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

analyze24.0ms (0.1%)

Memory

11.1MiB live, 48.1MiB 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)

sample1.6s (6.1%)

Memory

27.5MiB live, 1 260.0MiB allocated

Samples

1.0s	8 254×	0	valid
0.0ms	1×	2	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 560.0ms

ival-mult: 239.0ms (42.7% of total)

ival-add: 141.0ms (25.2% of total)

ival-div: 113.0ms (20.2% of total)

ival-sub: 49.0ms (8.8% of total)

exact: 8.0ms (1.4% of total)

ival-true: 6.0ms (1.1% of total)

ival-assert: 3.0ms (0.5% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess154.0ms (0.6%)

Memory

-7.6MiB live, 29.0MiB allocated

Algorithm

1×	egg-herbie

Rules

384×	`lower-fma.f64`
384×	`lower-fma.f32`
272×	`lower-*.f32`
270×	`lower-*.f64`
224×	`associate-l`

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

explain327.0ms (1.2%)

Memory

6.0MiB live, 127.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
32	-	-	`(/.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

114.0ms

512×

valid

Compiler

Compiled 108 to 40 computations (63% saved)

Precisions

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

ival-div: 7.0ms (42.3% of total)

ival-mult: 4.0ms (24.1% of total)

ival-sub: 2.0ms (12.1% of total)

ival-add: 2.0ms (12.1% of total)

exact: 1.0ms (6% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (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 13 to 9 computations (30.8% saved)

simplify36.0ms (0.1%)

Memory

-15.6MiB live, 23.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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))

Rules

384×	`lower-fma.f64`
384×	`lower-fma.f32`
272×	`lower-*.f32`
270×	`lower-*.f64`
224×	`associate-l`

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

localize86.0ms (0.3%)

Memory

1.1MiB live, 45.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
✓	accuracy	88.2%	(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))

Samples

76.0ms

256×

valid

Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions

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

ival-div: 6.0ms (54.7% of total)

ival-mult: 2.0ms (18.2% of total)

ival-sub: 1.0ms (9.1% of total)

ival-add: 1.0ms (9.1% of total)

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

exact: 0.0ms (0% of total)

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

series98.0ms (0.4%)

Memory

-16.8MiB live, 21.0MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<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))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>

Calls

30 calls:

Time	Variable		Point	Expression
89.0ms	x	@	-inf	(* x y)
1.0ms	x	@	-inf	(- x (/ y (+ 1 (/ (* x y) 2))))
1.0ms	y	@	0	(/ (* x y) 2)
1.0ms	x	@	inf	(/ (* x y) 2)
1.0ms	x	@	0	(/ (* x y) 2)

simplify673.0ms (2.6%)

Memory

30.2MiB live, 555.6MiB allocated

Algorithm

1×	egg-herbie

Rules

13 558×	`lower-fma.f64`
13 558×	`lower-fma.f32`
4 930×	`lower-*.f64`
4 930×	`lower-*.f32`
1 854×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	231	1053
1	738	1018
2	1942	987
3	6081	981
0	8428	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))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* 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)))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 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))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 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)))
(* 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 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)
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 (* 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
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 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))))))
(- 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)))
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)))))
(/ 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))))
(/ 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)))
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)))))
(/ 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)
(/ 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)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

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

rewrite18.3s (70.1%)

Memory

0.8MiB live, 548.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 754×	`lower-fma.f64`
5 754×	`lower-fma.f32`
4 124×	`lower-*.f32`
4 122×	`lower-*.f64`
2 962×	`lower-/.f32`

