Metrics for Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated

analyze61.0ms (1%)

Memory

5.2MiB live, 46.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
68.8%	68.7%	31.2%	0.1%	0%	0%	0%	6
78.1%	78%	21.9%	0.1%	0%	0%	0%	7
82.8%	82.7%	17.2%	0.1%	0%	0%	0%	8
88.3%	88.2%	11.7%	0.1%	0%	0%	0%	9
91%	90.9%	9%	0.1%	0%	0%	0%	10
93.9%	93.9%	6%	0.1%	0%	0%	0%	11
95.4%	95.3%	4.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.0s (17.6%)

Memory

18.0MiB live, 1 552.2MiB allocated

Samples

761.0ms	8 254×	0	valid
0.0ms	1×	3	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 458.0ms

ival-add: 127.0ms (27.7% of total)

ival-div: 124.0ms (27.1% of total)

ival-mult: 98.0ms (21.4% of total)

ival-sub: 91.0ms (19.9% of total)

exact: 9.0ms (2% of total)

ival-true: 6.0ms (1.3% of total)

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

adjust: 0.0ms (0% of total)

Bogosity

explain144.0ms (2.4%)

Memory

-13.4MiB live, 239.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
34	-	-	`(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))`
0	-	-	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 x y)`
0	-	-	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`y`
0	-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

63.0ms

512×

valid

Compiler

Compiled 132 to 40 computations (69.7% saved)

Precisions

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

ival-div: 7.0ms (40.9% of total)

ival-mult: 4.0ms (23.4% of total)

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

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

exact: 1.0ms (5.8% of total)

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

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

preprocess125.0ms (2.1%)

Memory

6.8MiB live, 79.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	63
1	57	61
2	121	57
3	253	55
4	541	55
5	888	55
6	995	55
7	1019	55
8	1029	55
9	1033	55
0	9	11
0	14	11
1	22	11
2	33	11
3	48	11
4	90	11
5	163	11
6	284	11
7	379	11
8	589	11
9	679	11
10	801	11
11	837	11
12	1000	11
13	1009	11
0	1009	10

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify26.0ms (0.4%)

Memory

14.9MiB live, 14.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	14	39
1	22	39
2	33	39
3	48	39
4	90	39
5	163	39
6	284	39
7	379	39
8	589	39
9	679	39
10	801	39
11	837	39
12	1000	39
13	1009	39
0	1009	36

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize65.0ms (1.1%)

Memory

-22.8MiB live, 24.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
accuracy	0	(*.f64 x y)
accuracy	0.00390625	(/.f64 (*.f64 x y) #s(literal 2 binary64))
accuracy	8.027722633838017	(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))

Samples

58.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 3.0ms (35.9% of total)

ival-mult: 2.0ms (24% of total)

ival-sub: 1.0ms (12% of total)

ival-add: 1.0ms (12% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (* x y)))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 x) (/ 1 y))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1/2 x) (/ 1 y)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (/ 2 x) (taylor -inf y) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt y (taylor 0 x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) (taylor inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (patch (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (patch (-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) (taylor -inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (patch (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify271.0ms (4.6%)

Memory

-10.0MiB live, 185.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	231	1053
1	738	1018
2	1944	987
3	6075	981
0	8419	934

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 115

Calls

Call 1

Inputs
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(* x y)
(* x y)
(* x y)
(* x y)

Outputs
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
y
(* y (+ 1 (* -1/2 (* x y))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 y x) #s(literal 1 binary64)) y)
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(fma.f64 (.f64 (.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) y) #s(literal -1/8 binary64))) y)) y #s(literal 1 binary64)) y)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* y (+ (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* y (+ (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* y (+ (* 1/2 x) (/ 1 y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x) x)
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(-.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x) x)
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(-.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 y)
(neg.f64 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal 1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1/4 binary64))) x (fma.f64 (*.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64))) x (neg.f64 y))
y
(+ y (* -1/2 (* x (pow y 2))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 y x) #s(literal 1 binary64)) y)
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(fma.f64 (.f64 (.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (.f64 y y) #s(literal -1/2 binary64) (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal -1/8 binary64))) x)) x y)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -16 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (*.f64 y y) x))) x))) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* 1/2 (* x y))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) x)) (/.f64 #s(literal 8 binary64) (.f64 y y))) x)) x) #s(literal -2 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)

rewrite267.0ms (4.5%)

