Metrics for Given's Rotation SVD example

analyze529.0ms (5.4%)

Memory

-5.0MiB live, 860.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	48.6%	51.4%	0%	0%	0%	0
0%	0%	48.6%	51.4%	0%	0%	0%	1
0%	0%	48.6%	51.4%	0%	0%	0%	2
0%	0%	48.6%	51.4%	0%	0%	0%	3
0%	0%	48.6%	51.4%	0%	0%	0%	4
31.3%	15.2%	33.4%	51.4%	0%	0%	0%	5
34.4%	16.7%	31.9%	51.4%	0%	0%	0%	6
51.6%	25.1%	23.6%	51.4%	0%	0%	0%	7
53.1%	25.8%	22.8%	51.4%	0%	0%	0%	8
62.5%	30.4%	18.2%	51.4%	0%	0%	0%	9
63.7%	31%	17.7%	51.4%	0%	0%	0%	10
68.6%	33.3%	15.3%	51.4%	0%	0%	0%	11
69.2%	33.7%	15%	51.4%	0%	0%	0%	12

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.4s (25.1%)

Memory

-108.7MiB live, 3 490.3MiB allocated

Samples

1.4s	6 275×	0	valid
290.0ms	983×	2	valid
161.0ms	611×	1	valid
132.0ms	387×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

const: 682.0ms (41.2% of total)

ival-mult: 256.0ms (15.5% of total)

ival-add: 212.0ms (12.8% of total)

ival-sqrt: 189.0ms (11.4% of total)

ival-div: 125.0ms (7.5% of total)

adjust: 78.0ms (4.7% of total)

ival-fabs: 48.0ms (2.9% of total)

ival-<: 42.0ms (2.5% of total)

ival-and: 12.0ms (0.7% of total)

exact: 10.0ms (0.6% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

preprocess65.0ms (0.7%)

Memory

19.4MiB live, 58.6MiB allocated

Algorithm

1×	egg-herbie

Rules

252×	`distribute-lft-neg-in`
218×	`unsub-neg`
198×	`associate-r`
196×	`associate-l`
162×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	93
1	90	87
2	194	87
3	401	87
4	661	87
5	999	87
6	1334	87
7	1544	87
8	1698	87
9	1932	87
10	1999	87
11	2027	87
12	2029	87
0	14	17
0	23	17
1	38	17
2	45	17
3	47	17
4	48	17
0	48	15

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Outputs

(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))

(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (*.f64 p p) (*.f64 x x)))) #s(literal 1/2 binary64)))

Symmetry

(abs p)

explain330.0ms (3.4%)

Memory

-28.5MiB live, 315.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
57	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
31	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
22	-	1	(2.8010399138901226e-221 -3.720652042287815e-63)	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
0	-	0	-	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`p`
0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	-	0	-	`#s(literal 1/2 binary64)`
0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	oflow-rescue	57	0
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	57
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	57
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	31	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	uflow-rescue	21	0
↳	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	underflow	4
↳	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`	underflow	25
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	25
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	14
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	54

Confusion

	Predicted +	Predicted -
+	52	0
-	57	147

Precision

0.47706422018348627

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	52	0	0
-	57	0	147

Precision?

0.47706422018348627

Recall?

1.0

Freqs

test

number	freq
0	147
1	109

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

81.0ms	400×	0	valid
36.0ms	50×	2	valid
13.0ms	20×	3	valid
7.0ms	42×	1	valid

Compiler

Compiled 230 to 60 computations (73.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 12.0ms (27.5% of total)

ival-sqrt: 10.0ms (22.9% of total)

ival-div: 9.0ms (20.6% of total)

ival-add: 7.0ms (16.1% of total)

adjust: 3.0ms (6.9% of total)

ival-true: 1.0ms (2.3% of total)

exact: 1.0ms (2.3% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.3%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify6.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
✓	cost-diff	128	(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
✓	cost-diff	128	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Rules