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
(exp.f64 (.f64 (-.f64 #s(literal 0 binary64) (log.f64 (.f64 (*.f64 x y) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(neg.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(/.f64 x (/.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y)))
(/.f64 (*.f64 x (neg.f64 y)) #s(literal -2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x y)))
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1 binary64))
(.f64 x (.f64 y #s(literal 1/2 binary64)))
(.f64 x (.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(.f64 y (.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 y (.f64 (neg.f64 x) #s(literal -1/2 binary64)))
(.f64 (.f64 x y) #s(literal 1/2 binary64))
(.f64 (.f64 (*.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x y) #s(literal 1/2 binary64)))
(.f64 (.f64 x (neg.f64 y)) #s(literal -1/2 binary64))
(.f64 (neg.f64 y) (.f64 x #s(literal -1/2 binary64)))
(*.f64 (neg.f64 y) (/.f64 x #s(literal -2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal -1 binary64)))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(.f64 #s(literal -1 binary64) (.f64 (*.f64 x y) #s(literal -1/2 binary64)))
(.f64 #s(literal -1/2 binary64) (.f64 x (neg.f64 y)))
(*.f64 (neg.f64 x) (/.f64 y #s(literal -2 binary64)))
(.f64 (neg.f64 x) (.f64 y #s(literal -1/2 binary64)))
(.f64 (.f64 x #s(literal 1/2 binary64)) y)
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)))
(+.f64 (.f64 (.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) #s(literal 1/2 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (/.f64 (.f64 y (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) (/.f64 (.f64 y (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 y (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 y (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
(fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (.f64 (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 y (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 y (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 y (*.f64 (neg.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 x y) #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64))
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(/.f64 (.f64 (/.f64 y (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 y (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (/.f64 y (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 y (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))) (fma.f64 (.f64 x y) (fma.f64 #s(literal 1/4 binary64) (.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(pow.f64 (/.f64 (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) y) #s(literal -1 binary64))
(.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(.f64 (neg.f64 y) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 y (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) y)
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 y (fma.f64 (.f64 x (.f64 y (*.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 y (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) (neg.f64 y))
(.f64 (/.f64 y (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 y (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 y (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 y (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(.f64 (/.f64 y (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(.f64 (/.f64 y (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (fma.f64 y (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) y))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (.f64 y (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) y) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)))) (fma.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 y (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64)))) (fma.f64 (.f64 x y) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(.f64 (/.f64 (neg.f64 y) (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (neg.f64 y) (fma.f64 (.f64 x (.f64 y (.f64 x y))) #s(literal -1/4 binary64) #s(literal 1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x y) #s(literal 1/2 binary64))))
(.f64 (/.f64 y (neg.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 y (+.f64 #s(literal -1 binary64) (.f64 y (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x y)))))) (+.f64 #s(literal -1 binary64) (.f64 (*.f64 x y) #s(literal 1/2 binary64))))
(.f64 (/.f64 y (fma.f64 y (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x y))) #s(literal -1 binary64))) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 y)))
(neg.f64 (*.f64 x (neg.f64 y)))
(*.f64 x y)
(*.f64 y x)
(*.f64 y (neg.f64 (neg.f64 x)))
(.f64 (.f64 x y) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x y))
(*.f64 (neg.f64 y) (neg.f64 x))
(.f64 #s(literal -1 binary64) (.f64 x (neg.f64 y)))
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 (neg.f64 x)) y)

eval46.0ms (0.2%)

Memory: 8.3MiB live, 124.9MiB allocated
Compiler: Compiled 11 052 to 1 049 computations (90.5% saved)

prune45.0ms (0.2%)

Memory

-21.1MiB live, 140.7MiB 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
	99.9%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)
▶	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
▶	63.9%	(-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))
	59.4%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x)))
▶	63.9%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
▶	74.4%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
▶	23.1%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 140 to 88 computations (37.1% saved)

simplify58.0ms (0.2%)

Memory

5.7MiB live, 87.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

640×	`lower-fma.f32`
638×	`lower-fma.f64`
416×	`lower-*.f32`
410×	`lower-*.f64`
280×	`associate-l`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	26	157
0	39	157
1	64	157
2	97	157
3	146	157
4	278	157
5	486	155
6	669	150
7	819	150
8	1123	150
9	1274	150
10	1517	150
11	1567	150
12	1716	150
13	1726	150
0	1726	150

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize66.0ms (0.3%)

Memory

6.4MiB live, 136.6MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	accuracy	88.2%	(/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 #s(literal 1/2 binary64) (.f64 x y))))
✓	accuracy	48.3%	#s(approx (+ 1 (/ (* x y) 2)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	accuracy	48.3%	#s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(-.f64 x y)
✓	accuracy	74.4%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
✓	accuracy	100.0%	(neg.f64 y)
✓	accuracy	23.1%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))
✓	accuracy	100.0%	(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))
✓	accuracy	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
✓	accuracy	88.2%	(/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64)))

Samples

41.0ms

256×

valid

Compiler

Compiled 129 to 21 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-div: 7.0ms (34.4% of total)

ival-mult: 6.0ms (29.5% of total)

ival-sub: 3.0ms (14.7% of total)

ival-add: 2.0ms (9.8% of total)

ival-neg: 1.0ms (4.9% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0%)

Memory

-19.7MiB live, 18.8MiB allocated

Counts

15 → 324

Calls

Call 1

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

Outputs
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<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))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (* -1 y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt x>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (* -1 y)>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<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))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<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))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>

Calls

81 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(- x y)
1.0ms	y	@	-inf	(- x y)
0.0ms	y	@	-inf	(* y 1/2)
0.0ms	y	@	inf	(* y 1/2)
0.0ms	y	@	inf	(neg y)

simplify308.0ms (1.2%)

Memory

9.8MiB live, 561.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 134×	`lower-fma.f64`
11 134×	`lower-fma.f32`
3 994×	`lower-*.f64`
3 994×	`lower-*.f32`
2 140×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	246	3409
1	781	3283
2	2078	3166
3	6386	3140
0	8109	2983

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 300

Calls

Call 1

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

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

rewrite289.0ms (1.1%)

Memory

-3.5MiB live, 551.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 652×	`lower-/.f32`
4 646×	`lower-/.f64`
4 418×	`lower-fma.f32`
4 416×	`lower-fma.f64`
4 158×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	142
0	39	142
1	170	135
2	1444	135
0	8245	135

