171875	(/.f64 x (/.f64 (-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x)) (fma.f64 #s(literal -1 binary64) y x)))
accuracy	2.1640480508114406	(-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x))
accuracy	30.534957951237576	(/.f64 (-.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) x)) (fma.f64 #s(literal -1 binary64) y x))
accuracy	0	(/.f64 y x)
accuracy	0	(-.f64 #s(literal 1 binary64) (/.f64 y x))
accuracy	32.65373626898453	#s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x)))
accuracy	0	(/.f64 x y)
accuracy	31.24288206812368	#s(approx (/ x (+ y x)) (/.f64 x y))
accuracy	32.12751731108861	#s(approx (/ x (+ y x)) #s(literal 1 binary64))
accuracy	0	(+.f64 y x)
accuracy	0	(neg.f64 x)
accuracy	0.01171875	(/.f64 #s(literal -1 binary64) (+.f64 y x))
accuracy	0.203125	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))

Samples

55.0ms

256×

valid

Compiler

Compiled 117 to 22 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 30.0ms (70.1% of total)

ival-mult: 6.0ms (14% of total)

ival-add: 3.0ms (7% of total)

ival-sub: 2.0ms (4.7% of total)

ival-neg: 2.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

series47.0ms (1.1%)

Memory

-3.0MiB live, 35.7MiB allocated

Counts

14 → 324

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	y	@	-inf	((* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (/ x (+ y x)) (/ x (+ y x)) (/ x y) (/ x (+ y x)) (- 1 (/ y x)) (/ y x) (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x)) (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x) (/ x (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x))))
2.0ms	y	@	0	((* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (/ x (+ y x)) (/ x (+ y x)) (/ x y) (/ x (+ y x)) (- 1 (/ y x)) (/ y x) (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x)) (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x) (/ x (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x))))
2.0ms	x	@	0	((* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (/ x (+ y x)) (/ x (+ y x)) (/ x y) (/ x (+ y x)) (- 1 (/ y x)) (/ y x) (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x)) (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x) (/ x (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x))))
2.0ms	y	@	inf	((* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (/ x (+ y x)) (/ x (+ y x)) (/ x y) (/ x (+ y x)) (- 1 (/ y x)) (/ y x) (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x)) (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x) (/ x (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x))))
2.0ms	x	@	-inf	((* (/ -1 (+ y x)) (neg x)) (/ -1 (+ y x)) (+ y x) (neg x) (/ x (+ y x)) (/ x (+ y x)) (/ x y) (/ x (+ y x)) (- 1 (/ y x)) (/ y x) (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x)) (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x) (/ x (/ (- (neg (* y y)) (* (neg x) x)) (+ (* -1 y) x))))

simplify206.0ms (4.9%)

Memory

-10.9MiB live, 145.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10 238×	`lower-fma.f64`
10 238×	`lower-fma.f32`
3 538×	`lower-*.f64`
3 538×	`lower-*.f32`
1 706×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	245	2464
1	743	2225
2	1878	2113
3	6616	2113
0	8219	2022

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 309

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

rewrite175.0ms (4.2%)

Memory

13.8MiB live, 216.5MiB allocated

Rules

4 972×	`lower-fma.f32`
4 970×	`lower-fma.f64`
3 628×	`lower-*.f32`
3 622×	`lower-*.f64`
3 420×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	99
0	38	79
1	152	72
2	1121	71
0	9282	70

Stop Event

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

Counts

14 → 832

Calls

Call 1

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

Outputs
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eval227.0ms (5.4%)

Memory: 1.6MiB live, 274.3MiB allocated
Compiler: Compiled 22 903 to 2 269 computations (90.1% saved)

prune36.0ms (0.9%)

Memory

6.9MiB live, 85.7MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	1 173	1	1 174
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	1 174	6	1 180

Accuracy

100.0%

Counts

1 180 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.0%	(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 #s(literal -1 binary64) y x)))
✓	100.0%	(/.f64 x (+.f64 y x))
✓	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
✓	51.2%	#s(approx (/ x (+ y x)) (/.f64 x y))
✓	49.0%	#s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x)))
✓	49.8%	#s(approx (/ x (+ y x)) #s(literal 1 binary64))

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify171.0ms (4.1%)

Memory

-23.7MiB live, 136.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (neg.f64 y) y (*.f64 x x))
cost-diff	0	(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 #s(literal -1 binary64) y x)))
cost-diff	192	(fma.f64 #s(literal -1 binary64) y x)
cost-diff	1536	(/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 #s(literal -1 binary64) y x))

Rules

10 016×	`lower-fma.f32`
10 012×	`lower-fma.f64`
2 444×	`lower-*.f32`
2 442×	`lower-*.f64`
1 444×	`lower--.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	9	45
0	17	45
1	28	42
2	49	42
3	102	42
4	266	30
5	775	26
6	2639	26
7	4831	26
8	6914	26
0	8232	26

