Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

analyze68.0ms (1.3%)

Memory

-31.7MiB live, 47.6MiB 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
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample581.0ms (11%)

Memory

30.2MiB live, 1 341.9MiB allocated

Samples

377.0ms	8 256×	0	valid
17.0ms	350×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 210.0ms

ival-mult: 96.0ms (45.7% of total)

ival-sqrt: 62.0ms (29.5% of total)

ival-add: 42.0ms (20% of total)

ival-true: 6.0ms (2.9% of total)

ival-assert: 4.0ms (1.9% of total)

Bogosity

preprocess44.0ms (0.8%)

Memory

-9.5MiB live, 29.8MiB allocated

Algorithm

2×	egg-herbie

Rules

64×	`sub-neg`
36×	`associate--r+`
34×	`associate-+l-`
32×	`distribute-lft-neg-in`
32×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	35	38
2	70	38
3	125	38
4	189	38
5	252	38
6	314	38
7	326	38
8	332	38
0	5	6
1	6	6
0	6	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) y))

Outputs
(sqrt (+ (* x x) y))
(sqrt.f64 (fma.f64 x x y))

Call 2

Inputs
(sqrt (+ (* x x) y))
(sqrt (+ (* (neg x) (neg x)) y))
(sqrt (+ (* x x) (neg y)))
(neg (sqrt (+ (* (neg x) (neg x)) y)))
(neg (sqrt (+ (* x x) (neg y))))
(sqrt (+ (* y y) x))

Outputs
(sqrt (+ (* x x) y))
(sqrt (+ (* (neg x) (neg x)) y))
(sqrt (+ (* x x) y))
(sqrt (+ (* x x) (neg y)))
(sqrt (- (* x x) y))
(neg (sqrt (+ (* (neg x) (neg x)) y)))
(neg (sqrt (+ (* x x) y)))
(neg (sqrt (+ (* x x) (neg y))))
(neg (sqrt (- (* x x) y)))
(sqrt (+ (* y y) x))
(sqrt (+ x (* y y)))

Symmetry

(abs x)

explain68.0ms (1.3%)

Memory

-9.9MiB live, 188.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
80	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
0	-	-	`(+.f64 (*.f64 x x) y)`
0	-	-	`y`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) y))`	oflow-rescue	80	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	80
↳	`(*.f64 x x)`	overflow	80

Confusion

	Predicted +	Predicted -
+	80	0
-	0	176

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	80	0	0
-	0	0	176

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	176
1	80

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 52 to 24 computations (53.8% saved)

Precisions

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

ival-mult: 4.0ms (34.8% of total)

ival-sqrt: 4.0ms (34.8% of total)

ival-add: 3.0ms (26.1% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.0%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify4.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`
2×	`-lowering-.f32`
2×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
1	6	16
0	6	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) y))
(+ (* x x) y)
(* x x)
x
y

Outputs
(sqrt (+ (* x x) y))
(sqrt.f64 (fma.f64 x x y))
(+ (* x x) y)
(fma.f64 x x y)
(* x x)
(*.f64 x x)
x
y

localize19.0ms (0.4%)

Memory

18.3MiB live, 59.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	71.0%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

13.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 4.0ms (54.7% of total)

ival-sqrt: 2.0ms (27.4% of total)

ival-add: 1.0ms (13.7% of total)

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

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

series6.0ms (0.1%)

Memory

-23.9MiB live, 14.4MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (+ (* x x) y)>
#<alt (sqrt (+ (* x x) y))>
#<alt (* x x)>

Outputs
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	(+ (* x x) y)
1.0ms	y	@	-inf	(sqrt (+ (* x x) y))
1.0ms	y	@	inf	(sqrt (+ (* x x) y))
0.0ms	x	@	inf	(sqrt (+ (* x x) y))
0.0ms	x	@	0	(sqrt (+ (* x x) y))

rewrite350.0ms (6.6%)

Memory

-3.7MiB live, 792.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 034×	`accelerator-lowering-fma.f32`
5 034×	`accelerator-lowering-fma.f64`
4 204×	`/-lowering-/.f32`
4 204×	`/-lowering-/.f64`
3 240×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	23	14
2	166	14
3	1514	14
0	8473	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 228

Calls

Call 1

Inputs
(+ (* x x) y)
(sqrt (+ (* x x) y))
(* x x)

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

simplify578.0ms (10.9%)