Memory

14.8MiB live, 256.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	14	35
1	63	35
2	500	35
3	6873	35
0	8527	32

Stop Event

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

Counts

5 → 279

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval115.0ms (1.9%)

Memory: -16.1MiB live, 190.7MiB allocated
Compiler: Compiled 9 214 to 1 087 computations (88.2% saved)

prune11.0ms (0.2%)

Memory

4.6MiB live, 42.5MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	387	7	394
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	388	7	395

Accuracy

100.0%

Counts

395 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
	99.9%	(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 y x) #s(literal 1 binary64)) y)))
▶	56.6%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
▶	68.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
	55.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x))
▶	79.3%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
▶	33.6%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 108 to 92 computations (14.8% saved)

simplify80.0ms (1.4%)

Memory

8.1MiB live, 46.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	25	144
0	37	144
1	59	144
2	97	144
3	179	144
4	366	144
5	696	141
6	1088	139
7	1417	139
8	1602	139
9	1730	139
10	1817	139
11	1927	139
12	1944	139
13	1953	139
14	1960	139
15	1961	139
0	1961	139

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize62.0ms (1%)

Memory

-0.3MiB live, 119.0MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y x)
accuracy	0.00390625	(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
accuracy	0.01953125	(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
accuracy	20.368667087352506	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x))
accuracy	0	(/.f64 #s(literal 2 binary64) x)
accuracy	0	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
accuracy	34.97677819422947	#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
accuracy	0	(-.f64 x y)
accuracy	13.229243614869704	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
accuracy	0	(neg.f64 y)
accuracy	42.52171186811543	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
accuracy	0	(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy	0	(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
accuracy	0	(*.f64 y x)
accuracy	8.027722633838017	(/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))

Samples

47.0ms

256×

valid

Compiler

Compiled 220 to 44 computations (80% saved)

Precisions

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

ival-div: 10.0ms (34.4% of total)

ival-sub: 6.0ms (20.6% of total)

ival-mult: 6.0ms (20.6% of total)

ival-add: 5.0ms (17.2% of total)

exact: 1.0ms (3.4% of total)

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

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

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

series18.0ms (0.3%)

Memory

-6.7MiB live, 31.2MiB allocated

Counts

14 → 312

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (* x y)))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (patch (-.f64 x (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (patch (/.f64 y (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (patch (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (patch (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (patch (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (patch (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) (patch #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) (taylor -inf x) (#s(alt #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) (patch #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) (patch #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) (patch #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) (patch (fma.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify182.0ms (3.1%)

Memory

-11.8MiB live, 179.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	278	3177
1	875	3073
2	2369	2971
3	7072	2957
0	8301	2778

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 289

Calls

Call 1

Inputs
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* 1/2 (* x y)) 1)))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
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Outputs
x
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(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
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y
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-1
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(* 1/2 (* x y))
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(* x y)
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(* x y)
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(/.f64 #s(literal 2 binary64) x)
(* -1 y)
(neg.f64 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal 1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1/4 binary64))) x (fma.f64 (.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64))) x) y)
(* -1 y)
(neg.f64 y)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
-1
#s(literal -1 binary64)
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
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(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
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(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
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(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x) (-.f64 (/.f64 #s(literal 16 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) #s(literal 2 binary64))) x)
(* 1/2 (* x y))
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(* x (+ (* 1/2 y) (/ 1 x)))
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(* x (+ (* 1/2 y) (/ 1 x)))
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(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64))
(* x y)
(*.f64 y x)
(* x y)
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(* x y)
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(* x y)
(*.f64 y x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
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(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
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(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) x)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x) (-.f64 (/.f64 #s(literal 16 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) #s(literal 2 binary64))) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (+ 1 (* 1/2 (pow y 2))))
(.f64 (fma.f64 (.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* 1/2 (* x y))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(* x (- (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x (- (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* x (- (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (-.f64 (/.f64 #s(literal 16 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (*.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x))) x)
(* 1/2 (* x y))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y))) y))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y))) y))
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (-.f64 (/.f64 #s(literal 16 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (*.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x))) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y))) y))
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(.f64 (fma.f64 (.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* 1/2 (* x y))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))

rewrite178.0ms (3%)