Stop Event

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

Counts

15 → 324

Calls

Call 1

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

Outputs
(+.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(+.f64 (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x)
(-.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (/.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(fma.f64 y (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) x)
(fma.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x)
(fma.f64 #s(literal -1 binary64) (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x)
(fma.f64 (/.f64 y (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 y #s(literal 1/2 binary64))) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))) x)
(fma.f64 (/.f64 y (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x y) (.f64 x y)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) x)
(fma.f64 (/.f64 y (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x y) (.f64 x y)) #s(literal 1/4 binary64)))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x y))))) x)
(fma.f64 (/.f64 y (fma.f64 (.f64 (.f64 x y) (.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 y #s(literal 1/2 binary64))) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x y) (.f64 x y)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (.f64 x y) (.f64 x y)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64)))) x)
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x y) (.f64 x y)) #s(literal 1/4 binary64)))) (/.f64 y (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x y))))) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (fma.f64 x x (-.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (neg.f64 (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (neg.f64 (fma.f64 x x (-.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 x (/.f64 (neg.f64 y) (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (neg.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (neg.f64 (-.f64 x (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (.f64 (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (.f64 (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))) (neg.f64 (neg.f64 (fma.f64 x x (.f64 (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (neg.f64 (neg.f64 (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (+.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (.f64 x (.f64 x x))) (+.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x x) (.f64 (/.f64 (neg.f64 y) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))) x))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (fma.f64 (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 (.f64 y y) (.f64 (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y (fma.f64 x (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal -1 binary64))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 (.f64 y y) (.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (+.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) (fma.f64 (/.f64 (/.f64 (.f64 y y) (.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (+.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) (/.f64 (/.f64 (.f64 y y) (.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (+.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) (.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) (/.f64 (/.f64 (.f64 y y) (.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (+.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) #s(literal -1 binary64))
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(.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) (.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (/.f64 (neg.f64 y) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (neg.f64 y) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) (*.f64 y #s(literal 1 binary64))))
(/.f64 (neg.f64 y) (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y)))
(/.f64 (.f64 y #s(literal 1 binary64)) #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 y))) (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) y)) (.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 (/.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) #s(literal 1 binary64))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (neg.f64 (/.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (neg.f64 y))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (neg.f64 y))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y)) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) #s(literal -1 binary64))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (/.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (.f64 (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 y)))) (.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 y))) (neg.f64 (neg.f64 (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (.f64 y #s(literal 1 binary64))) (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) #s(literal 3 binary64)) (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) (.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))))) (fma.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (+.f64 (/.f64 (.f64 y y) (.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))) (/.f64 (neg.f64 y) #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))))))
(pow.f64 (/.f64 #s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))) y) #s(literal -1 binary64))
(.f64 y (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(.f64 #s(literal 1 binary64) (/.f64 y #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) y)
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) #s(approx (+ 1 (/ ( x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
#s(approx (+ 1 (/ (* x y) 2)) (.f64 x (.f64 y #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x y))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(neg.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 #s(literal 1 binary64) (.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 #s(literal 1 binary64) (neg.f64 (.f64 x y)))))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 x y)) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 x y))) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 x y))) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 x y))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 x y)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 x y)))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1 binary64))
(.f64 x (.f64 y #s(literal 1/2 binary64)))
(.f64 x (.f64 (*.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(.f64 y (.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal -1 binary64)))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(.f64 (.f64 y #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 y #s(literal 1/2 binary64))))
(.f64 (.f64 x (*.f64 y #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x y) #s(literal 1/2 binary64))
(.f64 (neg.f64 (.f64 x y)) #s(literal -1/2 binary64))
(.f64 (.f64 x #s(literal 1/2 binary64)) y)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 y #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) y)

eval117.0ms (0.4%)

Memory: 10.1MiB live, 211.5MiB allocated
Compiler: Compiled 13 074 to 1 152 computations (91.2% saved)

prune90.0ms (0.3%)

Memory

-2.8MiB live, 118.6MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	623	1	624
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	624	7	631

Accuracy

100.0%

Counts

631 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)
✓	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
✓	63.9%	(-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))
▶	59.4%	(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))
✓	63.9%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	74.4%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
✓	23.1%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 70 to 44 computations (37.1% saved)

simplify143.0ms (0.5%)

Memory

22.5MiB live, 100.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)))
✓	cost-diff	192	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)
✓	cost-diff	0	#s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x))
✓	cost-diff	0	(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))

Rules

1 200×	`lower-fma.f32`
1 196×	`lower-fma.f64`
864×	`lower-*.f32`
860×	`lower-*.f64`
756×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	101
0	33	101
1	55	100
2	76	100
3	126	100
4	139	100
5	206	100
6	262	100
7	355	100
8	677	100
9	990	100
10	1456	100
11	2255	100
12	3122	100
13	3499	100
14	3647	100
15	3751	100
16	3825	100
17	3999	100
18	3999	100
0	3999	98

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))
x
#s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x)))
#s(literal 2 binary64)
(/.f64 #s(literal -4 binary64) (*.f64 y x))
#s(literal -4 binary64)
(*.f64 y x)
y
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)))
#s(literal 1 binary64)
(fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))
(*.f64 x y)
x
y
#s(literal -1/2 binary64)
#s(literal -1 binary64)

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

localize103.0ms (0.4%)

Memory

0.0MiB live, 78.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	99.9%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)))
✓	accuracy	100.0%	(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))
✓	accuracy	99.9%	(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)
✓	accuracy	99.0%	(/.f64 #s(literal -4 binary64) (*.f64 y x))
✓	accuracy	47.8%	#s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x))

