Metrics for Data.Colour.RGB:hslsv from colour-2.3.3, D

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze51.0ms (0.8%)

Memory

-6.9MiB live, 30.4MiB 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 9 to 7 computations (22.2% saved)

sample1.2s (18.8%)

Memory

-9.9MiB live, 559.7MiB allocated

Samples

725.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 393.0ms

ival-add: 205.0ms (52.2% of total)

ival-div: 112.0ms (28.5% of total)

ival-sub: 67.0ms (17.1% of total)

ival-true: 6.0ms (1.5% of total)

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

Bogosity

explain331.0ms (5.3%)

Memory

12.2MiB live, 87.5MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

22.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sub: 3.0ms (31% of total)

ival-div: 3.0ms (31% of total)

ival-add: 3.0ms (31% of total)

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

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

preprocess153.0ms (2.5%)

Memory

-20.7MiB live, 34.9MiB allocated

Algorithm

1×	egg-herbie

Rules

410×	`times-frac`
304×	`lower-fma.f64`
304×	`lower-fma.f32`
228×	`associate-l`
182×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	50	37
2	122	35
3	313	35
4	821	35
5	1352	35
6	1401	35
7	1441	35
8	1484	35
9	1496	35
0	5	7
0	8	7
1	14	7
2	21	7
3	33	7
4	60	7
5	104	7
6	171	7
7	279	7
8	458	7
9	773	7
10	781	7
11	819	7
12	848	7
0	848	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify111.0ms (1.8%)

Memory

-12.1MiB live, 26.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

304×	`lower-fma.f64`
304×	`lower-fma.f32`
176×	`lower-*.f64`
176×	`lower-*.f32`
142×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	15
2	21	15
3	33	15
4	60	15
5	104	15
6	171	15
7	279	15
8	458	15
9	773	15
10	781	15
11	819	15
12	848	15
0	848	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize25.0ms (0.4%)

Memory

8.7MiB live, 46.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(+.f64 x y)
accuracy	0.03515625	(/.f64 (-.f64 x y) (+.f64 x y))

Samples

21.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-div: 2.0ms (42.7% of total)

ival-sub: 1.0ms (21.3% of total)

ival-add: 1.0ms (21.3% of total)

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

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

series5.0ms (0.1%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

3 → 72

Calls

Call 1

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

Inputs

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

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

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

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

Calls

6 calls:

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

simplify236.0ms (3.8%)

Memory

-6.9MiB live, 234.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 876×	`lower-fma.f64`
11 876×	`lower-fma.f32`
3 410×	`lower-*.f64`
3 410×	`lower-*.f32`
2 360×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	142	462
1	439	441
2	1225	387
3	4744	375
0	8365	351

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 63

Calls

Call 1

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

rewrite185.0ms (3%)

Memory

2.2MiB live, 230.1MiB allocated

Rules

3 962×	`lower-*.f64`
3 962×	`lower-*.f32`
3 438×	`lower-/.f32`
3 436×	`lower-/.f64`
2 768×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	39	13
2	309	13
3	5153	13
0	8671	13

Stop Event

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

Counts

3 → 497

Calls

Call 1

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

Outputs
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eval90.0ms (1.5%)

Memory: -14.5MiB live, 187.4MiB allocated
Compiler: Compiled 12 341 to 1 248 computations (89.9% saved)

prune14.0ms (0.2%)

Memory

8.9MiB live, 55.9MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	552	8	560
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	552	9	561

Accuracy

100.0%

Counts

561 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(/.f64 (-.f64 x y) (+.f64 x y))
▶	46.5%	(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y))
▶	100.0%	(-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x)))
▶	52.0%	(.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x))
	99.8%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (-.f64 y x))
▶	54.7%	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)))
	46.9%	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 #s(literal 2 binary64) y) x #s(literal -1 binary64)))
	53.5%	#s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64))
▶	45.3%	#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64))

Compiler

Compiled 127 to 103 computations (18.9% saved)

simplify117.0ms (1.9%)

