Metrics for Kahan p9 Example

start0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated

analyze6.0ms (0.1%)

Memory

-20.2MiB live, 19.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	18.7%	81.3%	0%	0%	0%	0
0%	0%	18.7%	81.3%	0%	0%	0%	1
0%	0%	18.7%	81.3%	0%	0%	0%	2
50%	9.4%	9.4%	81.3%	0%	0%	0%	3
50%	9.4%	9.4%	81.3%	0%	0%	0%	4
87.5%	16.4%	2.3%	81.3%	0%	0%	0%	5
87.5%	16.4%	2.3%	81.3%	0%	0%	0%	6
96.9%	18.1%	0.6%	81.3%	0%	0%	0%	7
96.9%	18.1%	0.6%	81.3%	0%	0%	0%	8
99.2%	18.6%	0.1%	81.3%	0%	0%	0%	9
99.2%	18.6%	0.1%	81.3%	0%	0%	0%	10
99.8%	18.7%	0%	81.3%	0%	0%	0%	11
99.8%	18.7%	0%	81.3%	0%	0%	0%	12

Compiler

Compiled 27 to 17 computations (37% saved)

sample918.0ms (12.3%)

Memory

23.1MiB live, 1 951.0MiB allocated

Samples

617.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 432.0ms

ival-mult: 162.0ms (37.5% of total)

ival-add: 78.0ms (18.1% of total)

ival-<: 64.0ms (14.8% of total)

ival-div: 52.0ms (12% of total)

ival-sub: 47.0ms (10.9% of total)

ival-and: 16.0ms (3.7% of total)

exact: 10.0ms (2.3% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain99.0ms (1.3%)

Memory

15.2MiB live, 174.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
94	-	1	(1.0071129636301385e-162 -2.712042944503499e-155)	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`
0	-	0	-	`(*.f64 (-.f64 x y) (+.f64 x y))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`y`
0	-	0	-	`(+.f64 x y)`
0	-	0	-	`(-.f64 x y)`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`	o/o	53	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	overflow	53
↳	`(*.f64 y y)`	overflow	53
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	53
`/.f64`	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`	u/u	40	0
↳	`(*.f64 (-.f64 x y) (+.f64 x y))`	underflow	40
↳	`(*.f64 y y)`	underflow	79
↳	`(*.f64 x x)`	underflow	123
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	40

Confusion

	Predicted +	Predicted -
+	93	1
-	0	162

Precision

1.0

Recall

0.9893617021276596

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	93	0	1
-	0	0	162

Precision?

1.0

Recall?

0.9893617021276596

Freqs

test

number	freq
0	163
1	93

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 105 to 31 computations (70.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 10.0ms (47.3% of total)

ival-div: 4.0ms (18.9% of total)

ival-add: 4.0ms (18.9% of total)

ival-sub: 3.0ms (14.2% of total)

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

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

preprocess427.0ms (5.7%)

Memory

3.8MiB live, 239.4MiB allocated

Algorithm

1×	egg-herbie

Rules

16 712×	`lower-fma.f64`
16 712×	`lower-fma.f32`
2 536×	`lower-*.f32`
2 530×	`lower-*.f64`
2 028×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	83
1	94	83
2	301	75
3	799	75
4	2239	75
5	4876	75
6	5512	75
7	5947	75
8	6282	75
9	6355	75
10	6883	75
0	9	15
0	16	15
1	29	15
2	55	15
3	120	15
4	245	15
5	532	15
6	1278	15
7	2989	15
8	5193	15
9	6736	15
10	7289	15
11	7520	15
12	7616	15
13	7625	15
14	7625	15
15	7683	15
16	7687	15
17	7687	15
18	7687	15
19	7946	15
0	8006	14

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(abs x)

Compiler

Compiled 15 to 9 computations (40% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.6%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 15 to 9 computations (40% saved)

simplify293.0ms (3.9%)

Memory

14.2MiB live, 172.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x y)
cost-diff	0	(-.f64 x y)
cost-diff	0	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))

Rules

16 712×	`lower-fma.f64`
16 712×	`lower-fma.f32`
2 536×	`lower-*.f32`
2 530×	`lower-*.f64`
2 028×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	16	43
1	29	43
2	55	43
3	120	43
4	245	43
5	532	43
6	1278	43
7	2989	43
8	5193	43
9	6736	43
10	7289	43
11	7520	43
12	7616	43
13	7625	43
14	7625	43
15	7683	43
16	7687	43
17	7687	43
18	7687	43
19	7946	43
0	8006	41

Stop Event

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

Calls

Call 1

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

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

localize24.0ms (0.3%)

Memory

3.6MiB live, 42.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (-.f64 x y) (+.f64 x y))
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	23.013798665261923	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Samples

18.0ms

256×

valid

Compiler

Compiled 45 to 11 computations (75.6% saved)

Precisions

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

ival-mult: 5.0ms (46.4% of total)

ival-add: 2.0ms (18.5% of total)

ival-sub: 1.0ms (9.3% of total)

ival-div: 1.0ms (9.3% of total)

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

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

series11.0ms (0.1%)

Memory

-20.3MiB live, 18.3MiB allocated

Counts

7 → 144

Calls

Call 1

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

Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ x (* -1 x))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (/ x y)) 1) (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow y 2)) (taylor inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1)) (taylor inf y) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 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 (* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 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 (pow y 2) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (* -1 x)) y)) 1) (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1) (taylor -inf y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
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#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (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 (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x)))) (taylor inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (taylor inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (taylor inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (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 (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) 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 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify200.0ms (2.7%)

Memory

4.5MiB live, 156.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 408×	`lower-fma.f64`
12 408×	`lower-fma.f32`
3 670×	`lower-*.f64`
3 670×	`lower-*.f32`
2 732×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	189	1060
1	601	957
2	1966	905
3	7908	905
0	8902	851

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 135

Calls

Call 1

Inputs
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
x
(+ x y)
(+ x y)
(+ x y)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow x 2)
(+ (* y (+ x (* -1 x))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (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)))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 (pow y 2))
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
-1
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) 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)))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* -1 (pow y 2))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(* -1 y)
(- x y)
(- x y)
(- x y)
y
(+ x y)
(+ x y)
(+ x y)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (pow y 2))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))

Outputs
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -2 binary64) (.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y 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 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow x 2)
(*.f64 x x)
(+ (* y (+ x (* -1 x))) (pow x 2))
(*.f64 x x)
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (.f64 y y))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (.f64 y y))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (.f64 y y))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(* y (- (/ x y) 1))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(* y (- (/ x y) 1))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
y
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(.f64 (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal -1 binary64)) y) y)
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(.f64 (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal -1 binary64)) y) y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (.f64 y y))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (.f64 y y))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (.f64 y y))
-1
#s(literal -1 binary64)
(- (* -1 (/ (+ x (* -1 x)) y)) 1)
#s(literal -1 binary64)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 (/.f64 x y) y y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 (/.f64 x y) y y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 (/.f64 x y) y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(.f64 (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal -1 binary64)) y) y)
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(.f64 (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal -1 binary64)) y) y)
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (.f64 #s(literal -2 binary64) x) (/.f64 x (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (.f64 y y))) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 y #s(literal 4 binary64)))) (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 y y))) (.f64 x x) #s(literal -1 binary64))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(*.f64 (neg.f64 y) y)
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
x
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
x
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x x)
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x x)
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)

rewrite175.0ms (2.3%)