Samples

83.0ms

256×

valid

Compiler

Compiled 87 to 25 computations (71.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-mult: 34.0ms (50.7% of total)

ival-add: 24.0ms (35.8% of total)

ival-div: 6.0ms (9% of total)

ival-sub: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series57.0ms (0.2%)

Memory

-24.0MiB live, 14.7MiB allocated

Counts

9 → 216

Calls

Call 1

Inputs
#<alt (-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))>
#<alt #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x))>
#<alt (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)>
#<alt (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x)))>
#<alt (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)>
#<alt (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)))>
#<alt (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))>
#<alt (*.f64 x y)>
#<alt (/.f64 #s(literal -4 binary64) (*.f64 y x))>

Outputs
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<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))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (/ -4 (* (pow x 2) y))>
#<alt (/ (- (* 2 (/ y x)) (* 4 (/ 1 (pow x 2)))) y)>
#<alt (/ (- (* 2 (/ y x)) (* 4 (/ 1 (pow x 2)))) y)>
#<alt (/ (- (* 2 (/ y x)) (* 4 (/ 1 (pow x 2)))) y)>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (/ -4 (* (pow x 2) y))>
#<alt (/ (- (* 2 x) (* 4 (/ 1 y))) (pow x 2))>
#<alt (/ (- (* 2 x) (* 4 (/ 1 y))) (pow x 2))>
#<alt (/ (- (* 2 x) (* 4 (/ 1 y))) (pow x 2))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (/ -4 (* x y))>
#<alt (/ (- (* 2 y) (* 4 (/ 1 x))) y)>
#<alt (/ (- (* 2 y) (* 4 (/ 1 x))) y)>
#<alt (/ (- (* 2 y) (* 4 (/ 1 x))) y)>
#<alt 2>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt 2>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (/ -4 (* x y))>
#<alt (/ (- (* 2 x) (* 4 (/ 1 y))) x)>
#<alt (/ (- (* 2 x) (* 4 (/ 1 y))) x)>
#<alt (/ (- (* 2 x) (* 4 (/ 1 y))) x)>
#<alt 2>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt 2>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (- 2 (* 4 (/ 1 (* x y))))>
#<alt (* -1 y)>
#<alt (+ (* -1 y) (* x (- 1 (* -1/2 (pow y 2)))))>
#<alt (+ (* -1 y) (* x (- (+ 1 (* -1/4 (* x (pow y 3)))) (* -1/2 (pow y 2)))))>
#<alt (+ (* -1 y) (* x (- (+ 1 (* x (- (* 1/8 (* x (pow y 4))) (* 1/4 (pow y 3))))) (* -1/2 (pow y 2)))))>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (- (* -1/4 (* (pow x 2) y)) (* -1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt -1>
#<alt (- (* 1/2 (* x y)) 1)>
#<alt (- (* x (- (* -1/4 (* x (pow y 2))) (* -1/2 y))) 1)>
#<alt (- (* x (- (* x (- (* 1/8 (* x (pow y 3))) (* 1/4 (pow y 2)))) (* -1/2 y))) 1)>
#<alt (/ -2 (* x y))>
#<alt (/ (- (* 4 (/ 1 (* x (pow y 2)))) (* 2 (/ 1 y))) x)>
#<alt (/ (- (/ 4 (* x (pow y 2))) (+ (* 2 (/ 1 y)) (/ 8 (* (pow x 2) (pow y 3))))) x)>
#<alt (/ (- (+ (* 16 (/ 1 (* (pow x 3) (pow y 4)))) (/ 4 (* x (pow y 2)))) (+ (* 2 (/ 1 y)) (* 8 (/ 1 (* (pow x 2) (pow y 3)))))) x)>
#<alt (/ -2 (* x y))>
#<alt (* -1 (/ (- (* 2 (/ 1 y)) (* 4 (/ 1 (* x (pow y 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 4 (/ 1 (pow y 2))) (* 8 (/ 1 (* x (pow y 3))))) x)) (* 2 (/ 1 y))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow y 3))) (* 16 (/ 1 (* x (pow y 4))))) x)) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))>
#<alt -1>
#<alt (- (* 1/2 (* x y)) 1)>
#<alt (- (* y (- (* -1/4 (* (pow x 2) y)) (* -1/2 x))) 1)>
#<alt (- (* y (- (* y (- (* 1/8 (* (pow x 3) y)) (* 1/4 (pow x 2)))) (* -1/2 x))) 1)>
#<alt (/ -2 (* x y))>
#<alt (/ (- (* 4 (/ 1 (* (pow x 2) y))) (* 2 (/ 1 x))) y)>
#<alt (/ (- (/ 4 (* (pow x 2) y)) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) y)>
#<alt (/ (- (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) y)>
#<alt (/ -2 (* x y))>
#<alt (* -1 (/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) y))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) y))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))>
#<alt -1>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (* -1/2 (* x y))>
#<alt (* x (- (* -1/2 y) (/ 1 x)))>
#<alt (* x (- (* -1/2 y) (/ 1 x)))>
#<alt (* x (- (* -1/2 y) (/ 1 x)))>
#<alt (* -1/2 (* x y))>
#<alt (* -1 (* x (+ (* 1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (+ (* 1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (+ (* 1/2 y) (/ 1 x))))>
#<alt -1>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (* -1/2 (* x y))>
#<alt (* y (- (* -1/2 x) (/ 1 y)))>
#<alt (* y (- (* -1/2 x) (/ 1 y)))>
#<alt (* y (- (* -1/2 x) (/ 1 y)))>
#<alt (* -1/2 (* x y))>
#<alt (* -1 (* y (+ (* 1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (+ (* 1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (+ (* 1/2 x) (/ 1 y))))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>
#<alt (/ -4 (* x y))>