Memory

12.1MiB live, 255.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	128
0	37	123
1	179	123
2	1176	123
0	8327	123

Stop Event

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

Counts

14 → 316

Calls

Call 1

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

Outputs
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eval76.0ms (1.3%)

Memory: 27.5MiB live, 143.7MiB allocated
Compiler: Compiled 11 658 to 1 355 computations (88.4% saved)

prune21.0ms (0.4%)

Memory

-23.1MiB live, 52.7MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	629	2	631
Fresh	1	1	2
Picked	1	4	5
Done	0	0	0
Total	631	7	638

Accuracy

100.0%

Counts

638 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
▶	99.9%	(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)))
✓	56.6%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
▶	55.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x))
✓	79.3%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
✓	33.6%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
▶	34.5%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))

Compiler

Compiled 54 to 47 computations (13% saved)

simplify100.0ms (1.7%)

Memory

-3.9MiB live, 124.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
cost-diff	0	(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)))
cost-diff	320	(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)
cost-diff	384	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal -2 binary64) (*.f64 x x))
cost-diff	0	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x))
cost-diff	512	(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
cost-diff	0	(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
cost-diff	0	#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))
cost-diff	0	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	152
0	45	152
1	76	152
2	126	142
3	222	140
4	411	140
5	799	140
6	1585	139
7	2767	139
8	6002	139
0	8129	136

Stop Event

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

Calls

Call 1

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

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

localize78.0ms (1.3%)

Memory

-7.8MiB live, 68.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)))
accuracy	0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.0859375	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))
accuracy	7.998349561196835	(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)
accuracy	0	(*.f64 x x)
accuracy	0.43023337339644896	(/.f64 #s(literal -2 binary64) (*.f64 x x))
accuracy	19.157169246761615	(fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)
accuracy	27.801126378920067	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x))
accuracy	0.00390625	(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
accuracy	0.0390625	(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
accuracy	20.368667087352506	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))
accuracy	21.969331193040876	#s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))

Samples

51.0ms	255×	0	valid
0.0ms	1×	3	valid

Compiler

Compiled 234 to 49 computations (79.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 21.0ms (53.9% of total)

ival-div: 9.0ms (23.1% of total)

ival-add: 6.0ms (15.4% of total)

ival-sub: 2.0ms (5.1% of total)

exact: 1.0ms (2.6% of total)

adjust: 0.0ms (0% of total)

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

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

series16.0ms (0.3%)

Memory

19.6MiB live, 19.6MiB allocated

Counts

13 → 264

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 1/2 (* x y)) 1)) (taylor 0 y) (#s(alt (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
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#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- 2 (* 4 (/ 1 (* x y)))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 y) (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (pow y 2)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) (patch #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x (pow y 2))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) (patch (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) (patch (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) (patch (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) (patch (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) (patch (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x x)) (patch #s(approx (- x (/ y (+ 1 (/ ( x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (/ -2 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) (.f64 x x)) (patch (/.f64 #s(literal -2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ -2 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) (.f64 x x)) (patch (/.f64 #s(literal -2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ -2 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) (.f64 x x)) (patch (/.f64 #s(literal -2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ -2 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) (.f64 x x)) (patch (/.f64 #s(literal -2 binary64) (.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 (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) (patch (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 y) (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify310.0ms (5.2%)

Memory

-3.5MiB live, 147.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	280	2433
1	885	2346
2	2361	2242
3	7625	2240
0	8481	2091

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 250

Calls

Call 1

Inputs
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(* -1 y)
(* y (- (* 1/2 (* x y)) 1))
(* y (- (* 1/2 (* x y)) 1))
(* y (- (* 1/2 (* x y)) 1))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 1 y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(* y (- (* 1/2 x) (/ 1 y)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* (pow y 2) (+ (* -1 (/ (+ 1 (* -1 (/ x y))) y)) (* 1/2 x)))
(* 1/2 (* x (pow y 2)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(* -1 (* y (+ (* -1/2 x) (/ 1 y))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(* -1 y)
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(+ (* -1 y) (* x (+ 1 (* 1/2 (pow y 2)))))
(* -1 y)
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
(+ (* -1 y) (* 1/2 (* x (pow y 2))))
-1
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(- (* 1/2 (* x y)) 1)
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 1 y)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(* x (+ 1 (* 1/2 (pow y 2))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* x (+ 1 (+ (* -1 (/ y x)) (* 1/2 (pow y 2)))))
(* 1/2 (* x (pow y 2)))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* x (+ (* -1 (/ y x)) (* 1/2 (pow y 2))))
(* 1/2 (* x y))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
(* x (- (* 1/2 y) (/ 1 x)))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(* 1/2 (* x (pow y 2)))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))