Memory

18.5MiB live, 170.7MiB allocated

Rules

5 274×	`lower-*.f32`
5 268×	`lower-*.f64`
5 048×	`lower-fma.f64`
5 048×	`lower-fma.f32`
4 376×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	41
0	16	41
1	66	41
2	551	41
0	8160	39

Stop Event

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

Counts

7 → 836

Calls

Call 1

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

Outputs
#<batchref>
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eval172.0ms (2.3%)

Memory: 14.0MiB live, 249.9MiB allocated
Compiler: Compiled 27 787 to 2 632 computations (90.5% saved)

prune24.0ms (0.3%)

Memory

-8.1MiB live, 68.3MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	963	8	971
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	964	8	972

Accuracy

99.7%

Counts

972 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.9%	(/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
	63.6%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
	44.3%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
▶	21.7%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 x x)))
▶	29.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))
▶	74.6%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))
	26.9%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64))
▶	73.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 156 to 116 computations (25.6% saved)

simplify141.0ms (1.9%)

Memory

9.2MiB live, 170.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	0	(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
cost-diff	0	(-.f64 x y)
cost-diff	256	(/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
cost-diff	0	(*.f64 #s(literal -2 binary64) y)
cost-diff	0	(/.f64 (*.f64 #s(literal -2 binary64) y) x)
cost-diff	0	(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
cost-diff	0	(+.f64 x y)
cost-diff	0	(-.f64 x y)
cost-diff	0	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 x x)))
cost-diff	0	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))
cost-diff	0	(*.f64 (/.f64 x y) x)
cost-diff	0	(/.f64 #s(literal 2 binary64) y)
cost-diff	0	(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
cost-diff	0	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))

Rules

13 558×	`lower-fma.f32`
13 552×	`lower-fma.f64`
2 740×	`lower-*.f32`
2 732×	`lower-*.f64`
2 008×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	209
0	52	204
1	92	204
2	175	204
3	335	204
4	650	204
5	1277	204
6	2680	204
7	5866	204
0	8160	204

Stop Event

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

Calls

Call 1

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

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

localize93.0ms (1.2%)

Memory

6.6MiB live, 125.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
accuracy	22.20194659269253	(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
accuracy	0	(/.f64 y x)
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	0.12337875976844202	(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))
accuracy	45.34469166857723	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))
accuracy	0	(*.f64 (-.f64 x y) (+.f64 x y))
accuracy	0	(*.f64 x x)
accuracy	23.013798665261923	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 x x)))
accuracy	39.95832523774029	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
accuracy	17.197481483074675	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))
accuracy	0	(/.f64 #s(literal 2 binary64) y)
accuracy	0.08984375	(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))
accuracy	0.13671875	(*.f64 (/.f64 x y) x)
accuracy	16.284999421805303	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))

Samples

75.0ms

256×

valid

Compiler

Compiled 184 to 29 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-div: 33.0ms (59.1% of total)

ival-mult: 10.0ms (17.9% of total)

ival-sub: 6.0ms (10.7% of total)

ival-add: 6.0ms (10.7% of total)

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

exact: 0.0ms (0% of total)

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

series49.0ms (0.7%)

Memory

-41.5MiB live, 56.5MiB allocated

Counts

20 → 444

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow x 2) (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 2 binary64) y) (patch (/.f64 #s(literal 2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ 2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 2 binary64) y) (patch (/.f64 #s(literal 2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ 2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 2 binary64) y) (patch (/.f64 #s(literal 2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ 2 y) (taylor 0 y) (#s(alt (/.f64 #s(literal 2 binary64) y) (patch (/.f64 #s(literal 2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (.f64 (/.f64 x y) x) (patch (.f64 (/.f64 x y) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (.f64 (/.f64 x y) x) (patch (.f64 (/.f64 x y) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (.f64 (/.f64 x y) x) (patch (.f64 (/.f64 x y) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor 0 y) (#s(alt (.f64 (/.f64 x y) x) (patch (.f64 (/.f64 x y) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (patch #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (*.f64 x 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 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 (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor 0 y) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor 0 y) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor 0 y) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor 0 y) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt (* -2 y) (taylor 0 y) (#s(alt (.f64 #s(literal -2 binary64) y) (patch (.f64 #s(literal -2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (* -2 y) (taylor 0 y) (#s(alt (.f64 #s(literal -2 binary64) y) (patch (.f64 #s(literal -2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (* -2 y) (taylor 0 y) (#s(alt (.f64 #s(literal -2 binary64) y) (patch (.f64 #s(literal -2 binary64) y) #<representation binary64>) () ())) ())
#s(alt (* -2 y) (taylor 0 y) (#s(alt (.f64 #s(literal -2 binary64) y) (patch (.f64 #s(literal -2 binary64) y) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) (patch #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ y x)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal -2 binary64) y) x) (patch (/.f64 (.f64 #s(literal -2 binary64) y) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (patch (/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (patch (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (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 (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) 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 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) 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 (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt (/ y x) (taylor -inf x) (#s(alt (/.f64 y x) (patch (/.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	y	@	0	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ (* -2 y) x) (/ y x)) 1) (/ (* -2 y) x) (* -2 y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (* x x) (* (- x y) (+ x y)) (/ y x) (+ y x))
4.0ms	y	@	inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ (* -2 y) x) (/ y x)) 1) (/ (* -2 y) x) (* -2 y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (* x x) (* (- x y) (+ x y)) (/ y x) (+ y x))
3.0ms	y	@	-inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ (* -2 y) x) (/ y x)) 1) (/ (* -2 y) x) (* -2 y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (* x x) (* (- x y) (+ x y)) (/ y x) (+ y x))
2.0ms	x	@	inf	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ (* -2 y) x) (/ y x)) 1) (/ (* -2 y) x) (* -2 y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (* x x) (* (- x y) (+ x y)) (/ y x) (+ y x))
2.0ms	x	@	0	((/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ 2 y) (* (/ x y) x)) -1) (/ 2 y) (* (/ x y) x) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- x y) (+ x y) (+ (* x x) (* y y)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (/ (* -2 y) x) (/ y x)) 1) (/ (* -2 y) x) (* -2 y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (* x x) (* (- x y) (+ x y)) (/ y x) (+ y x))

simplify208.0ms (2.8%)

Memory

19.8MiB live, 247.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 694×	`lower-fma.f64`
11 694×	`lower-fma.f32`
4 622×	`lower-+.f64`
4 622×	`lower-+.f32`
4 608×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	293	3851
1	916	3567
2	2922	3221
0	8387	3012