Memory

25.1MiB live, 930.4MiB allocated

Algorithm

1×	egg-herbie

Rules

23 136×	`accelerator-lowering-fma.f32`
23 136×	`accelerator-lowering-fma.f64`
5 482×	`-lowering-.f32`
5 482×	`-lowering-.f64`
2 326×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	635
1	383	620
2	1206	612
3	4042	567
0	8636	515

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
y
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
y
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(-.f64 #s(literal 0 binary64) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(-.f64 #s(literal 0 binary64) (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 y (fma.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 y (fma.f64 x (.f64 x (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval35.0ms (0.7%)

Memory: 6.9MiB live, 81.9MiB allocated
Compiler: Compiled 11 271 to 848 computations (92.5% saved)

prune38.0ms (0.7%)

Memory

-2.9MiB live, 76.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	283	5	288
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	284	5	289

Accuracy

100.0%

Counts

289 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.4%	(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
▶	68.7%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
▶	71.0%	(sqrt.f64 (fma.f64 x x y))
▶	34.0%	(sqrt.f64 y)
▶	68.1%	x

Compiler

Compiled 74 to 46 computations (37.8% saved)

simplify12.0ms (0.2%)

Memory

20.8MiB live, 20.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
✓	cost-diff	(fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
✓	cost-diff	(/.f64 y x)
✓	cost-diff	(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
✓	cost-diff	(sqrt.f64 y)
✓	cost-diff	(fma.f64 x x y)
✓	cost-diff	(sqrt.f64 (fma.f64 x x y))

Rules

190×	`accelerator-lowering-fma.f32`
190×	`accelerator-lowering-fma.f64`
174×	`-lowering-.f32`
174×	`-lowering-.f64`
68×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	38	69
2	90	69
3	166	69
4	226	69
5	252	69
0	252	63

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) y))
(+ (* x x) y)
x
y
x
(sqrt y)
y
(+ (* y (/ 1/2 x)) x)
y
(/ 1/2 x)
1/2
x
(+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)
(/ y x)
y
x
(+ (* y (/ -1/8 (* x x))) 1/2)
(/ -1/8 (* x x))
-1/8
(* x x)
1/2

Outputs
(sqrt (+ (* x x) y))
(sqrt.f64 (fma.f64 x x y))
(+ (* x x) y)
(fma.f64 x x y)
x
y
x
(sqrt y)
(sqrt.f64 y)
y
(+ (* y (/ 1/2 x)) x)
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
y
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x
(+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)
(fma.f64 (/.f64 y x) (fma.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64)) x)
(/ y x)
(/.f64 y x)
y
x
(+ (* y (/ -1/8 (* x x))) 1/2)
(fma.f64 #s(literal -1/8 binary64) (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64))
(/ -1/8 (* x x))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
-1/8
#s(literal -1/8 binary64)
(* x x)
(*.f64 x x)
1/2
#s(literal 1/2 binary64)

localize56.0ms (1%)

Memory

-20.7MiB live, 90.6MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
✓	accuracy	99.5%	(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
✓	accuracy	94.8%	(fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	99.9%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
✓	accuracy	100.0%	(sqrt.f64 y)
✓	accuracy	100.0%	(fma.f64 x x y)
✓	accuracy	86.9%	(sqrt.f64 (fma.f64 x x y))

Samples

21.0ms	160×	0	valid
14.0ms	96×	0	invalid

Compiler

Compiled 65 to 19 computations (70.8% saved)

Precisions

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

ival-mult: 6.0ms (30.3% of total)

ival-div: 5.0ms (25.3% of total)

ival-add: 5.0ms (25.3% of total)

ival-sqrt: 3.0ms (15.2% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Memory

21.4MiB live, 21.4MiB allocated

Counts

10 → 192

Calls

Call 1

Inputs
#<alt (sqrt (+ (* x x) y))>
#<alt (+ (* x x) y)>
#<alt (sqrt y)>
#<alt (+ (* y (/ 1/2 x)) x)>
#<alt (/ 1/2 x)>
#<alt (+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)>
#<alt (/ y x)>
#<alt (+ (* y (/ -1/8 (* x x))) 1/2)>
#<alt (/ -1/8 (* x x))>
#<alt (* x x)>