Outputs
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 y)
(neg.f64 y)
(* y (- (* 1/2 (* x y)) 1))
(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* y (- (* 1/2 (* x y)) 1))
(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* y (- (* 1/2 (* x y)) 1))
(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
-1
#s(literal -1 binary64)
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* 1/2 (* x y)) 1)
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
y
(* y (+ 1 (* -1/2 (* x y))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) y #s(literal 1 binary64)) y)
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(fma.f64 (.f64 (.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) y) #s(literal -1/8 binary64))) y)) y #s(literal 1 binary64)) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(/ (+ 1 (* 1/2 (* x y))) y)
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(/ (+ 1 (* 1/2 (* x y))) y)
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
(+ 1 (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x)) x) x)
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x)) x) (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) x))
(* 1/2 (* x (pow y 2)))
(.f64 (.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* (pow y 2) (- (* 1/2 x) (/ 1 y)))
(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 x (.f64 y y))) y #s(literal -1 binary64)) y)
(* (pow y 2) (- (+ (* 1/2 x) (/ x (pow y 2))) (/ 1 y)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 x (.f64 y y))) y #s(literal -1 binary64)) y)
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(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x)) x) x)
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.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)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) x)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x) (-.f64 (/.f64 #s(literal 16 binary64) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) #s(literal 2 binary64))) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x)) x) x)
(* 1/2 (* x y))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
(* x (+ (* 1/2 y) (/ 1 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x)) x) x)
(* -1 (* x (- (* -1/2 (pow y 2)) 1)))
(.f64 (fma.f64 (.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* -1 (* x (- (+ (* -1/2 (pow y 2)) (/ y x)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(* 1/2 (* x (pow y 2)))
(.f64 (.f64 (*.f64 y y) #s(literal 1/2 binary64)) x)
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* -1 (* x (+ (* -1/2 (pow y 2)) (/ y x))))
(.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* 1/2 (* x y))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(* -1 (* x (+ (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x)) x) x)
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.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)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x))) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (-.f64 (/.f64 #s(literal 16 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (*.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x))) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 8 binary64) (.f64 (.f64 y y) x)) (/.f64 #s(literal 4 binary64) y)) x)) x) x)
(* 1/2 (* x y))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x #s(literal 1 binary64))

rewrite450.0ms (7.6%)

Memory

-119.5MiB live, 161.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	139
0	45	133
1	204	133
2	1317	127
0	8735	125

Stop Event

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

Counts

13 → 411

Calls

Call 1

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

Outputs
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eval216.0ms (3.6%)

Memory: -1.5MiB live, 150.6MiB allocated
Compiler: Compiled 11 749 to 1 822 computations (84.5% saved)

prune101.0ms (1.7%)

Memory

-10.4MiB live, 43.4MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	659	2	661
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	660	8	668

Accuracy

100.0%

Counts

668 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
▶	99.9%	(-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))))
✓	56.6%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	55.2%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (fma.f64 (/.f64 #s(literal -2 binary64) (*.f64 x x)) x x))
✓	79.3%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
✓	33.6%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
▶	10.3%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)))
✓	34.5%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))

Compiler

Compiled 58 to 53 computations (8.6% saved)

simplify207.0ms (3.5%)

Memory

10.6MiB live, 84.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	110
0	33	110
1	57	110
2	92	102
3	132	102
4	204	102
5	453	102
6	894	102
7	2024	102
8	6084	102
0	8204	98

Stop Event

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

Calls

Call 1

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

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

localize149.0ms (2.5%)

Memory

16.9MiB live, 54.1MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))))
accuracy	0	#s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))
accuracy	0.00390625	(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
accuracy	0.0859375	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))
accuracy	0	(/.f64 #s(literal -2 binary64) x)
accuracy	27.801126378920067	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)))
accuracy	29.977465184410168	#s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))