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 423

Calls

Call 1

Inputs
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 2 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
x
(+ x y)
(+ x y)
(+ x y)
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(* -2 (/ y x))
(* -2 (/ y x))
(* -2 (/ y x))
(* -2 (/ y x))
(* -2 y)
(* -2 y)
(* -2 y)
(* -2 y)
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
x
(+ x (* -1 y))
(+ x (* y (- (* 2 (/ y x)) 1)))
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow x 2)
(+ (* y (+ x (* -1 x))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
x
(+ x y)
(+ x y)
(+ x y)
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (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)))
(pow y 2)
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y
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(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(/ y x)
(/ y x)
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y
(* y (+ 1 (/ x y)))
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(- (* -1 (/ (+ x (* -1 x)) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
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(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
y
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(* -1 (* y (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (- (* -1 (pow x 2)) (pow x 2))) y)) (* -1 (pow x 2))) (pow x 2)) y)) x) y)) 1)))
(pow y 2)
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(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
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(* -1 (pow y 2))
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(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
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(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
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(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
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(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
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(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(* -1 y)
(- x y)
(- x y)
(- x y)
y
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(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(* -2 (/ (pow y 2) (pow x 2)))
(/ (+ (* -2 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -2 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -2 (pow y 2)) (pow x 2)) (pow x 2))
(* -2 (/ y x))
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(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
y
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(+ y (* x (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1)))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow x 2)
(pow x 2)
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(* -1 (pow y 2))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
y
(+ x y)
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1
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(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
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(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
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(/ (pow x 2) y)
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(/ (pow x 2) y)
(/ (pow x 2) y)
1
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(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
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(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
x
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x
(* x (+ 1 (/ y x)))
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(pow x 2)
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1
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(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
1
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1
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(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
x
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(* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))
(pow x 2)
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(/ y x)
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(/ y x)
(/ y x)
x
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1
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(* 2 (/ (pow x 2) (pow y 2)))
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(* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
(/ (pow x 2) y)
1
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1
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x
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x
(* -1 (* x (- (* -1 (/ y x)) 1)))
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(* -1 (* x (- (* -1 (/ y x)) 1)))
(pow x 2)
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1
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(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(* -2 (/ y x))
(* -2 (/ y x))
(* -2 (/ y x))
(* -2 (/ y x))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
x
(* -1 (* x (- (/ y x) 1)))
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(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
(pow x 2)
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(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
x
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(* -1 (* x (- (* -1 (/ y x)) 1)))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -2 binary64) (.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
(* 2 (/ (pow x 2) (pow y 2)))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 x x) y)) y)
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/.f64 (neg.f64 (fma.f64 (.f64 x #s(literal -2 binary64)) x (.f64 y y))) (*.f64 y y))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/.f64 (neg.f64 (fma.f64 (.f64 x #s(literal -2 binary64)) x (.f64 y y))) (*.f64 y y))
(/ (+ (* -1 (pow y 2)) (* 2 (pow x 2))) (pow y 2))
(/.f64 (neg.f64 (fma.f64 (.f64 x #s(literal -2 binary64)) x (.f64 y y))) (*.f64 y y))
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -2 binary64) (.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -2 binary64) (.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y 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)
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
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(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(* -2 (/ y x))
(*.f64 (/.f64 y x) #s(literal -2 binary64))
(* -2 (/ y x))
(*.f64 (/.f64 y x) #s(literal -2 binary64))
(* -2 (/ y x))
(*.f64 (/.f64 y x) #s(literal -2 binary64))
(* -2 (/ y x))
(*.f64 (/.f64 y x) #s(literal -2 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (/.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) y) x) #s(literal 1 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) x) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)

rewrite295.0ms (3.9%)

Memory

-0.1MiB live, 194.4MiB allocated

Rules

5 764×	`lower-/.f32`
5 750×	`lower-/.f64`
4 608×	`lower-*.f32`
4 600×	`lower-*.f64`
2 468×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	187
0	52	182
1	212	182
2	1752	180
0	8184	178

Stop Event

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

Counts

20 → 941

Calls

Call 1

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

Outputs
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eval369.0ms (4.9%)

Memory: -14.4MiB live, 333.1MiB allocated
Compiler: Compiled 32 177 to 3 240 computations (89.9% saved)

prune71.0ms (0.9%)

Memory

-2.1MiB live, 85.4MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	1 448	3	1 451
Fresh	1	2	3
Picked	1	4	5
Done	0	0	0
Total	1 450	9	1 459

Accuracy

99.7%

Counts

1 459 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.9%	(/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
▶	28.2%	(/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))
▶	63.6%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
▶	44.3%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
▶	26.9%	#s(approx (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) #s(literal 1 binary64))
✓	29.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))
✓	74.6%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))
▶	22.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64)))
✓	73.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 158 to 116 computations (26.6% saved)

simplify152.0ms (2%)

Memory

-13.5MiB live, 136.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))
cost-diff	128	(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
cost-diff	192	(fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))
cost-diff	384	(/.f64 (/.f64 y x) x)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff	0	(+.f64 x y)
cost-diff	0	(-.f64 x y)
cost-diff	0	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
cost-diff	0	(/.f64 y (*.f64 x x))
cost-diff	0	(*.f64 #s(literal -2 binary64) y)
cost-diff	0	(fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) #s(literal 1 binary64))
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	0	(+.f64 x y)
cost-diff	0	(-.f64 x y)
cost-diff	128	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))

Rules

11 602×	`lower-fma.f32`
11 592×	`lower-fma.f64`
2 550×	`lower-*.f32`
2 542×	`lower-*.f64`
1 882×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	270
0	62	267
1	107	267
2	192	267
3	381	267
4	878	267
5	1773	267
6	3841	262
7	7123	262
0	8075	258

Stop Event

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

Calls

Call 1

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

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

localize105.0ms (1.4%)

Memory

-0.6MiB live, 123.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.1328125	(/.f64 (/.f64 y x) x)
accuracy	1.2292441222790835	(fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
accuracy	4.976270368401204	(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
accuracy	46.78394228674421	#s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))
accuracy	0	(*.f64 (-.f64 x y) (+.f64 x y))
accuracy	0	(*.f64 y y)
accuracy	11.660835579181505	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	23.013798665261923	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y)))
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	4.980176618401204	(fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
accuracy	9.152181014628825	(/.f64 y (*.f64 x x))
accuracy	45.34469166857723	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64)))
accuracy	46.783618027517704	#s(approx (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) #s(literal 1 binary64))
accuracy	0	(+.f64 x y)
accuracy	0	(*.f64 (-.f64 x y) (+.f64 x y))
accuracy	0	(*.f64 x x)
accuracy	23.013798665261923	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))

