Metrics for Linear.Projection:perspective from linear-1.19.1.3, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze11.0ms (0.2%)

Memory

22.2MiB live, 22.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample993.0ms (21.2%)

Memory

12.1MiB live, 961.7MiB allocated

Samples

401.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 189.0ms

ival-div: 68.0ms (36% of total)

ival-add: 61.0ms (32.3% of total)

ival-sub: 50.0ms (26.5% of total)

ival-true: 7.0ms (3.7% of total)

ival-assert: 4.0ms (2.1% of total)

Bogosity

explain145.0ms (3.1%)

Memory

-22.1MiB live, 100.0MiB allocated

FPErrors

Click to see full error table

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

119.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sub: 3.0ms (33.3% of total)

ival-div: 3.0ms (33.3% of total)

ival-add: 3.0ms (33.3% of total)

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

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

preprocess117.0ms (2.5%)

Memory

14.0MiB live, 87.2MiB allocated

Algorithm

1×	egg-herbie

Rules

528×	`times-frac`
304×	`lower-fma.f64`
304×	`lower-fma.f32`
250×	`div-sub`
216×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	41	37
2	96	35
3	249	35
4	642	35
5	1390	35
6	1427	35
7	1431	35
8	1499	35
9	1556	35
0	5	7
0	8	7
1	11	7
2	16	7
3	22	7
4	31	7
5	54	7
6	90	7
7	129	7
8	213	7
9	439	7
10	843	7
11	970	7
12	972	7
13	1010	7
14	1039	7
0	1039	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 y x) (-.f64 x y))

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify39.0ms (0.8%)

Memory

-8.3MiB live, 38.5MiB 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`
216×	`times-frac`
200×	`div-sub`
176×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	11	15
2	16	15
3	22	15
4	31	15
5	54	15
6	90	15
7	129	15
8	213	15
9	439	15
10	843	15
11	970	15
12	972	15
13	1010	15
14	1039	15
0	1039	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 y x) (-.f64 x y))
(+.f64 x y)
(+.f64 y x)
x
y
(-.f64 x y)

localize111.0ms (2.4%)

Memory

-12.5MiB live, 26.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(+.f64 x y)
accuracy	0.01953125	(/.f64 (+.f64 x y) (-.f64 x y))

Samples

106.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-sub: 96.0ms (96.1% of total)

ival-div: 2.0ms (2% of total)

ival-add: 1.0ms (1% of total)

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

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

series5.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB 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 y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (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 -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 (/ x y)) (+ 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 y)) (/ (* x (- (* -1 x) x)) (pow y 2))) (+ 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 y)) (/ (* (pow x 2) (- (* -1 x) x)) (pow y 3))) (+ 1 (+ (* -1 (/ (* x (- (* -1 x) x)) (pow y 2))) (/ 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 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 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 -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 (/ (- x (* -1 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 (/ (- (+ x (/ (* x (- x (* -1 x))) y)) (* -1 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 (/ (- (+ x (* -1 (/ (- (* -1 (/ (* (pow x 2) (- x (* -1 x))) y)) (* x (- x (* -1 x)))) y))) (* -1 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 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 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 -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 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 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 (/ y x)) (* -1 (/ 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 (+ (/ y x) (/ (* y (- y (* -1 y))) (pow x 2)))) (* -1 (/ 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 (+ (/ y x) (/ (* (pow y 2) (- y (* -1 y))) (pow x 3)))) (+ (* -1 (/ y x)) (* -1 (/ (* y (- y (* -1 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 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 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 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 (/ y x)) (* -1 (/ 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 (- y (* -1 y))) (* -1 (/ (* y (- y (* -1 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 (- y (* -1 y))) (* -1 (/ (+ (* y (- y (* -1 y))) (/ (* (pow y 2) (- y (* -1 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 (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor -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>) () ())) ())

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	y	@	0	((/ (+ x y) (- x y)) (+ x y) (- x y))

simplify407.0ms (8.7%)

Memory

11.0MiB live, 180.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 976×	`lower-fma.f64`
11 976×	`lower-fma.f32`
3 278×	`lower-*.f64`
3 278×	`lower-*.f32`
1 780×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	140	458
1	432	439
2	1258	395
3	5371	377
0	8476	347

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

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

rewrite228.0ms (4.8%)

Memory

-7.9MiB live, 144.9MiB allocated

Rules

4 620×	`lower-*.f64`
4 620×	`lower-*.f32`
3 766×	`lower-fma.f64`
3 766×	`lower-fma.f32`
3 010×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	36	13
2	275	13
3	4496	13
0	8990	13

Stop Event

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

Counts

3 → 463

Calls

Call 1

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

Outputs
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eval196.0ms (4.2%)