Outputs
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (* 1/2 (/ y x))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* y (+ (* 1/2 (/ 1 x)) (/ x y)))>
#<alt (* 1/2 (/ y x))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))>
#<alt (* 1/2 (/ y x))>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt (/ (+ (* 1/2 y) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow y 2) (pow x 3)))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))>
#<alt (* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 1)))>
#<alt (* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 1)))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* y (- (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* y (- (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* y (- (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (* -1 (* y (- (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 y)))))>
#<alt (* -1 (* y (- (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 y)))))>
#<alt (* -1 (* y (- (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 y)))))>
#<alt (* -1/8 (/ y (pow x 2)))>
#<alt (/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (+ 1/2 (* -1/8 (/ y (pow x 2))))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)
1.0ms	y	@	0	(sqrt y)
1.0ms	y	@	0	(+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)
0.0ms	y	@	-inf	(+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)
0.0ms	x	@	0	(+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)

rewrite374.0ms (7.1%)

Memory

1.0MiB live, 607.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 880×	`accelerator-lowering-fma.f32`
5 880×	`accelerator-lowering-fma.f64`
3 894×	`-lowering-.f32`
3 894×	`-lowering-.f64`
3 764×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	58
1	111	58
2	952	58
0	8403	52

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 457

Calls

Call 1

Inputs
(sqrt (+ (* x x) y))
(+ (* x x) y)
(sqrt y)
(+ (* y (/ 1/2 x)) x)
(/ 1/2 x)
(+ (* (/ y x) (+ (* y (/ -1/8 (* x x))) 1/2)) x)
(/ y x)
(+ (* y (/ -1/8 (* x x))) 1/2)
(/ -1/8 (* x x))
(* x x)

Outputs
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x x y))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x))))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) y)) (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 (*.f64 x x) y)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (sqrt.f64 (fma.f64 y y (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x y))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x)))))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x y) (fma.f64 x (-.f64 #s(literal 0 binary64) x) y))) (sqrt.f64 (fma.f64 x (-.f64 #s(literal 0 binary64) x) y)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x)))) (sqrt.f64 (-.f64 y (*.f64 x x))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y))))) (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x)))))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) y))))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 x x y) (fma.f64 x x y)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x y))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (*.f64 x x))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (*.f64 x x)))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (*.f64 x x)))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 x x) y))))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 y (.f64 x x))))
(fma.f64 x x y)
(fma.f64 (*.f64 x x) #s(literal 1 binary64) y)
(fma.f64 y #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x) y)
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) y)
(fma.f64 #s(literal 1 binary64) y (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)) y)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) y)
(neg.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x)))))))
(neg.f64 (/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (fma.f64 x (-.f64 #s(literal 0 binary64) x) y)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x))))))
(neg.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 x (-.f64 #s(literal 0 binary64) x) y)) (-.f64 (.f64 x x) y)))
(/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (fma.f64 y y (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x y)))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 x x)) (.f64 (fma.f64 x x y) (-.f64 y (*.f64 x x)))))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (neg.f64 (fma.f64 y y (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x y))))))
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(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 y (.f64 y y)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 (*.f64 x x) #s(literal 8 binary64))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 y (.f64 y y)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 y (.f64 (.f64 x x) #s(literal -8 binary64))) (.f64 y #s(literal -1/8 binary64))) (.f64 (.f64 y #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64))) (+.f64 (/.f64 y (.f64 (*.f64 x x) #s(literal 8 binary64))) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 (*.f64 x x) #s(literal 8 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (.f64 (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 y (.f64 y y)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 (*.f64 x x) #s(literal 8 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)))) (neg.f64 (+.f64 (/.f64 y (.f64 (*.f64 x x) #s(literal 8 binary64))) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 (*.f64 x x) #s(literal 8 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (.f64 (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 y (.f64 y y)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 (.f64 x x) #s(literal 8 binary64))))))))
(.f64 (fma.f64 (.f64 y (.f64 y y)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 y (.f64 (.f64 x x) #s(literal -8 binary64))) (.f64 y #s(literal -1/8 binary64))) (.f64 (.f64 y #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (*.f64 x x)))))
(.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
(.f64 (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 y (.f64 y y)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 (.f64 x x) #s(literal 8 binary64)))))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 y (.f64 (.f64 x x) #s(literal 8 binary64))) #s(literal 1/2 binary64))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 y y) #s(literal 1/64 binary64)) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 (.f64 x x) #s(literal 8 binary64))))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal -8 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(neg.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal -8 binary64))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) x) x))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -8 binary64)))
(/.f64 (/.f64 #s(literal -1/8 binary64) x) x)
(/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 8 binary64)))
(/.f64 (/.f64 #s(literal 1/8 binary64) x) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal -1 binary64))
(.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/8 binary64) x))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal -8 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify698.0ms (13.2%)