Calls

54 calls:

Time	Variable		Point	Expression
47.0ms	x	@	-inf	(/ (+ 2 (/ -4 (* y x))) x)
1.0ms	x	@	inf	(/ (+ 2 (/ -4 (* y x))) x)
1.0ms	y	@	0	(/ (+ 2 (/ -4 (* y x))) x)
1.0ms	x	@	0	(/ (+ 2 (/ -4 (* y x))) x)
0.0ms	y	@	inf	(/ (+ 2 (/ -4 (* y x))) x)

simplify797.0ms (3%)

Memory

13.8MiB live, 409.3MiB allocated

Algorithm

1×	egg-herbie

Rules

9 280×	`lower-fma.f64`
9 280×	`lower-fma.f32`
3 552×	`lower-/.f32`
3 552×	`lower-/.f64`
3 386×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	341	2206
1	1070	2060
2	2764	1959
3	7421	1955
0	8678	1883

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 208

Calls

Call 1

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

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

rewrite612.0ms (2.3%)

Memory

14.0MiB live, 492.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

10 016×	`lower-fma.f32`
10 012×	`lower-fma.f64`
5 772×	`lower-*.f32`
5 768×	`lower-*.f64`
3 158×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	89
0	33	89
1	144	88
2	1040	88
0	8960	86

Stop Event

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

Counts

9 → 392

Calls

Call 1

Inputs
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))
#s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))
(*.f64 x y)
(/.f64 #s(literal -4 binary64) (*.f64 y x))

Outputs
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(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 y y))) #s(literal 1 binary64)) (.f64 y (.f64 x #s(literal -1/2 binary64))))) #s(literal 1 binary64)))
(.f64 (fma.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 y y))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (fma.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 y y))) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64)))))
(.f64 (fma.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 y y))) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (fma.f64 y (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 y (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 y y))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x y) #s(literal -1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))))
(.f64 (/.f64 (fma.f64 y (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 y (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 y (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 y)))
(neg.f64 (*.f64 x (neg.f64 y)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 (*.f64 x y) #s(literal 1 binary64))
(/.f64 (*.f64 x (neg.f64 y)) #s(literal -1 binary64))
(*.f64 x y)
(*.f64 y x)
(.f64 #s(literal 1 binary64) (.f64 x y))
(.f64 (.f64 x y) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (neg.f64 y)))
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x y) #s(literal -1/4 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 4 binary64) (*.f64 x y)))
(neg.f64 (/.f64 #s(literal 4 binary64) (*.f64 x y)))
(neg.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 x y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x y) #s(literal -1/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y (/.f64 #s(literal -4 binary64) x)))
(/.f64 #s(literal -4 binary64) (*.f64 x y))
(/.f64 #s(literal -1 binary64) (.f64 (.f64 x y) #s(literal 1/4 binary64)))
(/.f64 #s(literal 4 binary64) (*.f64 x (neg.f64 y)))
(/.f64 (/.f64 #s(literal -4 binary64) y) x)
(/.f64 (/.f64 #s(literal 4 binary64) y) (neg.f64 x))
(/.f64 (/.f64 #s(literal -4 binary64) x) y)
(/.f64 (neg.f64 (/.f64 #s(literal -4 binary64) x)) (neg.f64 y))
(pow.f64 (.f64 (.f64 x y) #s(literal -1/4 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -4 binary64) (.f64 x y)))
(.f64 #s(literal -4 binary64) (/.f64 #s(literal 1 binary64) (.f64 x y)))
(.f64 #s(literal -4 binary64) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal -4 binary64) (.f64 x y)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 4 binary64) (.f64 x y)))
(.f64 #s(literal 4 binary64) (/.f64 #s(literal -1 binary64) (.f64 x y)))
(.f64 #s(literal 4 binary64) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x y)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -4 binary64) y))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal -4 binary64))
(*.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal -4 binary64) y) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -4 binary64) x) (/.f64 #s(literal 1 binary64) y))
(.f64 (pow.f64 (.f64 (.f64 x y) #s(literal -1/4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 x y) #s(literal -1/4 binary64)) #s(literal -1/2 binary64)))

eval99.0ms (0.4%)

Memory: 11.7MiB live, 164.0MiB allocated
Compiler: Compiled 15 011 to 1 448 computations (90.4% saved)

prune121.0ms (0.5%)

Memory

-26.5MiB live, 131.3MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	599	1	600
Fresh	0	0	0
Picked	1	1	2
Done	1	4	5
Total	601	6	607