Stop Event

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

Calls

Call 1

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

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

localize68.0ms (1.6%)

Memory

-7.0MiB live, 98.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 y)
accuracy	0.01171875	(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 #s(literal -1 binary64) y x)))
accuracy	1.753886983238922	(fma.f64 (neg.f64 y) y (*.f64 x x))
accuracy	30.534957951237576	(/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (fma.f64 #s(literal -1 binary64) y x))

Samples

61.0ms

256×

valid

Compiler

Compiled 53 to 13 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-div: 35.0ms (65.1% of total)

ival-neg: 12.0ms (22.3% of total)

ival-mult: 5.0ms (9.3% of total)

ival-add: 2.0ms (3.7% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

13.6MiB live, 13.6MiB allocated

Counts

5 → 108

Calls

Call 1

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

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

Calls

6 calls:

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

simplify183.0ms (4.4%)

Memory

9.6MiB live, 197.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 350×	`lower-fma.f64`
12 350×	`lower-fma.f32`
3 788×	`lower-*.f64`
3 788×	`lower-*.f32`
2 248×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	633
1	395	578
2	1068	550
3	3615	546
0	8304	533

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 99

Calls

Call 1

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

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

rewrite183.0ms (4.4%)

Memory

-8.2MiB live, 238.3MiB allocated

Rules

4 782×	`lower-fma.f32`
4 778×	`lower-fma.f64`
4 266×	`lower-*.f32`
4 264×	`lower-*.f64`
3 344×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	17	39
1	70	24
2	542	20
3	6940	20
0	8027	20

Stop Event

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

Counts

5 → 627

Calls

Call 1

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

Outputs
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eval123.0ms (3%)

Memory: 15.1MiB live, 288.1MiB allocated
Compiler: Compiled 16 763 to 2 006 computations (88% saved)

prune17.0ms (0.4%)

Memory

-18.8MiB live, 63.3MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	725	1	726
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	726	6	732

Accuracy

100.0%

Counts

732 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.0%	(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y)))
✓	100.0%	(/.f64 x (+.f64 y x))
✓	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
✓	51.2%	#s(approx (/ x (+ y x)) (/.f64 x y))
✓	49.0%	#s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x)))
✓	49.8%	#s(approx (/ x (+ y x)) #s(literal 1 binary64))

Compiler

Compiled 38 to 33 computations (13.2% saved)

simplify142.0ms (3.4%)

Memory

11.4MiB live, 202.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 y)
cost-diff	0	(fma.f64 (neg.f64 y) y (*.f64 x x))
cost-diff	0	(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y)))
cost-diff	1536	(/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y))

Rules

7 556×	`lower-fma.f32`
7 554×	`lower-fma.f64`
2 418×	`lower-*.f32`
2 416×	`lower-*.f64`
1 406×	`lower--.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	8	41
0	15	41
1	26	41
2	44	41
3	98	41
4	241	29
5	638	25
6	1758	25
7	5257	25
8	7629	25
0	8042	25

Stop Event

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

Calls

Call 1

Inputs
(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y)))
x
(/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)
y
(*.f64 x x)
(-.f64 x y)

Outputs
(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y)))
(/.f64 x (+.f64 y x))
x
(/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y))
(+.f64 y x)
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)
y
(*.f64 x x)
(-.f64 x y)

localize26.0ms (0.6%)

Memory

-23.8MiB live, 64.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 y)
accuracy	0.01171875	(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y)))
accuracy	1.753886983238922	(fma.f64 (neg.f64 y) y (*.f64 x x))
accuracy	30.534957951237576	(/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y))

Samples

18.0ms

256×

valid

Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions

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

ival-div: 5.0ms (43.9% of total)

ival-mult: 3.0ms (26.4% of total)

ival-sub: 1.0ms (8.8% of total)

ival-add: 1.0ms (8.8% of total)

ival-neg: 1.0ms (8.8% of total)

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

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

series8.0ms (0.2%)

Memory

19.1MiB live, 19.1MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

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

simplify180.0ms (4.3%)

Memory

-10.8MiB live, 192.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 754×	`lower-fma.f64`
13 754×	`lower-fma.f32`
3 970×	`lower-*.f64`
3 970×	`lower-*.f32`
2 324×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	552
1	371	515
2	980	487
3	3684	483
0	8385	470

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite147.0ms (3.5%)

Memory

12.2MiB live, 166.4MiB allocated

Rules

4 664×	`lower-*.f32`
4 662×	`lower-*.f64`
4 446×	`lower-fma.f32`
4 444×	`lower-fma.f64`
3 838×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	33
0	15	33
1	66	17
2	497	17
3	7841	17
0	8401	17