Memory

-8.8MiB live, 675.2MiB allocated

Algorithm

1×	egg-herbie

Rules

17 214×	`accelerator-lowering-fma.f32`
17 214×	`accelerator-lowering-fma.f64`
6 006×	`-lowering-.f32`
6 006×	`-lowering-.f64`
1 540×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	193	1579
1	539	1564
2	1620	1550
3	5698	1435
0	8386	1326

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
x
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(* 1/2 (/ y x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* 1/2 (/ y x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (+ (/ 1/2 (* x y)) (/ x (pow y 2))) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(* (pow y 2) (- (* 1/2 (/ 1 (* x y))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))
(* (pow y 2) (- (* -1 (/ (- (* -1 (/ x y)) (* 1/2 (/ 1 x))) y)) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow y 2) (pow x 3)))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (* (pow x 2) y))) (pow x 3))
(/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))
(/ (+ (* -1/8 (pow y 2)) (* (pow x 2) (+ (* 1/2 y) (pow x 2)))) (pow x 3))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 1)))
(* -1 (* x (- (+ (* -1/2 (/ y (pow x 2))) (* 1/8 (/ (pow y 2) (pow x 4)))) 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)
1/2
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(* -1/8 (/ y (pow x 2)))
(* y (- (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow x 2)))))
(* y (- (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow x 2)))))
(* y (- (* 1/2 (/ 1 y)) (* 1/8 (/ 1 (pow x 2)))))
(* -1/8 (/ y (pow x 2)))
(* -1 (* y (- (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 y)))))
(* -1 (* y (- (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 y)))))
(* -1 (* y (- (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 y)))))
(* -1/8 (/ y (pow x 2)))
(/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 2))
(/ (+ (* -1/8 y) (* 1/2 (pow x 2))) (pow x 2))
1/2
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(+ 1/2 (* -1/8 (/ y (pow x 2))))
1/2
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(+ 1/2 (* -1/8 (/ y (pow x 2))))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

eval87.0ms (1.6%)

Memory: -7.9MiB live, 198.7MiB allocated
Compiler: Compiled 17 431 to 1 440 computations (91.7% saved)

prune64.0ms (1.2%)

Memory

-9.8MiB live, 151.4MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	648	1	649
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	649	5	654

Accuracy

100.0%

Counts

654 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.7%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
▶	70.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
✓	71.0%	(sqrt.f64 (fma.f64 x x y))
✓	34.0%	(sqrt.f64 y)
✓	68.1%	x

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify4.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`/-lowering-/.f32`
4×	`/-lowering-/.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	33
1	11	33
0	11	29

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ 1 (sqrt (/ 1 (+ (* x x) y))))
1
(sqrt (/ 1 (+ (* x x) y)))
(/ 1 (+ (* x x) y))
(+ (* x x) y)
x
y

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

localize208.0ms (3.9%)

Memory

-7.8MiB live, 31.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x y)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (fma.f64 x x y))
✓	accuracy	71.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))

Samples

199.0ms

256×

valid

Compiler

Compiled 31 to 10 computations (67.7% saved)

Precisions

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

ival-div: 3.0ms (34.6% of total)

ival-mult: 2.0ms (23.1% of total)

ival-sqrt: 2.0ms (23.1% of total)

ival-add: 1.0ms (11.5% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#<alt (/ 1 (sqrt (/ 1 (+ (* x x) y))))>
#<alt (sqrt (/ 1 (+ (* x x) y)))>
#<alt (/ 1 (+ (* x x) y))>
#<alt (+ (* x x) y)>