Memory: 15.0MiB live, 85.3MiB allocated
Compiler: Compiled 11 925 to 1 303 computations (89.1% saved)

prune106.0ms (2.3%)

Memory

-22.2MiB live, 31.7MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	520	6	526
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	520	7	527

Accuracy

100.0%

Counts

527 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) y (*.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) x))
✓	100.0%	(/.f64 (+.f64 x y) (-.f64 x y))
▶	51.1%	(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
▶	100.0%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (+.f64 y x)))
▶	50.4%	#s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64)))
▶	49.5%	#s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64))
▶	50.5%	#s(approx (/ (+ x y) (- x y)) #s(literal -1 binary64))

Compiler

Compiled 89 to 75 computations (15.7% saved)

simplify88.0ms (1.9%)

Memory

11.4MiB live, 46.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 2 binary64) x)
cost-diff	0	(fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64)))
cost-diff	0	(neg.f64 y)
cost-diff	0	#s(approx (- x y) (neg.f64 y))
cost-diff	0	(+.f64 x y)
cost-diff	0	(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
cost-diff	0	#s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (+ x y) (- x y)) #s(literal -1 binary64))
cost-diff	0	(+.f64 y x)
cost-diff	0	(-.f64 x y)
cost-diff	0	(/.f64 (-.f64 x y) (+.f64 y x))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (+.f64 y x)))

Rules

960×	`lower-fma.f32`
958×	`lower-fma.f64`
640×	`lower-*.f64`
640×	`lower-*.f32`
484×	`div-sub`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	95
0	31	95
1	48	95
2	70	93
3	101	93
4	179	93
5	339	93
6	588	93
7	981	93
8	1395	93
9	1729	93
10	1961	93
11	2086	93
12	2222	93
13	2227	93
14	2227	93
0	2227	93

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize54.0ms (1.1%)

Memory

21.6MiB live, 58.5MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 2 binary64) x)
accuracy	0.08984375	(fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64))
accuracy	31.745843630437513	#s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64)))
accuracy	0	(+.f64 x y)
accuracy	0	(neg.f64 y)
accuracy	0.01953125	(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
accuracy	31.127834102118978	#s(approx (- x y) (neg.f64 y))
accuracy	32.34390343866322	#s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64))
accuracy	31.666399257791483	#s(approx (/ (+ x y) (- x y)) #s(literal -1 binary64))
accuracy	0	(-.f64 x y)
accuracy	0	(+.f64 y x)
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (+.f64 y x)))
accuracy	0.029628759768442016	(/.f64 (-.f64 x y) (+.f64 y x))

Samples

43.0ms

256×

valid

Compiler

Compiled 81 to 17 computations (79% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sub: 16.0ms (54.6% of total)

ival-div: 6.0ms (20.5% of total)

ival-add: 4.0ms (13.6% of total)

ival-mult: 2.0ms (6.8% of total)

ival-neg: 1.0ms (3.4% of total)

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

exact: 0.0ms (0% of total)

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

series29.0ms (0.6%)

Memory

0.9MiB live, 37.4MiB allocated

Counts

13 → 288

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	y	@	0	((/ 1 (/ (- x y) (+ y x))) (/ (- x y) (+ y x)) (- x y) (+ y x) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (+ x y) (- x y) (neg y) (/ (+ x y) (- x y)) (+ (* (/ 2 x) y) 1) (/ 2 x))
1.0ms	y	@	-inf	((/ 1 (/ (- x y) (+ y x))) (/ (- x y) (+ y x)) (- x y) (+ y x) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (+ x y) (- x y) (neg y) (/ (+ x y) (- x y)) (+ (* (/ 2 x) y) 1) (/ 2 x))
1.0ms	y	@	inf	((/ 1 (/ (- x y) (+ y x))) (/ (- x y) (+ y x)) (- x y) (+ y x) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (+ x y) (- x y) (neg y) (/ (+ x y) (- x y)) (+ (* (/ 2 x) y) 1) (/ 2 x))
1.0ms	x	@	inf	((/ 1 (/ (- x y) (+ y x))) (/ (- x y) (+ y x)) (- x y) (+ y x) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (+ x y) (- x y) (neg y) (/ (+ x y) (- x y)) (+ (* (/ 2 x) y) 1) (/ 2 x))
1.0ms	x	@	-inf	((/ 1 (/ (- x y) (+ y x))) (/ (- x y) (+ y x)) (- x y) (+ y x) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (/ (+ x y) (- x y)) (+ x y) (- x y) (neg y) (/ (+ x y) (- x y)) (+ (* (/ 2 x) y) 1) (/ 2 x))

simplify334.0ms (7.1%)