Memory

12.1MiB live, 170.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (neg.f64 y) y (*.f64 x x))
cost-diff	0	(-.f64 y x)
cost-diff	320	(.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x))
cost-diff	832	(/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (*.f64 x x)))
cost-diff	0	(/.f64 y x)
cost-diff	0	(fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x y)
cost-diff	0	(neg.f64 y)
cost-diff	0	#s(approx (- x y) (neg.f64 y))
cost-diff	0	(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y))
cost-diff	0	#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64))
cost-diff	0	(/.f64 y (+.f64 y x))
cost-diff	0	(+.f64 y x)
cost-diff	0	(/.f64 x (+.f64 y x))
cost-diff	896	(-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x)))

Rules

8 956×	`lower-fma.f32`
8 952×	`lower-fma.f64`
2 000×	`lower-*.f32`
1 996×	`lower-*.f64`
1 624×	`times-frac`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	25	129
0	41	117
1	70	117
2	106	117
3	204	117
4	565	117
5	1806	111
6	5941	111
0	8176	111

Stop Event

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

Calls

Call 1

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

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

localize89.0ms (1.4%)

Memory

-10.8MiB live, 106.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 y)
accuracy	0.13671875	(.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x))
accuracy	3.0038732212667223	(fma.f64 (neg.f64 y) y (*.f64 x x))
accuracy	29.326496489677822	(/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (*.f64 x x)))
accuracy	0	(fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))
accuracy	0	(/.f64 y x)
accuracy	29.001776369657108	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)))
accuracy	0	(+.f64 x y)
accuracy	0	(neg.f64 y)
accuracy	0.03515625	(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y))
accuracy	34.34381198454888	#s(approx (- x y) (neg.f64 y))
accuracy	35.007575865039136	#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64))
accuracy	0	(+.f64 y x)
accuracy	0.0078125	(/.f64 x (+.f64 y x))
accuracy	0.01171875	(/.f64 y (+.f64 y x))
accuracy	0.03515625	(-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x)))

Samples

74.0ms

256×

valid

Compiler

Compiled 120 to 24 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-sub: 23.0ms (37.4% of total)

ival-mult: 22.0ms (35.7% of total)

ival-div: 8.0ms (13% of total)

ival-add: 6.0ms (9.7% of total)

ival-neg: 1.0ms (1.6% of total)

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

exact: 0.0ms (0% of total)

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

series39.0ms (0.6%)