Outputs
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ y (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))>
#<alt x>
#<alt (+ x (* 1/2 (/ y x)))>
#<alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt (/ 1 y))>
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))>
#<alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))>
#<alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)>
#<alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)>
#<alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x))>
#<alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x))>
#<alt (/ 1 x)>
#<alt (+ (* -1/2 (/ y (pow x 3))) (/ 1 x))>
#<alt (+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))>
#<alt (+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))>
#<alt (sqrt (/ 1 y))>
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))>
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))>
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))))>
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))>
#<alt (/ 1 y)>
#<alt (+ (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y))>
#<alt (+ (* (pow x 2) (- (/ (pow x 2) (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 2)))>
#<alt (+ (* y (- (/ y (pow x 6)) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))>
#<alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))>
#<alt (/ 1 y)>
#<alt (/ (+ 1 (* -1 (/ (pow x 2) y))) y)>
#<alt (/ (- (+ 1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y)) y)>
#<alt (/ (- (+ 1 (* -1 (/ (pow x 6) (pow y 3)))) (+ (* -1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y))) y)>
#<alt (/ 1 y)>
#<alt (* -1 (/ (- (/ (pow x 2) y) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 2)) y)) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (pow x 4)) y)) (pow x 2)) y)) 1) y))>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (/ 1 (+ (* x x) y)))
1.0ms	y	@	-inf	(sqrt (/ 1 (+ (* x x) y)))
1.0ms	x	@	inf	(sqrt (/ 1 (+ (* x x) y)))
1.0ms	y	@	inf	(sqrt (/ 1 (+ (* x x) y)))
0.0ms	y	@	0	(sqrt (/ 1 (+ (* x x) y)))

rewrite171.0ms (3.2%)

Memory

20.3MiB live, 139.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 392×	`-lowering-.f32`
1 392×	`-lowering-.f64`
1 204×	`accelerator-lowering-fma.f32`
1 204×	`accelerator-lowering-fma.f64`
1 002×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	45	25
2	273	25
0	2317	21

Stop Event

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

Counts

4 → 282

Calls

Call 1

Inputs
(/ 1 (sqrt (/ 1 (+ (* x x) y))))
(sqrt (/ 1 (+ (* x x) y)))
(/ 1 (+ (* x x) y))
(+ (* x x) y)

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

simplify771.0ms (14.5%)

Memory

5.2MiB live, 551.6MiB allocated

Algorithm

1×	egg-herbie

Rules

11 592×	`accelerator-lowering-fma.f32`
11 592×	`accelerator-lowering-fma.f64`
4 132×	`-lowering-.f32`
4 132×	`-lowering-.f64`
3 602×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	298	1506
1	871	1445
2	2628	1413
3	6262	1393
0	8395	1296

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))
(/ 1 x)
(/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)
(/ -1 x)
(* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x))
(/ 1 x)
(+ (* -1/2 (/ y (pow x 3))) (/ 1 x))
(+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(/ 1 y)
(+ (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y))
(+ (* (pow x 2) (- (/ (pow x 2) (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(/ 1 (pow x 2))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(/ 1 (pow x 2))
(+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 2)))
(+ (* y (- (/ y (pow x 6)) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(/ 1 y)
(/ (+ 1 (* -1 (/ (pow x 2) y))) y)
(/ (- (+ 1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 6) (pow y 3)))) (+ (* -1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y))) y)
(/ 1 y)
(* -1 (/ (- (/ (pow x 2) y) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 2)) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (pow x 4)) y)) (pow x 2)) y)) 1) y))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))))) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (*.f64 y (/.f64 #s(literal 1/2 binary64) x)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 x (fma.f64 (.f64 y #s(literal -1/8 binary64)) (/.f64 y (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (.f64 y (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
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(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 #s(literal -1 binary64) (*.f64 y (/.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
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(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
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x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 y (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
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(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
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(sqrt (/ 1 y))
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(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 3/8 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 (.f64 x x) #s(literal -5/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) #s(literal 3/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)
(/.f64 (fma.f64 y (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 y y) (/.f64 #s(literal -3/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 y (*.f64 x x))) #s(literal 1 binary64)) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)
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(/ -1 x)
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(* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x))
(/.f64 (fma.f64 y (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x)
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 y y) (/.f64 #s(literal -3/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 y (*.f64 x x))) #s(literal -1 binary64)) x)
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 y (fma.f64 (.f64 (.f64 y y) #s(literal -3/4 binary64)) #s(literal 1/2 binary64) (.f64 y y))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 y y) (/.f64 #s(literal -3/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 y (*.f64 x x)))) #s(literal -1 binary64)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1/2 (/ y (pow x 3))) (/ 1 x))
(fma.f64 y (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(fma.f64 y (fma.f64 y (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(fma.f64 y (fma.f64 y (fma.f64 y (/.f64 #s(literal -5/16 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y #s(literal 1/4 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(fma.f64 x (.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) #s(literal -1/2 binary64))) (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y #s(literal 1/4 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 y) (.f64 (.f64 x x) (.f64 x x))))) (.f64 y (.f64 y y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y))
(/.f64 (fma.f64 x (/.f64 x y) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))
(+ (* (pow x 2) (- (/ (pow x 2) (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(fma.f64 (.f64 x x) (fma.f64 x (/.f64 x (.f64 y (.f64 y y))) (/.f64 #s(literal -1 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) y))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))) (/.f64 (.f64 x x) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal -1 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) y))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/.f64 (fma.f64 y (/.f64 y (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x)))) (*.f64 x x))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (.f64 y y) (pow.f64 x #s(literal 6 binary64))) (fma.f64 y (/.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (.f64 x x) (.f64 x x))) (/.f64 y (.f64 x x))))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/.f64 (fma.f64 y (/.f64 y (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x)))) (*.f64 x x))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (.f64 y y) (pow.f64 x #s(literal 6 binary64))) (fma.f64 y (/.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (.f64 x x) (.f64 x x))) (/.f64 y (.f64 x x))))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x))) (.f64 x x))
(+ (* y (- (/ y (pow x 6)) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(fma.f64 y (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x))) (.f64 x x)))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(fma.f64 y (fma.f64 y (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 y (pow.f64 x #s(literal 8 binary64)))) #s(literal 0 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y (.f64 x x))) (.f64 x x)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* -1 (/ (pow x 2) y))) y)
(/.f64 (fma.f64 x (/.f64 x y) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))
(/ (- (+ 1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y)) y)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) y) (.f64 x x)) y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 6) (pow y 3)))) (+ (* -1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y))) y)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) y) (.f64 (.f64 x x) (*.f64 x x))) y)) y)) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* -1 (/ (- (/ (pow x 2) y) 1) y))
(/.f64 (fma.f64 x (/.f64 x y) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 2)) y)) 1) y))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) y) (.f64 x x)) y)) y)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (pow x 4)) y)) (pow x 2)) y)) 1) y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) y) (.f64 (.f64 x x) (*.f64 x x))) y)) y)) y)
y
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
y
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)