Accuracy

100.0%

Counts

607 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.8%	(fma.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 y x))) y x)
✓	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
✓	59.4%	(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))
✓	63.9%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	74.4%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
✓	23.1%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 56 to 34 computations (39.3% saved)

simplify6.0ms (0%)

Memory

14.0MiB live, 14.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

28×	`lower-*.f32`
26×	`lower-*.f64`
16×	`lower-fma.f32`
14×	`lower-fma.f64`
12×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	44
0	18	44
1	30	44
2	39	44
3	41	44
0	41	42

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize39.0ms (0.1%)

Memory

15.4MiB live, 88.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	99.9%	(fma.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 y x))) y x)
✓	accuracy	99.0%	(/.f64 #s(literal -2 binary64) (*.f64 y x))
✓	accuracy	48.0%	#s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 y x)))

Samples

28.0ms

256×

valid

Compiler

Compiled 35 to 16 computations (54.3% saved)

Precisions

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

ival-mult: 6.0ms (46.5% of total)

ival-div: 3.0ms (23.3% of total)

ival-add: 2.0ms (15.5% of total)

exact: 1.0ms (7.8% of total)

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

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

series5.0ms (0%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

4 → 96

Calls

Call 1

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

Outputs
#<alt (* -1 y)>
#<alt (+ (* -1 y) (* x (- 1 (* -1/2 (pow y 2)))))>
#<alt (+ (* -1 y) (* x (- (+ 1 (* -1/4 (* x (pow y 3)))) (* -1/2 (pow y 2)))))>
#<alt (+ (* -1 y) (* x (- (+ 1 (* x (- (* 1/8 (* x (pow y 4))) (* 1/4 (pow y 3))))) (* -1/2 (pow y 2)))))>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (- (* -1/4 (* (pow x 2) y)) (* -1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<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))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt -1>
#<alt (- (* 1/2 (* x y)) 1)>
#<alt (- (* x (- (* -1/4 (* x (pow y 2))) (* -1/2 y))) 1)>
#<alt (- (* x (- (* x (- (* 1/8 (* x (pow y 3))) (* 1/4 (pow y 2)))) (* -1/2 y))) 1)>
#<alt (/ -2 (* x y))>
#<alt (/ (- (* 4 (/ 1 (* x (pow y 2)))) (* 2 (/ 1 y))) x)>
#<alt (/ (- (/ 4 (* x (pow y 2))) (+ (* 2 (/ 1 y)) (/ 8 (* (pow x 2) (pow y 3))))) x)>
#<alt (/ (- (+ (* 16 (/ 1 (* (pow x 3) (pow y 4)))) (/ 4 (* x (pow y 2)))) (+ (* 2 (/ 1 y)) (* 8 (/ 1 (* (pow x 2) (pow y 3)))))) x)>
#<alt (/ -2 (* x y))>
#<alt (* -1 (/ (- (* 2 (/ 1 y)) (* 4 (/ 1 (* x (pow y 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 4 (/ 1 (pow y 2))) (* 8 (/ 1 (* x (pow y 3))))) x)) (* 2 (/ 1 y))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow y 3))) (* 16 (/ 1 (* x (pow y 4))))) x)) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))>
#<alt -1>
#<alt (- (* 1/2 (* x y)) 1)>
#<alt (- (* y (- (* -1/4 (* (pow x 2) y)) (* -1/2 x))) 1)>
#<alt (- (* y (- (* y (- (* 1/8 (* (pow x 3) y)) (* 1/4 (pow x 2)))) (* -1/2 x))) 1)>
#<alt (/ -2 (* x y))>
#<alt (/ (- (* 4 (/ 1 (* (pow x 2) y))) (* 2 (/ 1 x))) y)>
#<alt (/ (- (/ 4 (* (pow x 2) y)) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2))))) y)>
#<alt (/ (- (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2)))))) y)>
#<alt (/ -2 (* x y))>
#<alt (* -1 (/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) y))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x))) y))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (/ -2 (* x y))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>

Calls

24 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(/ -2 (* y x))
0.0ms	y	@	0	(/ -2 (* y x))
0.0ms	x	@	0	(/ -2 (* y x))
0.0ms	x	@	inf	(/ -2 (* y x))
0.0ms	x	@	-inf	(/ -2 (* y x))

simplify555.0ms (2.1%)

Memory

-6.6MiB live, 678.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 946×	`lower-fma.f64`
10 946×	`lower-fma.f32`
4 286×	`lower-*.f64`
4 286×	`lower-*.f32`
2 472×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	933
1	676	904
2	1769	894
3	5143	881
0	8493	851

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 93

Calls

Call 1

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

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

rewrite378.0ms (1.4%)

Memory

-40.0MiB live, 733.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 966×	`lower-fma.f32`
5 964×	`lower-fma.f64`
4 188×	`lower-*.f32`
4 186×	`lower-*.f64`
3 448×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
0	18	41
1	70	41
2	420	41
3	3858	41
0	8953	39