Memory

-3.7MiB live, 37.8MiB allocated

Counts

16 → 372

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 y) (#s(alt (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) (patch (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) (patch (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) (patch (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) (patch (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) #<representation binary64>) () ())) ())
#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 (/ y x) (taylor 0 y) (#s(alt (/.f64 y (+.f64 y x)) (patch (/.f64 y (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1 (/ y (pow x 2))) (/ 1 x))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 y x)) (patch (/.f64 y (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 y x)) (patch (/.f64 y (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 y x)) (patch (/.f64 y (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) (patch #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) (patch #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) (patch #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) (patch #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) (patch (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor 0 y) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (/ y (pow x 2)) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x 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 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (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 (taylor inf y) (#s(alt (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) (patch (-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 y) y)) (* -1 (/ (+ (* -1 (* y (- (* -1 y) y))) (/ (* (pow y 2) (- (* -1 y) y)) x)) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) (patch #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1 (/ y x))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1 (/ (+ y (* -1 (/ (pow y 2) x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1 (/ (+ y (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x))) x))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (/ (- (pow y 2) (* -1 (pow y 2))) x)) (* 2 y)) x))) (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (/ (- (+ (* -2 (/ (pow y 3) x)) (pow y 2)) (* -1 (pow y 2))) x)) (* 2 y)) x))) (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) (patch (.f64 (/.f64 (-.f64 y x) (fma.f64 (neg.f64 y) y (.f64 x x))) (-.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())) ())
#s(alt (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	y	@	-inf	((- (/ x (+ y x)) (/ y (+ y x))) (/ x (+ y x)) (+ y x) (/ y (+ y x)) (/ (- x y) (+ x y)) (/ (- x y) (+ x y)) (- x y) (neg y) (+ x y) (/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ y x) (/ (- y x) (+ (* (neg y) y) (* x x))) (* (/ (- y x) (+ (* (neg y) y) (* x x))) (- y x)) (- y x) (+ (* (neg y) y) (* x x)))
3.0ms	y	@	inf	((- (/ x (+ y x)) (/ y (+ y x))) (/ x (+ y x)) (+ y x) (/ y (+ y x)) (/ (- x y) (+ x y)) (/ (- x y) (+ x y)) (- x y) (neg y) (+ x y) (/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ y x) (/ (- y x) (+ (* (neg y) y) (* x x))) (* (/ (- y x) (+ (* (neg y) y) (* x x))) (- y x)) (- y x) (+ (* (neg y) y) (* x x)))
3.0ms	x	@	-inf	((- (/ x (+ y x)) (/ y (+ y x))) (/ x (+ y x)) (+ y x) (/ y (+ y x)) (/ (- x y) (+ x y)) (/ (- x y) (+ x y)) (- x y) (neg y) (+ x y) (/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ y x) (/ (- y x) (+ (* (neg y) y) (* x x))) (* (/ (- y x) (+ (* (neg y) y) (* x x))) (- y x)) (- y x) (+ (* (neg y) y) (* x x)))
2.0ms	y	@	0	((- (/ x (+ y x)) (/ y (+ y x))) (/ x (+ y x)) (+ y x) (/ y (+ y x)) (/ (- x y) (+ x y)) (/ (- x y) (+ x y)) (- x y) (neg y) (+ x y) (/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ y x) (/ (- y x) (+ (* (neg y) y) (* x x))) (* (/ (- y x) (+ (* (neg y) y) (* x x))) (- y x)) (- y x) (+ (* (neg y) y) (* x x)))
2.0ms	x	@	inf	((- (/ x (+ y x)) (/ y (+ y x))) (/ x (+ y x)) (+ y x) (/ y (+ y x)) (/ (- x y) (+ x y)) (/ (- x y) (+ x y)) (- x y) (neg y) (+ x y) (/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ y x) (/ (- y x) (+ (* (neg y) y) (* x x))) (* (/ (- y x) (+ (* (neg y) y) (* x x))) (- y x)) (- y x) (+ (* (neg y) y) (* x x)))

simplify707.0ms (11.4%)

Memory

9.5MiB live, 204.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 600×	`lower-fma.f64`
14 600×	`lower-fma.f32`
3 774×	`lower-*.f64`
3 774×	`lower-*.f32`
3 418×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	472	3465
1	1502	3277
2	4051	2932
0	8347	2739

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 354

Calls

Call 1

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

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

rewrite707.0ms (11.4%)

Memory

7.3MiB live, 285.3MiB allocated

Rules

5 444×	`lower-/.f32`
5 434×	`lower-/.f64`
5 360×	`lower-*.f32`
5 356×	`lower-*.f64`
2 022×	`lower--.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	113
0	41	109
1	182	107
2	1622	107
0	8201	107

Stop Event

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

Counts

16 → 1 129

Calls

Call 1

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

Outputs
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eval257.0ms (4.1%)

Memory: 26.9MiB live, 528.1MiB allocated
Compiler: Compiled 40 953 to 3 859 computations (90.6% saved)

prune34.0ms (0.6%)

Memory

-13.4MiB live, 112.0MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	1 646	3	1 649
Fresh	2	1	3
Picked	1	4	5
Done	0	1	1
Total	1 649	9	1 658

Accuracy

100.0%

Counts

1 658 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(/.f64 (-.f64 x y) (+.f64 x y))
▶	84.0%	(/.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (+.f64 x y))
✓	46.5%	(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y))
✓	100.0%	(-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x)))
▶	99.8%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (-.f64 y x))
✓	54.7%	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)))
▶	46.9%	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal -1 binary64)))
▶	53.5%	#s(approx (/ (- x y) (+ x y)) #s(approx (+ (* (/ y x) -2) 1) #s(literal 1 binary64)))
✓	45.3%	#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64))