Stop Event

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

Counts

4 → 563

Calls

Call 1

Inputs
(/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y))
(/.f64 x (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 x y)))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)

Outputs
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eval88.0ms (2.1%)

Memory: -5.0MiB live, 111.2MiB allocated
Compiler: Compiled 14 864 to 1 812 computations (87.8% saved)

prune46.0ms (1.1%)

Memory

-2.9MiB live, 35.9MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	640	1	641
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	641	6	647

Accuracy

100.0%

Counts

647 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.5%	(/.f64 (.f64 (-.f64 x y) x) (fma.f64 (neg.f64 y) y (.f64 x x)))
✓	100.0%	(/.f64 x (+.f64 y x))
✓	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (neg.f64 x))
✓	51.2%	#s(approx (/ x (+ y x)) (/.f64 x y))
✓	49.0%	#s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x)))
✓	49.8%	#s(approx (/ x (+ y x)) #s(literal 1 binary64))

Compiler

Compiled 119 to 65 computations (45.4% saved)

regimes11.0ms (0.3%)

Memory

20.3MiB live, 20.3MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 8 computations (-14.3% saved)

regimes9.0ms (0.2%)

Memory

-22.0MiB live, 15.1MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	x
2.0ms	y
2.0ms	(/.f64 x (+.f64 y x))

Results

Accuracy	Segments	Branch
77.0%	3	`x`
78.9%	3	`y`
97.9%	2	`(/.f64 x (+.f64 y x))`

Compiler

Compiled 7 to 8 computations (-14.3% saved)

regimes2.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

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

Results

Accuracy	Segments	Branch
97.6%	2	`(/.f64 x (+.f64 y x))`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes4.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
49.8%	1	`x`
49.8%	1	`y`
49.8%	1	`(/.f64 x (+.f64 y x))`

Compiler

Compiled 7 to 8 computations (-14.3% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0029065307329530043	0.7812629923704648

Compiler

Compiled 8 to 9 computations (-12.5% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0029065307329530043	0.7812629923704648

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify30.0ms (0.7%)

Memory

-5.2MiB live, 78.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	23	64
2	31	64
3	37	64
4	42	64
5	44	64

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 y x))
(if (<=.f64 (/.f64 x (+.f64 y x)) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (/ x (+ y x)) (/.f64 x y)) #s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x))))
(if (<=.f64 (/.f64 x (+.f64 y x)) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (/ x (+ y x)) (/.f64 x y)) #s(approx (/ x (+ y x)) #s(literal 1 binary64)))
#s(approx (/ x (+ y x)) #s(literal 1 binary64))

Outputs
(/.f64 x (+.f64 y x))
(if (<=.f64 (/.f64 x (+.f64 y x)) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (/ x (+ y x)) (/.f64 x y)) #s(approx (/ x (+ y x)) (-.f64 #s(literal 1 binary64) (/.f64 y x))))
(if (<=.f64 (/.f64 x (+.f64 y x)) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (/ x (+ y x)) (/.f64 x y)) #s(approx (/ x (+ y x)) #s(literal 1 binary64)))
#s(approx (/ x (+ y x)) #s(literal 1 binary64))

soundness287.0ms (6.9%)

Memory

-19.6MiB live, 223.3MiB 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×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 52 to 32 computations (38.5% saved)

preprocess49.0ms (1.2%)

Memory: 15.9MiB live, 52.6MiB allocated
Compiler: Compiled 88 to 38 computations (56.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	31
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	31
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%)

analyze15.0ms (0.4%)

sample613.0ms (14.7%)

explain84.0ms (2%)

preprocess56.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize12.0ms (0.3%)

series3.0ms (0.1%)

simplify181.0ms (4.3%)

rewrite353.0ms (8.5%)

eval60.0ms (1.4%)

prune25.0ms (0.6%)

simplify179.0ms (4.3%)

localize110.0ms (2.6%)

series47.0ms (1.1%)

simplify206.0ms (4.9%)

rewrite175.0ms (4.2%)

eval227.0ms (5.4%)

prune36.0ms (0.9%)

simplify171.0ms (4.1%)

localize68.0ms (1.6%)

series7.0ms (0.2%)

simplify183.0ms (4.4%)

rewrite183.0ms (4.4%)

eval123.0ms (3%)

prune17.0ms (0.4%)

simplify142.0ms (3.4%)

localize26.0ms (0.6%)

series8.0ms (0.2%)

simplify180.0ms (4.3%)

rewrite147.0ms (3.5%)

eval88.0ms (2.1%)

prune46.0ms (1.1%)

regimes11.0ms (0.3%)

regimes9.0ms (0.2%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify30.0ms (0.7%)

soundness287.0ms (6.9%)

preprocess49.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	31
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