Samples

50.0ms

256×

valid

Compiler

Compiled 229 to 33 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 12.0ms (35.4% of total)

ival-div: 11.0ms (32.5% of total)

ival-add: 9.0ms (26.6% of total)

ival-sub: 1.0ms (3% of total)

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

exact: 0.0ms (0% of total)

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

series30.0ms (0.4%)

Memory

29.0MiB live, 64.8MiB allocated

Counts

20 → 444

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow y 2) (pow x 2)))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 y) (#s(alt (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) (patch (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 y x) x) (patch (/.f64 (/.f64 y x) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 2 (/ y x)) 2) x)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 2 (/ y x)) 2) x)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 2 (/ y x)) 2) x)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) (patch (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ y x)) 1) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) (patch (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) (patch (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) (patch (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) (patch (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ y x)) (/ y x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) (patch (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) (patch (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) (patch (/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (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 (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x y) (+.f64 x y)) (patch (.f64 (-.f64 x y) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) 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 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) 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 #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) (patch #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) (patch #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) (patch #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) (patch #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ (* -1 y) (* 2 (/ (pow y 2) x))) x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -2 (pow y 2)) (* 2 (/ (pow y 3) x))) x))) x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	inf	((/ (* (- x y) (+ x y)) (+ (* y y) (* x x))) (- x y) (+ x y) (+ (* y y) (* x x)) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (* -2 y) (/ y (* x x))) 1) (* -2 y) (/ y (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (/ y x) x) (+ (* (/ (/ y x) x) -2) (/ 2 x)) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (* x x) (* (- x y) (+ x y)) (* y y) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x))
4.0ms	x	@	-inf	((/ (* (- x y) (+ x y)) (+ (* y y) (* x x))) (- x y) (+ x y) (+ (* y y) (* x x)) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (* -2 y) (/ y (* x x))) 1) (* -2 y) (/ y (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (/ y x) x) (+ (* (/ (/ y x) x) -2) (/ 2 x)) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (* x x) (* (- x y) (+ x y)) (* y y) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x))
3.0ms	y	@	-inf	((/ (* (- x y) (+ x y)) (+ (* y y) (* x x))) (- x y) (+ x y) (+ (* y y) (* x x)) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (* -2 y) (/ y (* x x))) 1) (* -2 y) (/ y (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (/ y x) x) (+ (* (/ (/ y x) x) -2) (/ 2 x)) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (* x x) (* (- x y) (+ x y)) (* y y) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x))
2.0ms	y	@	0	((/ (* (- x y) (+ x y)) (+ (* y y) (* x x))) (- x y) (+ x y) (+ (* y y) (* x x)) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (* -2 y) (/ y (* x x))) 1) (* -2 y) (/ y (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (/ y x) x) (+ (* (/ (/ y x) x) -2) (/ 2 x)) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (* x x) (* (- x y) (+ x y)) (* y y) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x))
1.0ms	x	@	inf	((/ (* (- x y) (+ x y)) (+ (* y y) (* x x))) (- x y) (+ x y) (+ (* y y) (* x x)) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* (* -2 y) (/ y (* x x))) 1) (* -2 y) (/ y (* x x)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (+ (* x x) (* y y)) (/ (/ y x) x) (+ (* (/ (/ y x) x) -2) (/ 2 x)) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (* x x) (* (- x y) (+ x y)) (* y y) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x))

simplify187.0ms (2.5%)

Memory

-15.4MiB live, 276.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 298×	`lower-fma.f64`
11 298×	`lower-fma.f32`
3 854×	`lower-*.f64`
3 854×	`lower-*.f32`
3 448×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	395	4219
1	1226	3939
2	3938	3621
0	8310	3394

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 426

Calls

Call 1

Inputs
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
x
(+ x y)
(+ x y)
(+ x y)
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(* -2 y)
(* -2 y)
(* -2 y)
(* -2 y)
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ 2 x)
(+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))
(+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))
(+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))
-1
(- (* 2 (/ y x)) 1)
(- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)
(- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(pow x 2)
(+ (* y (+ x (* -1 x))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* -1 y))
(+ x (* y (- (* 2 (/ y x)) 1)))
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 2 (/ y x)) 1)))
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (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)))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
-1
(- (+ (* -1 (/ x y)) (/ x y)) 1)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
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(* -2 (/ y (pow x 2)))
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(* y (- (* 2 (/ 1 (* x y))) (* 2 (/ 1 (pow x 2)))))
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(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
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(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)))) y)) 1)
(- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (- (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (pow x 2)) (* -1 (pow x 2))) y)))) y)) 1)
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y
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(* -1 (* y (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (- (* -1 (pow x 2)) (pow x 2))) y)) (* -1 (pow x 2))) (pow x 2)) y)) x) y)) 1)))
(* -2 (/ (pow y 3) (pow x 2)))
(* -1 (* (pow y 3) (- (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 (* x y))))))
(* -1 (* (pow y 3) (+ (* -1 (/ (- (* 2 (/ 1 x)) (/ 1 y)) y)) (* 2 (/ 1 (pow x 2))))))
(* -1 (* (pow y 3) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 2 (/ 1 x))) y)) (* 2 (/ 1 (pow x 2))))))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(* -1 y)
(- x y)
(- x y)
(- x y)
y
(+ x y)
(+ x y)
(+ x y)
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
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(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(* -2 (/ (pow y 2) (pow x 2)))
(/ (+ (* -2 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -2 (pow y 2)) (pow x 2)) (pow x 2))
(/ (+ (* -2 (pow y 2)) (pow x 2)) (pow x 2))
(/ y (pow x 2))
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(/ y (pow x 2))
(/ y (pow x 2))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(pow y 2)
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(/ y (pow x 2))
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(/ y (pow x 2))
(/ y (pow x 2))
(* -2 (/ y (pow x 2)))
(/ (+ (* -2 y) (* 2 x)) (pow x 2))
(/ (+ (* -2 y) (* 2 x)) (pow x 2))
(/ (+ (* -2 y) (* 2 x)) (pow x 2))
(* -2 (/ (pow y 2) (pow x 2)))
(/ (+ (* -2 (pow y 2)) (* 2 (* x y))) (pow x 2))
(/ (+ (* -2 (pow y 2)) (* x (+ (* -1 x) (* 2 y)))) (pow x 2))
(/ (+ (* -2 (pow y 2)) (* x (+ (* -1 x) (* 2 y)))) (pow x 2))
-1
(- (* 2 (/ (pow x 2) (pow y 2))) 1)
(- (* (pow x 2) (+ (* -2 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 2 (/ (pow x 2) (pow y 6))) (* 2 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2))))) 1)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (pow y 2))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
y
(+ y (* -1 x))
(+ y (* x (- (* 2 (/ x y)) 1)))
(+ y (* x (- (* x (+ (* -2 (/ x (pow y 2))) (* 2 (/ 1 y)))) 1)))
(* -2 (/ (pow y 3) (pow x 2)))
(/ (+ (* -2 (pow y 3)) (* 2 (* x (pow y 2)))) (pow x 2))
(/ (+ (* -2 (pow y 3)) (* x (+ (* -1 (* x y)) (* 2 (pow y 2))))) (pow x 2))
(/ (+ (* -2 (pow y 3)) (* x (+ (* 2 (pow y 2)) (* x (+ x (* -1 y)))))) (pow x 2))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
x
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x
(* x (+ 1 (/ y x)))
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1
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1
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1
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(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ 2 x)
(/ (+ 2 (* -2 (/ y x))) x)
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(/ (+ 2 (* -2 (/ y x))) x)
-1
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(- (+ (* -2 (/ (pow y 2) (pow x 2))) (* 2 (/ y x))) 1)
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1
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(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
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(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
x
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x
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1
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x
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x
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1
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(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
1
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1
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(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ 2 x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(* -1 (/ (- (* 2 (/ y x)) 2) x))
-1
(- (* 2 (/ y x)) 1)
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
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(pow x 2)
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(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* 2 (/ (pow y 2) x))) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -2 (pow y 2)) (* 2 (/ (pow y 3) x))) x))) x)) 1)))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -2 binary64) (.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y 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)
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 #s(literal -2 binary64) (.f64 x x))) (*.f64 y y) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
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#s(literal -1 binary64)
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(fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64))
(- (+ (* -2 (/ (pow y 2) (pow x 2))) (* 2 (/ y x))) 1)
(fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
(- (+ (* -2 (/ (pow y 2) (pow x 2))) (* 2 (/ y x))) 1)
(fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))) (/ (pow y 2) (pow x 2)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) (pow x 3))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))) (/ (pow y 2) (pow x 2)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
x
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))
(fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal -2 binary64) (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x)) x x)
x
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* x (+ 1 (+ (* -2 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* 2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal -2 binary64) (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x)) x x)
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
-1
#s(literal -1 binary64)
(- (* 2 (/ y x)) 1)
(fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64))
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 y (/.f64 y x)) #s(literal 2 binary64) (.f64 y #s(literal -2 binary64))) x))
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 y (/.f64 y x)) #s(literal 2 binary64) (.f64 y #s(literal -2 binary64))) x))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 y (/.f64 y x)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (.f64 (fma.f64 (/.f64 (neg.f64 y) x) (/.f64 y x) #s(literal 1 binary64)) x) x)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
(.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 y) y (/.f64 (pow.f64 y #s(literal 3 binary64)) x))) x) y) #s(literal 1 binary64)) x)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* 2 (/ (pow y 2) x))) x)) 1)))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -2 (pow y 2)) (* 2 (/ (pow y 3) x))) x))) x)) 1)))
(.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 y) y (/.f64 (pow.f64 y #s(literal 3 binary64)) x))) x) y) #s(literal 1 binary64)) x)