Compiler

Compiled 65 to 56 computations (13.8% saved)

simplify323.0ms (5.2%)

Memory

20.5MiB live, 211.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (/.f64 x y) #s(literal 1 binary64))
cost-diff	0	#s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
cost-diff	0	(/.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (+.f64 x y))
cost-diff	1024	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
cost-diff	0	(-.f64 y x)
cost-diff	0	(+.f64 y x)
cost-diff	0	(/.f64 #s(literal -1 binary64) (+.f64 y x))
cost-diff	320	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (-.f64 y x))
cost-diff	0	(/.f64 x y)
cost-diff	0	(fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal -1 binary64))
cost-diff	0	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal -1 binary64)))
cost-diff	0	#s(approx (+ (* (/ y x) -2) 1) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (- x y) (+ x y)) #s(approx (+ (* (/ y x) -2) 1) #s(literal 1 binary64)))

Rules

24 384×	`lower-fma.f32`
24 382×	`lower-fma.f64`
4 036×	`lower-*.f32`
4 032×	`lower-*.f64`
1 872×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	124
0	37	124
1	63	123
2	100	122
3	151	122
4	252	110
5	556	110
6	1212	110
7	3244	110
8	5150	110
9	6081	110
10	6289	110
11	6461	110
12	6594	110
13	6615	110
14	6825	110
15	7082	110
16	7084	110
17	7084	110
18	7084	110
0	8629	108

Stop Event

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

Calls

Call 1

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

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

localize125.0ms (2%)

Memory

-36.0MiB live, 137.3MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x y)
accuracy	0	#s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
accuracy	0.03515625	(/.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (+.f64 x y))
accuracy	9.745328777070517	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
accuracy	0	(-.f64 y x)
accuracy	0	(+.f64 y x)
accuracy	0.015625	(/.f64 #s(literal -1 binary64) (+.f64 y x))
accuracy	0.13671875	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (-.f64 y x))
accuracy	0	(fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal -1 binary64))
accuracy	0	(/.f64 x y)
accuracy	33.984687871764756	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal -1 binary64)))
accuracy	29.001776369657108	#s(approx (/ (- x y) (+ x y)) #s(approx (+ (* (/ y x) -2) 1) #s(literal 1 binary64)))
accuracy	29.264475570125622	#s(approx (+ (* (/ y x) -2) 1) #s(literal 1 binary64))

Samples

76.0ms

256×

valid

Compiler

Compiled 92 to 23 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-mult: 28.0ms (43.6% of total)

ival-add: 25.0ms (39% of total)

ival-div: 7.0ms (10.9% of total)

ival-sub: 4.0ms (6.2% of total)

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

exact: 0.0ms (0% of total)

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

series20.0ms (0.3%)

Memory

26.8MiB live, 64.2MiB allocated

Counts

14 → 336

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ (- x y) (+ x y)) (+ (* (/ x y) 2) -1) (/ x y) (* (/ -1 (+ y x)) (- y x)) (/ -1 (+ y x)) (+ y x) (- y x) (* (- (/ x y) 1) y) (/ (- x y) (+ x y)) (- x y) (- (/ x y) 1) (+ x y))
3.0ms	y	@	-inf	((/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ (- x y) (+ x y)) (+ (* (/ x y) 2) -1) (/ x y) (* (/ -1 (+ y x)) (- y x)) (/ -1 (+ y x)) (+ y x) (- y x) (* (- (/ x y) 1) y) (/ (- x y) (+ x y)) (- x y) (- (/ x y) 1) (+ x y))
2.0ms	x	@	inf	((/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ (- x y) (+ x y)) (+ (* (/ x y) 2) -1) (/ x y) (* (/ -1 (+ y x)) (- y x)) (/ -1 (+ y x)) (+ y x) (- y x) (* (- (/ x y) 1) y) (/ (- x y) (+ x y)) (- x y) (- (/ x y) 1) (+ x y))
1.0ms	y	@	inf	((/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ (- x y) (+ x y)) (+ (* (/ x y) 2) -1) (/ x y) (* (/ -1 (+ y x)) (- y x)) (/ -1 (+ y x)) (+ y x) (- y x) (* (- (/ x y) 1) y) (/ (- x y) (+ x y)) (- x y) (- (/ x y) 1) (+ x y))
1.0ms	y	@	0	((/ (- x y) (+ x y)) (+ (* (/ y x) -2) 1) (/ (- x y) (+ x y)) (+ (* (/ x y) 2) -1) (/ x y) (* (/ -1 (+ y x)) (- y x)) (/ -1 (+ y x)) (+ y x) (- y x) (* (- (/ x y) 1) y) (/ (- x y) (+ x y)) (- x y) (- (/ x y) 1) (+ x y))