eval119.0ms (2.2%)

Memory: -20.0MiB live, 55.7MiB allocated
Compiler: Compiled 9 573 to 1 302 computations (86.4% saved)

prune110.0ms (2.1%)

Memory

11.2MiB live, 88.8MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	378	0	378
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	378	5	383

Accuracy

100.0%

Counts

383 → 5

Alt Table

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Status	Accuracy	Program
✓	68.7%	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
✓	70.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
✓	71.0%	(sqrt.f64 (fma.f64 x x y))
✓	34.0%	(sqrt.f64 y)
✓	68.1%	x

Compiler

Compiled 77 to 41 computations (46.8% saved)

regimes49.0ms (0.9%)

Memory

-6.7MiB live, 32.3MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
x
(sqrt.f64 y)
(sqrt.f64 (fma.f64 x x y))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(sqrt.f64 (+.f64 (*.f64 x x) y))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
x

Calls

5 calls:

37.0ms	x
3.0ms	y
3.0ms	(+.f64 (*.f64 x x) y)
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
86.9%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes8.0ms (0.2%)

Memory

19.5MiB live, 19.5MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
x
(sqrt.f64 y)
(sqrt.f64 (fma.f64 x x y))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)

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

Calls

4 calls:

2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes58.0ms (1.1%)

Memory

-54.0MiB live, 15.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
x
(sqrt.f64 y)
(sqrt.f64 (fma.f64 x x y))

Outputs
(sqrt.f64 (fma.f64 x x y))
x

Calls

4 calls:

52.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	x
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`x`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes6.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
x
(sqrt.f64 y)

Outputs
(sqrt.f64 y)
x

Calls

4 calls:

1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	x
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
89.9%	2	`x`
77.9%	4	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
77.9%	4	`(+.f64 (*.f64 x x) y)`
89.9%	2	`(*.f64 x x)`

Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes6.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

5 calls:

1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	y
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
68.1%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
68.1%	1	`(+.f64 (*.f64 x x) y)`
68.1%	1	`y`
68.1%	1	`x`
68.1%	1	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0166165064633262e+231	7.226472159496221e+235

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.646567795393787e+188	3.4699788284544374e+192

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0166165064633262e+231	7.226472159496221e+235

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.944281307033192e-70	1.0359545584090169e-66