rewrite242.0ms (3.2%)

Memory

18.7MiB live, 365.8MiB allocated

Rules

6 444×	`lower-/.f32`
6 430×	`lower-/.f64`
5 126×	`lower-*.f32`
5 118×	`lower-*.f64`
3 070×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	231
0	62	228
1	259	228
2	2099	228
0	9223	228

Stop Event

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

Counts

20 → 996

Calls

Call 1

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

Outputs
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eval384.0ms (5.1%)

Memory: -8.8MiB live, 465.6MiB allocated
Compiler: Compiled 49 135 to 4 532 computations (90.8% saved)

prune121.0ms (1.6%)

Memory

-16.2MiB live, 112.0MiB allocated

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	1 824	5	1 829
Fresh	0	0	0
Picked	2	3	5
Done	0	4	4
Total	1 826	12	1 838

Accuracy

99.7%

Counts

1 838 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.9%	(/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
▶	28.2%	(/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x)))
✓	63.6%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
▶	28.2%	(/.f64 (.f64 (.f64 (/.f64 (-.f64 x y) (+.f64 y x)) (/.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y)) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))
▶	28.2%	(/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) #s(approx (/ (+ ( y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))
▶	45.0%	(.f64 (/.f64 (+.f64 y x) #s(approx (+ ( x x) (* y y)) (*.f64 y y))) (-.f64 x y))
▶	45.0%	(.f64 (+.f64 y x) (/.f64 (-.f64 x y) #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
✓	26.9%	#s(approx (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) #s(literal 1 binary64))
✓	29.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))
✓	74.6%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))
✓	22.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64)))
✓	73.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 279 to 185 computations (33.7% saved)

simplify185.0ms (2.5%)

Memory

-22.9MiB live, 149.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (.f64 (.f64 (/.f64 (-.f64 x y) (+.f64 y x)) (/.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y)) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))
cost-diff	320	(.f64 (.f64 (/.f64 (-.f64 x y) (+.f64 y x)) (/.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y))
cost-diff	704	(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
cost-diff	2496	(*.f64 (/.f64 (-.f64 x y) (+.f64 y x)) (/.f64 (+.f64 y x) (-.f64 x y)))
cost-diff	0	#s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
cost-diff	0	(/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) #s(approx (/ (+ ( y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))
cost-diff	704	(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
cost-diff	1024	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
cost-diff	0	(fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x)
cost-diff	0	#s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x))
cost-diff	0	(-.f64 x y)
cost-diff	0	(/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x)))
cost-diff	0	(-.f64 x y)
cost-diff	0	(/.f64 (-.f64 x y) #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
cost-diff	0	(+.f64 y x)
cost-diff	0	(.f64 (+.f64 y x) (/.f64 (-.f64 x y) #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff	0	(+.f64 y x)
cost-diff	0	(/.f64 (+.f64 y x) #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
cost-diff	0	(.f64 (/.f64 (+.f64 y x) #s(approx (+ ( x x) (* y y)) (*.f64 y y))) (-.f64 x y))

Rules

9 652×	`lower-fma.f32`
9 640×	`lower-fma.f64`
3 134×	`lower-*.f32`
3 124×	`lower-*.f64`
2 740×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	616
0	83	582
1	131	582
2	257	582
3	712	568
4	2315	550
5	7473	550
0	8367	530

Stop Event

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

Calls

Call 1

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

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

localize116.0ms (1.6%)

Memory

32.7MiB live, 226.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1328125	(/.f64 (/.f64 y x) x)
accuracy	1.2292441222790835	(fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
accuracy	4.976270368401204	(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
accuracy	46.78394228674421	#s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))
accuracy	0.1328125	(/.f64 (/.f64 y x) x)
accuracy	1.2292441222790835	(fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
accuracy	4.976270368401204	(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
accuracy	46.78394228674421	#s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x))
accuracy	0.0546875	(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
accuracy	1.2292441222790835	(fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x)
accuracy	4.976270368401204	(fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64))
accuracy	46.78394228674421	#s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x))
accuracy	0	(*.f64 y y)
accuracy	0.197597509768442	(.f64 (+.f64 y x) (/.f64 (-.f64 x y) #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
accuracy	11.660835579181505	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	22.281856923634347	(/.f64 (-.f64 x y) #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(*.f64 y y)
accuracy	0.18359375	(.f64 (/.f64 (+.f64 y x) #s(approx (+ ( x x) (* y y)) (*.f64 y y))) (-.f64 x y))
accuracy	11.660835579181505	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	22.278440750644002	(/.f64 (+.f64 y x) #s(approx (+ (* x x) (* y y)) (*.f64 y y)))