Stop Event

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

Counts

4 → 170

Calls

Call 1

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

Outputs
(+.f64 x (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y)))))
(+.f64 (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y)))) x)
(+.f64 (/.f64 (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y))) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y))) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))))) (/.f64 (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y))) (-.f64 x (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y)))))))
(fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) x)
(fma.f64 y (/.f64 (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))))) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x)))))
(fma.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) y x)
(fma.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (/.f64 (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y)) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x)))))
(fma.f64 (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))) (/.f64 (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x)))))
(fma.f64 (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x)))))
(fma.f64 (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))) (/.f64 (.f64 y y) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x)))))
(fma.f64 (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))))) (/.f64 y (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x)))))
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(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (.f64 (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) (neg.f64 x))))
(.f64 (.f64 (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (-.f64 x (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y)))))))
(.f64 (/.f64 (.f64 (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (.f64 (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x)))) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))) x))
(.f64 (/.f64 (.f64 (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 x x (.f64 (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 x (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))))) (.f64 (-.f64 x (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))))) (-.f64 x (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))))))) (pow.f64 (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))) #s(literal 6 binary64)))) (fma.f64 (.f64 x (-.f64 x (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))))) (-.f64 (.f64 x (-.f64 x (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y)))) (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y)) (.f64 #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y)))))))
(.f64 (/.f64 (.f64 (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 x x (.f64 (.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))))) (.f64 (fma.f64 x x (.f64 (.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y)))) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x)))) (fma.f64 (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x)) (.f64 (.f64 x y) #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))))))) (fma.f64 (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x)) (.f64 (.f64 x y) #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y))))))
(.f64 (/.f64 (.f64 (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (fma.f64 y #s(approx (/ 1 (+ ( (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (neg.f64 x))) (fma.f64 y (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y)))) (neg.f64 (.f64 x (.f64 x x))))) (fma.f64 x (fma.f64 y #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) x) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (.f64 x y))) (.f64 y y)))))
#s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 x y)))
(exp.f64 (neg.f64 (log.f64 (.f64 #s(literal -1/2 binary64) (.f64 x y)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y)))
(neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 x y))))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 y (/.f64 #s(literal -2 binary64) x)))
(/.f64 #s(literal -1 binary64) (.f64 (.f64 x y) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 y (/.f64 #s(literal -2 binary64) x))))
(/.f64 #s(literal -2 binary64) (*.f64 x y))
(/.f64 #s(literal 2 binary64) (neg.f64 (*.f64 x y)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal -1/2 binary64))
(/.f64 (/.f64 #s(literal -2 binary64) y) x)
(/.f64 (/.f64 #s(literal -2 binary64) y) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 #s(literal 2 binary64) y) (neg.f64 x))
(/.f64 (/.f64 #s(literal 2 binary64) y) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x y)) #s(literal 1/2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 y #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) x) y)
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 y #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (*.f64 x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal -2 binary64) x)) (neg.f64 y))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) y)) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) y)
(/.f64 (*.f64 (/.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)) x)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) y)
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (neg.f64 y))
(/.f64 (/.f64 #s(literal 2 binary64) x) (neg.f64 y))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal -2 binary64) x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) y))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) (neg.f64 y))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal -2 binary64) y) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) (neg.f64 y))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (/.f64 #s(literal 2 binary64) x)) (neg.f64 (neg.f64 y)))
(pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 x y)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (*.f64 x y)) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 y (.f64 (.f64 x y) #s(literal 1/4 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 y (/.f64 #s(literal -2 binary64) x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x y)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (.f64 x y)))
(.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x y)))
(.f64 (/.f64 #s(literal -2 binary64) (.f64 x y)) #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) (.f64 x y)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal -2 binary64))
(*.f64 (/.f64 #s(literal -2 binary64) y) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x y)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -2 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal -2 binary64) x))
(*.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 #s(literal 1 binary64) y))
(.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (.f64 (log.f64 (.f64 x y)) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (*.f64 x y)))
(neg.f64 (neg.f64 (*.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x y)))
(/.f64 (*.f64 x y) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 x y)) #s(literal -1 binary64))
(pow.f64 (*.f64 x y) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x y)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x y))
(*.f64 x y)
(*.f64 x (neg.f64 (neg.f64 y)))
(*.f64 x (/.f64 y #s(literal 1 binary64)))
(*.f64 y x)
(*.f64 y (neg.f64 (neg.f64 x)))
(*.f64 y (/.f64 x #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (.f64 x y)))
(.f64 (.f64 x y) #s(literal 1 binary64))
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 (neg.f64 (neg.f64 x)) y)
(*.f64 (neg.f64 (neg.f64 y)) x)

eval56.0ms (0.2%)

Memory: 1.7MiB live, 127.5MiB allocated
Compiler: Compiled 7 725 to 591 computations (92.3% saved)

prune29.0ms (0.1%)

Memory

16.0MiB live, 93.2MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	263	6	269

Accuracy

100.0%

Counts

269 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.8%	(fma.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 y x))) y x)
✓	100.0%	(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
✓	59.4%	(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))
✓	63.9%	(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
✓	74.4%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (-.f64 x y))
✓	23.1%	#s(approx (- x (/ y (+ 1 (/ (* x y) 2)))) (neg.f64 y))