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify8.0ms (0.2%)

Memory

9.2MiB live, 9.2MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	22	52

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 2000000000000000112950822041041682829681252763966116749401130328310913127935156394378439523178919965959536338695072724193131961289213847754610320291206559558839567880608124639637128476165182553839199176610603506544803697392590258176 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 500000000000000011546545651348935774464919112425849637715282289077421094839728844432880898433975380555391192719129287098299595056567936753438014858326845092856015715723317824379483334901760 binary64)) (sqrt.f64 (fma.f64 x x y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))
(if (<=.f64 (*.f64 x x) #s(literal 2000000000000000112950822041041682829681252763966116749401130328310913127935156394378439523178919965959536338695072724193131961289213847754610320291206559558839567880608124639637128476165182553839199176610603506544803697392590258176 binary64)) (sqrt.f64 (fma.f64 x x y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 1942668892225729/3885337784451458141838923813647037813284813678104279042503624819477808570410416996352 binary64)) (sqrt.f64 y) x)
x

Outputs
(if (<=.f64 (.f64 x x) #s(literal 2000000000000000112950822041041682829681252763966116749401130328310913127935156394378439523178919965959536338695072724193131961289213847754610320291206559558839567880608124639637128476165182553839199176610603506544803697392590258176 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 500000000000000011546545651348935774464919112425849637715282289077421094839728844432880898433975380555391192719129287098299595056567936753438014858326845092856015715723317824379483334901760 binary64)) (sqrt.f64 (fma.f64 x x y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))
(if (<=.f64 (*.f64 x x) #s(literal 2000000000000000112950822041041682829681252763966116749401130328310913127935156394378439523178919965959536338695072724193131961289213847754610320291206559558839567880608124639637128476165182553839199176610603506544803697392590258176 binary64)) (sqrt.f64 (fma.f64 x x y)) x)
(if (<=.f64 (*.f64 x x) #s(literal 1942668892225729/3885337784451458141838923813647037813284813678104279042503624819477808570410416996352 binary64)) (sqrt.f64 y) x)
x

soundness542.0ms (10.2%)

Memory

-14.7MiB live, 297.6MiB allocated

Rules

23 136×	`accelerator-lowering-fma.f32`
23 136×	`accelerator-lowering-fma.f64`
5 482×	`-lowering-.f32`
5 482×	`-lowering-.f64`
5 034×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	635
1	383	620
2	1206	612
3	4042	567
0	8636	515
0	5	14
1	23	14
2	166	14
3	1514	14
0	8473	12

Stop Event

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

Compiler

Compiled 92 to 45 computations (51.1% saved)

preprocess136.0ms (2.6%)

Memory: 8.0MiB live, 124.8MiB allocated
Compiler: Compiled 216 to 100 computations (53.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	17	38
1	35	38
2	70	38
3	125	38
4	189	38
5	252	38
6	314	38
7	326	38
8	332	38
0	5	6
1	6	6
0	6	5

Iter	Nodes	Cost
0	17	38
1	35	38
2	70	38
3	125	38
4	189	38
5	252	38
6	314	38
7	326	38
8	332	38
0	5	6
1	6	6
0	6	5

analyze68.0ms (1.3%)

sample581.0ms (11%)

preprocess44.0ms (0.8%)

explain68.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize19.0ms (0.4%)

series6.0ms (0.1%)

rewrite350.0ms (6.6%)

simplify578.0ms (10.9%)

eval35.0ms (0.7%)

prune38.0ms (0.7%)

simplify12.0ms (0.2%)

localize56.0ms (1%)

series12.0ms (0.2%)

rewrite374.0ms (7.1%)

simplify698.0ms (13.2%)

eval87.0ms (1.6%)

prune64.0ms (1.2%)

simplify4.0ms (0.1%)

localize208.0ms (3.9%)

series6.0ms (0.1%)

rewrite171.0ms (3.2%)

simplify771.0ms (14.5%)

eval119.0ms (2.2%)

prune110.0ms (2.1%)

regimes49.0ms (0.9%)

regimes8.0ms (0.2%)

regimes58.0ms (1.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.2%)

soundness542.0ms (10.2%)

preprocess136.0ms (2.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	17	38
1	35	38
2	70	38
3	125	38
4	189	38
5	252	38
6	314	38
7	326	38
8	332	38
0	5	6
1	6	6
0	6	5