Memory

-25.0MiB live, 297.3MiB allocated

Algorithm

1×	egg-herbie

Rules

15 236×	`lower-fma.f64`
15 236×	`lower-fma.f32`
2 940×	`lower-*.f64`
2 940×	`lower-*.f32`
2 672×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	2440
1	722	2214
2	2125	1995
3	6598	1995
0	8294	1809

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 270

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

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

rewrite181.0ms (3.9%)

Memory

5.2MiB live, 244.0MiB allocated

Rules

5 210×	`lower-fma.f32`
5 208×	`lower-fma.f64`
4 972×	`lower-*.f64`
4 972×	`lower-*.f32`
3 764×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	84
0	31	82
1	124	82
2	849	82
0	8571	82

Stop Event

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

Counts

13 → 961

Calls

Call 1

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

Outputs
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eval454.0ms (9.7%)

Memory: 9.2MiB live, 331.3MiB allocated
Compiler: Compiled 25 057 to 2 780 computations (88.9% saved)

prune40.0ms (0.8%)

Memory

1.9MiB live, 80.8MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	1 230	1	1 231
Fresh	1	0	1
Picked	0	5	5
Done	0	1	1
Total	1 231	7	1 238

Accuracy

100.0%

Counts

1 238 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (-.f64 x y))
✓	51.1%	(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
▶	99.8%	(/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 y (-.f64 (neg.f64 y) x))))
✓	100.0%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (+.f64 y x)))
✓	50.4%	#s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64)))
✓	49.5%	#s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64))
✓	50.5%	#s(approx (/ (+ x y) (- x y)) #s(literal -1 binary64))

Compiler

Compiled 50 to 45 computations (10% saved)

simplify42.0ms (0.9%)

Memory

-19.7MiB live, 26.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -1 binary64) (+.f64 y x))
cost-diff	0	(neg.f64 x)
cost-diff	704	(/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 y (-.f64 (neg.f64 y) x))))
cost-diff	1344	(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 y (-.f64 (neg.f64 y) x)))

Rules

480×	`lower-fma.f32`
478×	`lower-fma.f64`
288×	`lower-*.f64`
288×	`lower-*.f32`
236×	`associate-/r*`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	12	56
0	21	56
1	35	54
2	63	52
3	118	50
4	229	50
5	360	46
6	523	42
7	623	40
8	811	40
9	1102	40
10	1420	40
11	1428	40
12	1458	40
13	1466	40
0	1466	40

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize45.0ms (1%)

Memory

13.8MiB live, 52.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(/.f64 y (-.f64 (neg.f64 y) x))
accuracy	0.01171875	(/.f64 #s(literal -1 binary64) (+.f64 y x))
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 y (-.f64 (neg.f64 y) x))))
accuracy	0.11328125	(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 y (-.f64 (neg.f64 y) x)))

Samples

21.0ms

256×

valid

Compiler

Compiled 60 to 15 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-div: 5.0ms (39.7% of total)

ival-add: 2.0ms (15.9% of total)

ival-mult: 2.0ms (15.9% of total)

ival-neg: 2.0ms (15.9% of total)

ival-sub: 1.0ms (7.9% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.3%)

Memory

-20.4MiB live, 18.3MiB allocated

Counts

5 → 108

Calls

Call 1

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

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

Calls

6 calls:

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

simplify146.0ms (3.1%)

Memory

23.7MiB live, 213.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 674×	`lower-fma.f64`
11 674×	`lower-fma.f32`
3 722×	`lower-+.f64`
3 722×	`lower-+.f32`
3 638×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	375	1559
1	1206	1373
2	3684	1255
0	8592	1175

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

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

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

rewrite138.0ms (2.9%)

Memory

-11.3MiB live, 194.7MiB allocated

Rules

5 098×	`lower-fma.f32`
5 096×	`lower-fma.f64`
2 680×	`lower-*.f64`
2 680×	`lower-*.f32`
1 438×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	43
0	21	41
1	90	39
2	780	26
0	11001	26

Stop Event

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

Counts

5 → 1 027

Calls

Call 1

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

Outputs
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eval180.0ms (3.8%)

Memory: 23.4MiB live, 332.0MiB allocated
Compiler: Compiled 29 849 to 2 415 computations (91.9% saved)

prune101.0ms (2.2%)

Memory

9.2MiB live, 87.0MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	1 135	0	1 135
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	1 135	7	1 142

Accuracy

100.0%

Counts

1 142 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (-.f64 x y))
✓	51.1%	(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
✓	99.8%	(/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 y (-.f64 (neg.f64 y) x))))
✓	100.0%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (+.f64 y x)))
✓	50.4%	#s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64)))
✓	49.5%	#s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64))
✓	50.5%	#s(approx (/ (+ x y) (- x y)) #s(literal -1 binary64))