Compiler

Compiled 146 to 73 computations (50% saved)

regimes15.0ms (0.1%)

Memory

-12.3MiB live, 29.0MiB allocated

Counts

10 → 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))
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
(fma.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 y x))) y x)
(-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))
(-.f64 x (/.f64 y (fma.f64 (*.f64 y #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) #s(literal -1/2 binary64) #s(literal -1 binary64))) y x)
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x y)) #s(literal -2 binary64)) x)))
(-.f64 x #s(approx (/ y (+ (* (* y 1/2) x) 1)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) (*.f64 y x))) x)))
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))

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

Calls

3 calls:

7.0ms	y
4.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
3.0ms	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 19 to 13 computations (31.6% saved)

regimes8.0ms (0%)

Memory

20.6MiB live, 20.6MiB allocated

Counts

5 → 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))
(-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x)))
(fma.f64 #s(approx (/ 1 (+ (* (* x y) -1/2) -1)) (/.f64 #s(literal -2 binary64) (*.f64 y x))) y x)
(-.f64 x (/.f64 y #s(approx (+ 1 (/ (* x y) 2)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))

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:

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

Results

Accuracy	Segments	Branch
88.3%	3	`x`
94.6%	3	`y`
89.2%	3	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes38.0ms (0.1%)

Memory

-26.9MiB live, 12.4MiB allocated

Counts

2 → 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))

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

Calls

3 calls:

34.0ms	y
2.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
2.0ms	x

Results

Accuracy	Segments	Branch
74.4%	1	`x`
74.4%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
74.4%	1	`y`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes4.0ms (0%)

Memory

10.8MiB live, 10.8MiB 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	x
1.0ms	y

Results

Accuracy	Segments	Branch
23.1%	1	`x`
23.1%	1	`y`
23.1%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch35.0ms (0.1%)

Memory

-5.7MiB live, 33.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
26.0ms	5.0434307053461065e+125	2.990388917495551e+127
7.0ms	-2.9268433533167603e+124	-1.2907831719799352e+124

Samples

26.0ms

192×

valid

Compiler

Compiled 208 to 134 computations (35.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 18.0ms (81.2% of total)

ival-div: 2.0ms (9% of total)

ival-sub: 1.0ms (4.5% of total)

ival-add: 1.0ms (4.5% of total)

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

exact: 0.0ms (0% of total)

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

simplify8.0ms (0%)

Memory

21.5MiB live, 21.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
14×	`sub-neg_binary64`
10×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

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 #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -19999999999999998967063748934624286428789536754564174703921029226169858140974054838505074898178041767770400845226851252043776 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 1900000000000000082708835022374465758225011944462547704800054042426766567853940017638077049151764114643010955923741002403151872 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 #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -19999999999999998967063748934624286428789536754564174703921029226169858140974054838505074898178041767770400845226851252043776 binary64)) (-.f64 x #s(approx (/ y (+ 1 (/ (* x y) 2))) (/.f64 #s(literal 2 binary64) x))) (if (<=.f64 y #s(literal 1900000000000000082708835022374465758225011944462547704800054042426766567853940017638077049151764114643010955923741002403151872 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))

soundness605.0ms (2.3%)

Memory

-13.8MiB live, 331.3MiB allocated

Rules

13 558×	`lower-fma.f64`
13 558×	`lower-fma.f32`
5 754×	`lower-fma.f64`
5 754×	`lower-fma.f32`
4 930×	`lower-*.f64`

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
0	231	1053
1	738	1018
2	1942	987
3	6081	981
0	8428	934

Stop Event

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

Compiler

Compiled 87 to 47 computations (46% saved)

preprocess59.0ms (0.2%)

Memory: 9.1MiB live, 136.0MiB allocated
Compiler: Compiled 112 to 56 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze24.0ms (0.1%)

sample1.6s (6.1%)

preprocess154.0ms (0.6%)

explain327.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify36.0ms (0.1%)

localize86.0ms (0.3%)

series98.0ms (0.4%)

simplify673.0ms (2.6%)

rewrite18.3s (70.1%)

eval46.0ms (0.2%)

prune45.0ms (0.2%)

simplify58.0ms (0.2%)

localize66.0ms (0.3%)

series10.0ms (0%)

simplify308.0ms (1.2%)

rewrite289.0ms (1.1%)

eval117.0ms (0.4%)

prune90.0ms (0.3%)

simplify143.0ms (0.5%)

localize103.0ms (0.4%)

series57.0ms (0.2%)

simplify797.0ms (3%)

rewrite612.0ms (2.3%)

eval99.0ms (0.4%)

prune121.0ms (0.5%)

simplify6.0ms (0%)

localize39.0ms (0.1%)

series5.0ms (0%)

simplify555.0ms (2.1%)

rewrite378.0ms (1.4%)

eval56.0ms (0.2%)

prune29.0ms (0.1%)

regimes15.0ms (0.1%)

regimes8.0ms (0%)

regimes38.0ms (0.1%)

regimes4.0ms (0%)

bsearch35.0ms (0.1%)

simplify8.0ms (0%)

soundness605.0ms (2.3%)

preprocess59.0ms (0.2%)

end0.0ms (0%)

Profiling