Samples

136.0ms	255×	0	valid
0.0ms	1×	3	valid

Compiler

Compiled 128 to 40 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-mult: 106.0ms (84.2% of total)

ival-div: 12.0ms (9.5% of total)

ival-add: 5.0ms (4% of total)

ival-sub: 2.0ms (1.6% of total)

exact: 1.0ms (0.8% of total)

adjust: 0.0ms (0% of total)

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

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

series26.0ms (0.4%)

Memory

-27.2MiB live, 20.2MiB allocated

Counts

7 → 144

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* 1/2 (* x y)) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1))) (taylor 0 y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (* x y)))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor 0 y) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* 1/2 (* x y))) y) (taylor 0 y) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* 1/2 (* x y))) y) (taylor 0 y) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* 1/2 (* x y))) y) (taylor 0 y) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* 1/2 (* x y))) y) (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* 1/2 (* x y))) y) (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* 1/2 (* x y))) y) (taylor 0 y) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- x (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x))) (taylor inf y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) (taylor inf y) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf y) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (/ 1 y)) (taylor inf y) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
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#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 2 (* 4 (/ 1 (* x y)))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) (patch #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) (patch #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -2 binary64) x) (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y)))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) (patch (-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) (patch #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 (* x y)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify370.0ms (6.3%)

Memory

25.5MiB live, 139.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	226	1473
1	715	1425
2	1886	1382
3	5926	1372
0	8259	1284

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 134

Calls

Call 1

Inputs
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 1 y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ 1 y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 1 y)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(/ 1 y)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))

Outputs
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
y
(* y (+ 1 (* -1/2 (* x y))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 y x) #s(literal 1 binary64)) y)
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(fma.f64 (.f64 (.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) y) #s(literal -1/8 binary64))) y)) y #s(literal 1 binary64)) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64)) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64)) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64)) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64)) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64)) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y #s(literal 1 binary64)) y)
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x) x)
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x) x)
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(-.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x) x)
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal 2 binary64)) x) x)
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x) x)
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal -16 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) y))) y)) y)) (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(-.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* -1 y)
(neg.f64 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal 1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1/4 binary64))) x (fma.f64 (*.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64))) x (neg.f64 y))
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ (- (pow x 2) 2) x)
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(/ (- (pow x 2) 2) x)
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(/ (- (pow x 2) 2) x)
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(* -1 y)
(neg.f64 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(fma.f64 (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y x)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(fma.f64 (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal -1/4 binary64) x) y #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (neg.f64 y))
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal 1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1/4 binary64))) x (fma.f64 (*.f64 y y) #s(literal 1/2 binary64) #s(literal 1 binary64))) x (neg.f64 y))
y
(+ y (* -1/2 (* x (pow y 2))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 y x) #s(literal 1 binary64)) y)
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(fma.f64 (.f64 (.f64 y y) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) y #s(literal -1/2 binary64))) x y)
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(fma.f64 (fma.f64 (.f64 y y) #s(literal -1/2 binary64) (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) x) #s(literal -1/8 binary64))) x)) x y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(+ (* 1/2 x) (/ 1 y))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (-.f64 (/.f64 #s(literal -16 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (*.f64 y y) x))) x))) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) x) x x)
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(fma.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x x)
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x (/.f64 (-.f64 (/.f64 #s(literal -8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) y)) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 (.f64 y y) x))) x) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 (-.f64 (/.f64 #s(literal 16 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) x)) (/.f64 #s(literal 8 binary64) (.f64 y y))) x)) x) #s(literal -2 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))
(* x (+ 1/2 (/ 1 (* x y))))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y))

rewrite214.0ms (3.6%)

Memory

5.3MiB live, 124.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	101
0	33	101
1	169	101
2	1393	93
0	8450	89

Stop Event

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

Counts

7 → 139

Calls

Call 1

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

Outputs
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eval267.0ms (4.5%)

Memory: 1.8MiB live, 40.1MiB allocated
Compiler: Compiled 4 614 to 721 computations (84.4% saved)

prune65.0ms (1.1%)

Memory

-2.8MiB live, 43.9MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	0	0	0
Picked	0	2	2
Done	1	5	6
Total	273	8	281