Compiler

Compiled 114 to 73 computations (36% saved)

regimes20.0ms (0.4%)

Memory

-7.4MiB live, 31.8MiB allocated

Counts

8 → 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))
(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
#s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64)))
(/.f64 (+.f64 x y) (-.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (+.f64 y x)))
(/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 y (-.f64 (neg.f64 y) x))))
(fma.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) y (*.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) x))

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

Calls

3 calls:

13.0ms	(/.f64 (+.f64 x y) (-.f64 x y))
3.0ms	x
3.0ms	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

-19.4MiB live, 26.2MiB 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))
(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
#s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
84.4%	3	`x`
73.8%	3	`y`
98.7%	2	`(/.f64 (+.f64 x y) (-.f64 x y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes2.0ms (0%)

Memory

4.9MiB live, 4.9MiB 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))
(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))

Outputs
(/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y)))
#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
98.4%	2	`(/.f64 (+.f64 x y) (-.f64 x y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes1.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

2 → 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))

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
98.4%	2	`(/.f64 (+.f64 x y) (-.f64 x y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes4.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB 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	x
1.0ms	y
1.0ms	(/.f64 (+.f64 x y) (-.f64 x y))

Results

Accuracy	Segments	Branch
50.5%	1	`y`
50.5%	1	`x`
50.5%	1	`(/.f64 (+.f64 x y) (-.f64 x y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999982487274779	0.9193468993528985

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999982487274779	0.9193468993528985

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch15.0ms (0.3%)

Memory

3.7MiB live, 43.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	-0.9999982487274779	0.9193468993528985

Samples

6.0ms

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)

simplify42.0ms (0.9%)

Memory

-8.7MiB live, 69.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`-commutative-binary64-.f64`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	107
1	33	107
2	36	107
3	37	107

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (-.f64 x y))
(if (<=.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1/2 binary64)) (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y))) #s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64))))
(if (<=.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1/2 binary64)) (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y))) #s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 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 y) (-.f64 x y))
(/.f64 (+.f64 y x) (-.f64 x y))
(if (<=.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1/2 binary64)) (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y))) #s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64))))
(if (<=.f64 (/.f64 (+.f64 y x) (-.f64 x y)) #s(literal -1/2 binary64)) (/.f64 (+.f64 y x) #s(approx (- x y) (neg.f64 y))) #s(approx (/ (+ x y) (- x y)) (fma.f64 (/.f64 #s(literal 2 binary64) x) y #s(literal 1 binary64))))
(if (<=.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal -1/2 binary64)) (/.f64 (+.f64 x y) #s(approx (- x y) (neg.f64 y))) #s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (+.f64 y x) (-.f64 x y)) #s(literal -1/2 binary64)) (/.f64 (+.f64 y x) #s(approx (- x y) (neg.f64 y))) #s(approx (/ (+ x y) (- x y)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (-.f64 x y)) #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 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 y x) (-.f64 x y)) #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 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))

soundness345.0ms (7.3%)

Memory

-24.5MiB live, 223.8MiB allocated

Rules

11 976×	`lower-fma.f64`
11 976×	`lower-fma.f32`
3 278×	`lower-*.f64`
3 278×	`lower-*.f32`
1 780×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	140	458
1	432	439
2	1258	395
3	5371	377
0	8476	347

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 88 to 51 computations (42% saved)

preprocess44.0ms (0.9%)

Memory: -2.2MiB live, 117.7MiB allocated
Compiler: Compiled 172 to 72 computations (58.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze11.0ms (0.2%)

sample993.0ms (21.2%)

explain145.0ms (3.1%)

preprocess117.0ms (2.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify39.0ms (0.8%)

localize111.0ms (2.4%)

series5.0ms (0.1%)

simplify407.0ms (8.7%)

rewrite228.0ms (4.8%)

eval196.0ms (4.2%)

prune106.0ms (2.3%)

simplify88.0ms (1.9%)

localize54.0ms (1.1%)

series29.0ms (0.6%)

simplify334.0ms (7.1%)

rewrite181.0ms (3.9%)

eval454.0ms (9.7%)

prune40.0ms (0.8%)

simplify42.0ms (0.9%)

localize45.0ms (1%)

series16.0ms (0.3%)

simplify146.0ms (3.1%)

rewrite138.0ms (2.9%)

eval180.0ms (3.8%)

prune101.0ms (2.2%)

regimes20.0ms (0.4%)

regimes10.0ms (0.2%)

regimes2.0ms (0%)

regimes1.0ms (0%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch15.0ms (0.3%)

simplify42.0ms (0.9%)

soundness345.0ms (7.3%)

preprocess44.0ms (0.9%)

end0.0ms (0%)

Profiling