simplify195.0ms (3.1%)

Memory

0.5MiB live, 241.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 786×	`lower-fma.f64`
12 786×	`lower-fma.f32`
3 544×	`lower-*.f64`
3 544×	`lower-*.f32`
2 204×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	281	2468
1	862	2271
2	2500	2039
3	7057	2039
0	8088	1891

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 315

Calls

Call 1

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

rewrite305.0ms (4.9%)

Memory

-16.5MiB live, 244.8MiB allocated

Rules

4 806×	`lower-/.f32`
4 800×	`lower-/.f64`
4 208×	`lower-*.f32`
4 204×	`lower-*.f64`
3 824×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	110
0	37	110
1	157	109
2	1217	108
0	8593	106

Stop Event

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

Counts

14 → 679

Calls

Call 1

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

Outputs
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eval149.0ms (2.4%)

Memory: 3.1MiB live, 248.3MiB allocated
Compiler: Compiled 19 705 to 2 219 computations (88.7% saved)

prune21.0ms (0.3%)

Memory

24.7MiB live, 63.4MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	1 043	0	1 043
Fresh	0	0	0
Picked	0	4	4
Done	0	5	5
Total	1 043	9	1 052

Accuracy

100.0%

Counts

1 052 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(/.f64 (-.f64 x y) (+.f64 x y))
✓	84.0%	(/.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) (+.f64 x y))
✓	46.5%	(/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y))
✓	100.0%	(-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x)))
✓	99.8%	(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 y x)) (-.f64 y x))
✓	54.7%	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64)))
✓	46.9%	#s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 x y) #s(literal 2 binary64) #s(literal -1 binary64)))
✓	53.5%	#s(approx (/ (- x y) (+ x y)) #s(approx (+ (* (/ y x) -2) 1) #s(literal 1 binary64)))
✓	45.3%	#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64))

Compiler

Compiled 154 to 96 computations (37.7% saved)

regimes32.0ms (0.5%)

Memory

-23.0MiB live, 16.0MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

24.0ms	y
4.0ms	x
3.0ms	(/.f64 (-.f64 x y) (+.f64 x y))

Results

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

Compiler

Compiled 9 to 9 computations (0% saved)

regimes10.0ms (0.2%)

Memory

13.2MiB live, 13.2MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(/.f64 (-.f64 x y) (+.f64 x y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes9.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
74.0%	3	`x`
83.1%	3	`y`
98.4%	2	`(/.f64 (-.f64 x y) (+.f64 x y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes3.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
98.1%	2	`(/.f64 (-.f64 x y) (+.f64 x y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes12.0ms (0.2%)

Memory

-41.9MiB live, 3.7MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

11.0ms

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

Results

Accuracy	Segments	Branch
97.3%	2	`(/.f64 (-.f64 x y) (+.f64 x y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes2.0ms (0%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

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

Results

Accuracy	Segments	Branch
97.2%	2	`(/.f64 (-.f64 x y) (+.f64 x y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes4.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
45.3%	1	`x`
45.3%	1	`y`
45.3%	1	`(/.f64 (-.f64 x y) (+.f64 x y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9706598739330518	1.0

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9706598739330518	1.0

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9706598739330518	1.0

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch17.0ms (0.3%)

Memory

-14.1MiB live, 22.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-0.9706598739330518	1.0