Accuracy

100.0%

Counts

281 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
✓	99.9%	(-.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* (* 1/2 y) x) 1) y) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1 binary64) y)))))
✓	56.6%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	79.3%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
✓	33.6%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
✓	10.3%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (/.f64 #s(literal -2 binary64) x)))
	9.0%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (/ -2 (* x x)) x) x) (.f64 (/.f64 #s(literal -2 binary64) (.f64 x x)) x)))
✓	34.5%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) #s(approx (+ (* (+ (* (* y x) 1/2) -1) y) x) (.f64 (fma.f64 (.f64 y x) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)))

Compiler

Compiled 170 to 107 computations (37.1% saved)

regimes18.0ms (0.3%)

Memory

-4.6MiB live, 31.0MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
4.0ms	y
4.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes14.0ms (0.2%)

Memory

-13.0MiB live, 23.2MiB allocated

Counts

8 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

3 calls:

7.0ms	x
3.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
3.0ms	y

Results

Accuracy	Segments	Branch
92.2%	3	`x`
95.1%	3	`y`
86.3%	3	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes6.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

2.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
79.3%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
79.3%	1	`x`
79.3%	1	`y`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes4.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
33.6%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
33.6%	1	`y`
33.6%	1	`x`

Compiler

Compiled 13 to 13 computations (0% saved)

bsearch37.0ms (0.6%)

Memory

-50.9MiB live, 46.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	2.196911396538043e+155	8.231743104180885e+157
13.0ms	-1.7889479399058567e+94	-2.9595084192377802e+85

Samples

15.0ms

272×

valid

Compiler

Compiled 184 to 218 computations (-18.5% saved)

Precisions

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

ival-div: 3.0ms (34.3% of total)

ival-mult: 2.0ms (22.9% of total)

ival-sub: 1.0ms (11.4% of total)

ival-add: 1.0ms (11.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify26.0ms (0.4%)

Memory

6.1MiB live, 44.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	92
1	39	92
2	51	92
3	58	92
4	62	92
5	63	92

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -520000000000000014233638012869875212041787981475565065177942222611865202366620327120732160 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 499999999999999991679590111595860857280186137508735268183503807230234208750506277265738938472969370875618694172181552533767253674082286866732755185163042816 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Outputs
(-.f64 x (/.f64 y (fma.f64 (*.f64 y x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -520000000000000014233638012869875212041787981475565065177942222611865202366620327120732160 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 499999999999999991679590111595860857280186137508735268183503807230234208750506277265738938472969370875618694172181552533767253674082286866732755185163042816 binary64)) #s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

soundness455.0ms (7.7%)

Memory

6.9MiB live, 324.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	231	1053
1	738	1018
2	1944	987
3	6075	981
0	8419	934
0	9	35
0	14	35
1	63	35
2	500	35
3	6873	35
0	8527	32

Stop Event

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

Compiler

Compiled 75 to 50 computations (33.3% saved)

preprocess31.0ms (0.5%)

Memory: 20.5MiB live, 96.8MiB allocated
Compiler: Compiled 104 to 62 computations (40.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze61.0ms (1%)

sample1.0s (17.6%)

explain144.0ms (2.4%)

preprocess125.0ms (2.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify26.0ms (0.4%)

localize65.0ms (1.1%)

series11.0ms (0.2%)

simplify271.0ms (4.6%)

rewrite267.0ms (4.5%)

eval115.0ms (1.9%)

prune11.0ms (0.2%)

simplify80.0ms (1.4%)

localize62.0ms (1%)

series18.0ms (0.3%)

simplify182.0ms (3.1%)

rewrite178.0ms (3%)

eval76.0ms (1.3%)

prune21.0ms (0.4%)

simplify100.0ms (1.7%)

localize78.0ms (1.3%)

series16.0ms (0.3%)

simplify310.0ms (5.2%)

rewrite450.0ms (7.6%)

eval216.0ms (3.6%)

prune101.0ms (1.7%)

simplify207.0ms (3.5%)

localize149.0ms (2.5%)

series26.0ms (0.4%)

simplify370.0ms (6.3%)

rewrite214.0ms (3.6%)

eval267.0ms (4.5%)

prune65.0ms (1.1%)

regimes18.0ms (0.3%)

regimes14.0ms (0.2%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch37.0ms (0.6%)

simplify26.0ms (0.4%)

soundness455.0ms (7.7%)

preprocess31.0ms (0.5%)

end0.0ms (0%)

Profiling