Samples

82.0ms

256×

valid

Compiler

Compiled 451 to 40 computations (91.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 21.0ms (40.4% of total)

ival-div: 17.0ms (32.7% of total)

ival-add: 11.0ms (21.1% of total)

ival-sub: 2.0ms (3.8% of total)

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

exact: 0.0ms (0% of total)

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

series44.0ms (0.6%)

Memory

-28.0MiB live, 130.5MiB allocated

Counts

23 → 540

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	0	((* (/ (+ y x) (+ (* x x) (* y y))) (- x y)) (/ (+ y x) (+ (* x x) (* y y))) (+ y x) (+ (* x x) (* y y)) (* (+ y x) (/ (- x y) (+ (* x x) (* y y)))) (/ (- x y) (+ (* x x) (* y y))) (- x y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (* (- (/ x y) 1) y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (- x y) (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (+ (* y y) (* x x)) (+ y x))) (* y y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (+ (* (/ y x) -2) 2) x) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (/ (/ y x) x))
4.0ms	x	@	inf	((* (/ (+ y x) (+ (* x x) (* y y))) (- x y)) (/ (+ y x) (+ (* x x) (* y y))) (+ y x) (+ (* x x) (* y y)) (* (+ y x) (/ (- x y) (+ (* x x) (* y y)))) (/ (- x y) (+ (* x x) (* y y))) (- x y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (* (- (/ x y) 1) y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (- x y) (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (+ (* y y) (* x x)) (+ y x))) (* y y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (+ (* (/ y x) -2) 2) x) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (/ (/ y x) x))
3.0ms	y	@	-inf	((* (/ (+ y x) (+ (* x x) (* y y))) (- x y)) (/ (+ y x) (+ (* x x) (* y y))) (+ y x) (+ (* x x) (* y y)) (* (+ y x) (/ (- x y) (+ (* x x) (* y y)))) (/ (- x y) (+ (* x x) (* y y))) (- x y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (* (- (/ x y) 1) y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (- x y) (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (+ (* y y) (* x x)) (+ y x))) (* y y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (+ (* (/ y x) -2) 2) x) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (/ (/ y x) x))
2.0ms	y	@	inf	((* (/ (+ y x) (+ (* x x) (* y y))) (- x y)) (/ (+ y x) (+ (* x x) (* y y))) (+ y x) (+ (* x x) (* y y)) (* (+ y x) (/ (- x y) (+ (* x x) (* y y)))) (/ (- x y) (+ (* x x) (* y y))) (- x y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (* (- (/ x y) 1) y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (- x y) (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (+ (* y y) (* x x)) (+ y x))) (* y y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (+ (* (/ y x) -2) 2) x) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (/ (/ y x) x))
2.0ms	x	@	-inf	((* (/ (+ y x) (+ (* x x) (* y y))) (- x y)) (/ (+ y x) (+ (* x x) (* y y))) (+ y x) (+ (* x x) (* y y)) (* (+ y x) (/ (- x y) (+ (* x x) (* y y)))) (/ (- x y) (+ (* x x) (* y y))) (- x y) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (* (- (/ x y) 1) y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) (- x y) (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (* (* (/ (- x y) (+ y x)) (/ (+ y x) (- x y))) (- x y)) (/ (+ (* y y) (* x x)) (+ y x))) (* y y) (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) (/ (+ (* (/ y x) -2) 2) x) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* (+ (* (+ (* (/ (/ y x) x) -2) (/ 2 x)) y) -1) y) x) (/ (/ y x) x))

simplify211.0ms (2.8%)

Memory

23.3MiB live, 295.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 960×	`lower-fma.f64`
9 960×	`lower-fma.f32`
4 302×	`lower-*.f64`
4 302×	`lower-*.f32`
2 814×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	509	5365
1	1569	5032
2	4690	4614
0	8669	4354