Samples

5.0ms

240×

valid

Compiler

Compiled 70 to 160 computations (-128.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

simplify28.0ms (0.4%)

Memory

15.0MiB live, 51.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	155
1	45	155
2	54	155
3	62	155
4	69	155
5	72	155
6	73	155

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x)))
(/.f64 (-.f64 x y) (+.f64 x y))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 #s(literal 2 binary64) y) x #s(literal -1 binary64))) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 #s(literal 2 binary64) y) x #s(literal -1 binary64))) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64))

Outputs
(-.f64 (/.f64 x (+.f64 y x)) (/.f64 y (+.f64 y x)))
(/.f64 (-.f64 x y) (+.f64 x y))
(/.f64 (-.f64 x y) (+.f64 y x))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 #s(literal 2 binary64) y) x #s(literal -1 binary64))) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 #s(literal 2 binary64) y) x #s(literal -1 binary64))) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 #s(literal 2 binary64) y) x #s(literal -1 binary64))) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)) #s(approx (/ (- x y) (+ x y)) (fma.f64 (/.f64 #s(literal 2 binary64) y) x #s(literal -1 binary64))) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -1/2 binary64)) (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 x y)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)) (/.f64 #s(approx (- x y) (neg.f64 y)) (+.f64 y x)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 x y)) #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (-.f64 x y) (+.f64 y x)) #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64)) #s(approx (/ (- x y) (+ x y)) #s(literal 1 binary64)))
#s(approx (/ (- x y) (+ x y)) #s(literal -1 binary64))

soundness532.0ms (8.6%)

Memory

31.5MiB live, 347.0MiB allocated

Rules

11 876×	`lower-fma.f64`
11 876×	`lower-fma.f32`
3 962×	`lower-*.f64`
3 962×	`lower-*.f32`
3 438×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	39	13
2	309	13
3	5153	13
0	8671	13
0	142	462
1	439	441
2	1225	387
3	4744	375
0	8365	351

Stop Event

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

Compiler

Compiled 154 to 80 computations (48.1% saved)

preprocess94.0ms (1.5%)

Memory: -32.7MiB live, 125.9MiB allocated
Compiler: Compiled 228 to 84 computations (63.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	15
2	21	15
3	33	15
4	60	15
5	104	15
6	171	15
7	279	15
8	458	15
9	773	15
10	781	15
11	819	15
12	848	15
0	848	15

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	15
2	21	15
3	33	15
4	60	15
5	104	15
6	171	15
7	279	15
8	458	15
9	773	15
10	781	15
11	819	15
12	848	15
0	848	15

start0.0ms (0%)

analyze51.0ms (0.8%)

sample1.2s (18.8%)

explain331.0ms (5.3%)

preprocess153.0ms (2.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify111.0ms (1.8%)

localize25.0ms (0.4%)

series5.0ms (0.1%)

simplify236.0ms (3.8%)

rewrite185.0ms (3%)

eval90.0ms (1.5%)

prune14.0ms (0.2%)

simplify117.0ms (1.9%)

localize89.0ms (1.4%)

series39.0ms (0.6%)

simplify707.0ms (11.4%)

rewrite707.0ms (11.4%)

eval257.0ms (4.1%)

prune34.0ms (0.6%)

simplify323.0ms (5.2%)

localize125.0ms (2%)

series20.0ms (0.3%)

simplify195.0ms (3.1%)

rewrite305.0ms (4.9%)

eval149.0ms (2.4%)

prune21.0ms (0.3%)

regimes32.0ms (0.5%)

regimes10.0ms (0.2%)

regimes9.0ms (0.1%)

regimes3.0ms (0%)

regimes12.0ms (0.2%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch17.0ms (0.3%)

simplify28.0ms (0.4%)

soundness532.0ms (8.6%)

preprocess94.0ms (1.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	15
2	21	15
3	33	15
4	60	15
5	104	15
6	171	15
7	279	15
8	458	15
9	773	15
10	781	15
11	819	15
12	848	15
0	848	15