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 504

Calls

Call 1

Inputs
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(/ 1 x)
(+ (/ 1 x) (/ y (pow x 2)))
(+ (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (+ (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
x
(+ x y)
(+ x y)
(+ x y)
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(/ 1 x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(+ (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (- (* y (- (/ y (pow x 4)) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
1
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
x
(+ x (* -1 y))
(+ x (* y (- (* 2 (/ y x)) 1)))
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 2 (/ y x)) 1)))
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x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(/ 1 x)
(* -1 (/ (- (/ y x) 1) x))
(* -1 (/ (- (* -1 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x)) 1) x))
(* -1 (/ (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow y 3) x)) (pow y 2)) x))) x)) 1) x))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* 2 (/ (pow y 2) x))) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -2 (pow y 2)) (* 2 (/ (pow y 3) x))) x))) x)) 1)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
-1
(- (* 2 (/ y x)) 1)
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
1
1
1
1
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
1
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
-1
(- (* 2 (/ y x)) 1)
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(/ 2 x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(* -1 (/ (- (* 2 (/ y x)) 2) x))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* 2 (/ (pow y 2) x))) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -2 (pow y 2)) (* 2 (/ (pow y 3) x))) x))) x)) 1)))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))
(/ y (pow x 2))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) y) y) (fma.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (/ 1 x) (/ y (pow x 2)))
(+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(+ (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 y (pow.f64 x #s(literal 3 binary64)))) y (/.f64 #s(literal 1 binary64) x))
(+ (* y (+ (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 y (pow.f64 x #s(literal 4 binary64)))) y (/.f64 #s(literal 1 binary64) (*.f64 x x))) y (/.f64 #s(literal 1 binary64) x))
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) y) y) (fma.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(+ (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(fma.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 y (pow.f64 x #s(literal 3 binary64)))) y (/.f64 #s(literal 1 binary64) x))
(+ (* y (- (* y (- (/ y (pow x 4)) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(fma.f64 (fma.f64 (-.f64 (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y (/.f64 #s(literal -1 binary64) (*.f64 x x))) y (/.f64 #s(literal 1 binary64) x))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) y) y) (fma.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 2 (/ y x)) 1)))
(fma.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 2 (/ y x)) 1)))
(fma.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
-1
#s(literal -1 binary64)
(- (* 2 (/ y x)) 1)
(fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64))
(- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)
(fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
(- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)
(fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) y) y) (fma.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
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
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* 2 (/ (pow y 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) y) y) (fma.f64 y (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -2 (/ (pow y 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 y y) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 y y) #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
-1
#s(literal -1 binary64)
(- (* 2 (/ y x)) 1)
(fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64))
(- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)
(fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
(- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)
(fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))
(fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))
(+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))
(fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))
(+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))
(fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 2 (/ y x)) 1)))
(fma.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 2 (/ y x)) 1)))
(fma.f64 (fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -2 (/ y (pow x 2))) (* 2 (/ 1 x)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (/ x y)) y)
(/.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(/ (+ 1 (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/.f64 (+.f64 (/.f64 (fma.f64 (neg.f64 x) (/.f64 x y) x) y) #s(literal 1 binary64)) y)
(/ (- (+ 1 (+ (* -1 (/ (pow x 3) (pow y 3))) (/ x y))) (/ (pow x 2) (pow y 2))) y)
(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 3 binary64))) (/.f64 (fma.f64 (neg.f64 x) (/.f64 x y) x) y)) y)
y
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y) y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y) y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y) y)
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(/ -1 y)
(/.f64 #s(literal -1 binary64) y)
(/ (- (/ x y) 1) y)
(/.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(/ (- (+ (/ x y) (/ (pow x 2) (pow y 2))) 1) y)
(/.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) y)
(/ (- (+ (* -1 (/ (pow x 3) (pow y 3))) (/ x y)) (+ 1 (* -1 (/ (pow x 2) (pow y 2))))) y)
(/.f64 (-.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (-.f64 (/.f64 x y) #s(literal 1 binary64))) (pow.f64 (/.f64 x y) #s(literal 3 binary64))) y)
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(* y (- (/ x y) 1))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(* y (- (/ x y) 1))
(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
-1
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (/ x y)) 1)
#s(literal -1 binary64)
(- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
(- (+ (* -1 (/ x y)) (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3))) (+ (/ x y) (/ (pow x 2) (pow y 2))))) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 x (/.f64 x y)) #s(literal -1 binary64))
y
(* y (+ 1 (* -1 (/ x y))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(* y (- (+ 1 (/ (pow x 2) (pow y 2))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))))
(fma.f64 (/.f64 (-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) y) x) y) y y)
(* y (- (+ 1 (+ (* -1 (/ (* x (- (pow x 2) (* -1 (pow x 2)))) (pow y 3))) (/ (pow x 2) (pow y 2)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))))
(fma.f64 y (fma.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) (/.f64 x (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) y) x) y)) y)
(* -2 (/ (pow y 3) (pow x 2)))
(/.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -2 binary64)) x) x)
(* (pow y 3) (- (* 2 (/ 1 (* x y))) (* 2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) y) (/.f64 #s(literal 2 binary64) (.f64 x x))) (pow.f64 y #s(literal 3 binary64)))
(* (pow y 3) (- (/ 2 (* x y)) (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow y 2)))))
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(fma.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -2 (/ y x))) x)
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
(/ (+ 2 (* -2 (/ y x))) x)
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
(/ (+ 2 (* -2 (/ y x))) x)
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
x
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* x (- (+ 1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* x (- (+ 1 (+ (* -1 (/ (* y (- (pow y 2) (* -1 (pow y 2)))) (pow x 3))) (/ (pow y 2) (pow x 2)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))))
(fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal -2 binary64) (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x)) x x)
x
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* x (+ 1 (+ (* -2 (/ (pow y 3) (pow x 3))) (+ (* -1 (/ y x)) (* 2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal -2 binary64) (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x)) x x)
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* -1 (/ y x)) 1) x))
(/.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ y (* -1 (/ (pow y 2) x))) x)) 1) x))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (neg.f64 y) (/.f64 y x) y) x)) (neg.f64 x))
(* -1 (/ (- (* -1 (/ (+ y (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x))) x)) 1) x))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 y (/.f64 (fma.f64 y y (/.f64 (pow.f64 y #s(literal 3 binary64)) x)) x)) x)) (neg.f64 x))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ y x) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (/ (- (* -1 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x)) 1) x))
(/.f64 (+.f64 (/.f64 (neg.f64 (fma.f64 y (/.f64 y x) y)) x) #s(literal 1 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow y 3) x)) (pow y 2)) x))) x)) 1) x))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (neg.f64 y) y (/.f64 (pow.f64 y #s(literal 3 binary64)) x)) x) y) x) #s(literal 1 binary64)) x)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) y) y (/.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -2 binary64)) x)) x) y) x) #s(literal 1 binary64)) x)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* 2 (/ (pow y 2) x))) x)) 1)))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -2 (pow y 2)) (* 2 (/ (pow y 3) x))) x))) x)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) y) y (/.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -2 binary64)) x)) x) y) x) #s(literal 1 binary64)) x)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
-1
#s(literal -1 binary64)
(- (* 2 (/ y x)) 1)
(fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64))
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 y (/.f64 y x)) #s(literal 2 binary64) (.f64 y #s(literal -2 binary64))) x))
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 y (/.f64 y x)) #s(literal 2 binary64) (.f64 y #s(literal -2 binary64))) x))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ y x)) (/ y x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) (* -1 (/ (pow y 2) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (- (pow y 2) (* -1 (pow y 2)))) (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x))) x))) x)))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 y (.f64 x x)) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ y x)) 1)
(fma.f64 (/.f64 y x) #s(literal 2 binary64) #s(literal -1 binary64))
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 y (/.f64 y x)) #s(literal 2 binary64) (.f64 y #s(literal -2 binary64))) x))
(- (* -1 (/ (+ (* -2 y) (* 2 (/ (pow y 2) x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 y (/.f64 y x)) #s(literal 2 binary64) (.f64 y #s(literal -2 binary64))) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
(* -1 (/ (- (* 2 (/ y x)) 2) x))
(/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (pow y 2)) (pow y 2)) x)) y) x)) 1)))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* y (- (* -1 (pow y 2)) (pow y 2))) x)) (* -1 (pow y 2))) (pow y 2)) x)) y) x)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) y) y (/.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -2 binary64)) x)) x) y) x) #s(literal 1 binary64)) x)
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* 2 (/ (pow y 2) x))) x)) 1)))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 2 binary64) (neg.f64 y)) x) x x)
(* -1 (* x (- (* -1 (/ (+ (* -1 y) (* -1 (/ (+ (* -2 (pow y 2)) (* 2 (/ (pow y 3) x))) x))) x)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) y) y (/.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -2 binary64)) x)) x) y) x) #s(literal 1 binary64)) x)
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))

rewrite232.0ms (3.1%)

Memory

22.5MiB live, 366.9MiB allocated

Rules

5 258×	`lower-/.f32`
5 234×	`lower-/.f64`
4 802×	`lower-*.f32`
4 792×	`lower-*.f64`
2 654×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	423
0	82	407
1	318	377
2	2755	377
0	8878	367

Stop Event

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

Counts

23 → 857

Calls

Call 1

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

Outputs
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eval750.0ms (10%)

Memory: -113.8MiB live, 610.5MiB allocated
Compiler: Compiled 79 358 to 5 147 computations (93.5% saved)

prune163.0ms (2.2%)

Memory

-14.9MiB live, 215.8MiB allocated

Pruning

16 alts after pruning (6 fresh and 10 done)

	Pruned	Kept	Total
New	2 433	6	2 439
Fresh	0	0	0
Picked	2	3	5
Done	0	7	7
Total	2 435	16	2 451

Accuracy

99.7%

Counts

2 451 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.9%	(/.f64 (-.f64 x y) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
✓	28.2%	(/.f64 (-.f64 x y) #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x)))
✓	63.6%	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
	28.2%	(/.f64 (.f64 (+.f64 x y) (/.f64 (-.f64 x y) #s(approx (/ (+ ( y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))) (+.f64 x y))
	28.2%	(/.f64 (.f64 (.f64 (/.f64 (-.f64 x y) (+.f64 y x)) (/.f64 (+.f64 y x) #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)))) (-.f64 x y)) #s(approx (/ (+ ( y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)))
	28.2%	(/.f64 #s(approx (- x y) (.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)) #s(approx (/ (+ ( y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 #s(approx (+ (* (/ (/ y x) x) -2) (/ 2 x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal -2 binary64) #s(literal 2 binary64)) x)) y #s(literal -1 binary64)) y x)))
	28.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (+ (* y y) (* x x)) (+ y x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) y #s(literal -1 binary64)) y x)) #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))))
✓	45.0%	(.f64 (/.f64 (+.f64 y x) #s(approx (+ ( x x) (* y y)) (*.f64 y y))) (-.f64 x y))
✓	45.0%	(.f64 (+.f64 y x) (/.f64 (-.f64 x y) #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
	26.3%	(.f64 (+.f64 y x) #s(approx (/ (- x y) (+ ( x x) (* y y))) (/.f64 (+.f64 (+.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) (/.f64 (neg.f64 (fma.f64 y (/.f64 y x) y)) x)) #s(literal 1 binary64)) x)))
	26.6%	(.f64 #s(approx (/ (+ y x) (+ ( x x) (* y y))) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 y x) #s(literal 3 binary64))) (/.f64 (fma.f64 (neg.f64 y) (/.f64 y x) y) x)) x)) (-.f64 x y))
✓	26.9%	#s(approx (/ (- x y) (/ (+ (* y y) (* x x)) (+ y x))) #s(literal 1 binary64))
✓	29.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) y) x) (/.f64 y x) #s(literal 1 binary64)))
✓	74.6%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))
✓	22.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64)))
✓	73.1%	#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Compiler

Compiled 687 to 281 computations (59.1% saved)

regimes23.0ms (0.3%)

Memory

15.3MiB live, 50.2MiB allocated

Counts

23 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

10.0ms	x
7.0ms	y
6.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Results

Accuracy	Segments	Branch
82.2%	2	`x`
91.6%	3	`y`
93.5%	2	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes3.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

10 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
93.1%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes3.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

8 → 3

Calls

Call 1

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

Outputs

(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (*.f64 y y)))

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
92.2%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes9.0ms (0.1%)

Memory

-71.1MiB live, 7.1MiB allocated

Counts

7 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

9.0ms

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

Results

Accuracy	Segments	Branch
92.2%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes2.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
92.1%	3	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes4.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
73.1%	1	`x`
73.1%	1	`y`
73.1%	1	`(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))`

Compiler

Compiled 17 to 13 computations (23.5% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.9999464834265959	0.9999467061561507

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.9999464834265959	0.9999467061561507

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch1.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0	NaN
0.0ms	-0.9999464834265959	0.9999467061561507

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch30.0ms (0.4%)

Memory

21.7MiB live, 58.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	predicate-failed
1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.0	NaN
12.0ms	-0.9999464834265959	0.9999467061561507

Samples

10.0ms	416×	0	valid
2.0ms	101×	0	invalid

Compiler

Compiled 122 to 274 computations (-124.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

simplify27.0ms (0.4%)

Memory

-4.0MiB live, 72.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	470
1	60	470
2	63	470
3	65	470
4	66	470

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -1/2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64))) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -1/2 binary64)) (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (.f64 y y))) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -1/2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal +inf.0 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

Outputs
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal 2 binary64)) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (fma.f64 y y (.f64 x x))) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -1/2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64))) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -1/2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (.f64 (/.f64 x y) x) #s(literal -1 binary64))) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal 2 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 x y) x) #s(literal -1 binary64)))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -1/2 binary64)) (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) #s(approx (+ (* x x) (* y y)) (.f64 y y))) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -1/2 binary64)) (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(approx (+ (* x x) (* y y)) (.f64 y y))) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal 2 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -1/2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal 2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -1/2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal 2 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal -2 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64))) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y y))) #s(literal +inf.0 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal -202402253307311/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64)) (if (<=.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 (.f64 y y) (.f64 x x))) #s(literal +inf.0 binary64)) #s(approx (/ ( (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal 1 binary64)) #s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))))
#s(approx (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) #s(literal -1 binary64))

soundness699.0ms (9.3%)

Memory

1.2MiB live, 471.5MiB allocated

Rules

12 408×	`lower-fma.f64`
12 408×	`lower-fma.f32`
5 764×	`lower-/.f32`
5 750×	`lower-/.f64`
5 274×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	41
0	16	41
1	66	41
2	551	41
0	8160	39
0	34	187
0	52	182
1	212	182
2	1752	180
0	8184	178
0	189	1060
1	601	957
2	1966	905
3	7908	905
0	8902	851

Stop Event

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

Compiler

Compiled 376 to 131 computations (65.2% saved)

preprocess176.0ms (2.4%)

Memory

1.9MiB live, 95.5MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 822 to 228 computations (72.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze6.0ms (0.1%)

sample918.0ms (12.3%)

explain99.0ms (1.3%)

preprocess427.0ms (5.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify293.0ms (3.9%)

localize24.0ms (0.3%)

series11.0ms (0.1%)

simplify200.0ms (2.7%)

rewrite175.0ms (2.3%)

eval172.0ms (2.3%)

prune24.0ms (0.3%)

simplify141.0ms (1.9%)

localize93.0ms (1.2%)

series49.0ms (0.7%)

simplify208.0ms (2.8%)

rewrite295.0ms (3.9%)

eval369.0ms (4.9%)

prune71.0ms (0.9%)

simplify152.0ms (2%)

localize105.0ms (1.4%)

series30.0ms (0.4%)

simplify187.0ms (2.5%)

rewrite242.0ms (3.2%)

eval384.0ms (5.1%)

prune121.0ms (1.6%)

simplify185.0ms (2.5%)

localize116.0ms (1.6%)

series44.0ms (0.6%)

simplify211.0ms (2.8%)

rewrite232.0ms (3.1%)

eval750.0ms (10%)

prune163.0ms (2.2%)

regimes23.0ms (0.3%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes9.0ms (0.1%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch30.0ms (0.4%)

simplify27.0ms (0.4%)

soundness699.0ms (9.3%)

preprocess176.0ms (2.4%)

end0.0ms (0%)

Profiling