32×	`lower-*.f32`
24×	`lower-*.f64`
18×	`lower-fma.f64`
18×	`lower-fma.f32`
12×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	94
0	23	94
1	38	94
2	45	94
3	47	94
4	48	94
0	48	86

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
#s(literal 1 binary64)
(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
x
(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(.f64 (.f64 #s(literal 4 binary64) p) p)
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)

Outputs
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))) #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))))
#s(literal 1 binary64)
(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))))
x
(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(.f64 (.f64 #s(literal 4 binary64) p) p)
(.f64 #s(literal 4 binary64) (.f64 p p))
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)

localize65.0ms (0.7%)

Memory

2.8MiB live, 81.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
✓	accuracy	92.7%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
✓	accuracy	88.8%	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
✓	accuracy	79.3%	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

20.0ms	200×	0	valid
6.0ms	25×	2	valid
3.0ms	21×	1	valid
3.0ms	10×	3	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

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

ival-mult: 8.0ms (36.9% of total)

ival-sqrt: 5.0ms (23.1% of total)

ival-add: 4.0ms (18.5% of total)

ival-div: 3.0ms (13.8% of total)

adjust: 2.0ms (9.2% of total)

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

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

exact: 0.0ms (0% of total)

series46.0ms (0.5%)

Memory

1.2MiB live, 40.4MiB allocated

Counts

6 → 144

Calls

Call 1

Inputs
#<alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))>
#<alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))>
#<alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))>
#<alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))>
#<alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))>
#<alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt (pow x 2)>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))>
#<alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))>
#<alt (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))>
#<alt (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))>
#<alt (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ x p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt (* 1/2 (/ x p))>
#<alt (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt -1>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt (* 1/2 (/ x p))>
#<alt (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)>
#<alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)>
#<alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)>
#<alt (* -1/2 (/ x p))>
#<alt (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))>
#<alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))>
#<alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))>

Calls

36 calls:

Time	Variable		Point	Expression
27.0ms	p	@	0	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
3.0ms	x	@	-inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
1.0ms	x	@	inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
1.0ms	x	@	-inf	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1.0ms	x	@	inf	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

rewrite414.0ms (4.3%)

Memory

7.7MiB live, 442.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 862×	`lower-fma.f64`
4 862×	`lower-fma.f32`
3 532×	`lower-*.f32`
3 524×	`lower-*.f64`
2 388×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
0	23	78
1	77	78
2	501	78
3	6967	78
0	8492	70

Stop Event

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

Counts

6 → 302

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Outputs
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (/.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))))) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/8 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (.f64 #s(literal 1/2 binary64) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))))
(/.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
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(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (+.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 3 binary64)))) (fma.f64 (-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (-.f64 (-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)))))) (+.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (+.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (*.f64 p p)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p)))) (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (*.f64 #s(literal 4 binary64) p)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))))) (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 p p) #s(literal -4 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 #s(literal -16 binary64) (.f64 p (.f64 p (.f64 p p)))))) (sqrt.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))))) (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))
(.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p))))))
(.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (/.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) x))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (neg.f64 x)))
(/.f64 (/.f64 x (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) x) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1 binary64))
(.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) x)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) (neg.f64 x))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))))
(.f64 (/.f64 x (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 x (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))))) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))))
(.f64 (/.f64 x (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p)))))

simplify534.0ms (5.5%)

Memory

20.0MiB live, 605.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 048×	`lower-fma.f64`
10 048×	`lower-fma.f32`
7 228×	`lower-*.f64`
7 228×	`lower-*.f32`
4 784×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	472	2993
1	1444	2876
2	4985	2834
0	8534	2634

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

Calls

Call 1

Inputs
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
1
(+ 1 (* -1/2 (/ x p)))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* -1/2 (/ x p))
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 3/512 binary64) (.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(fma.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p)) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64))))) (.f64 #s(literal -256 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p)))))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 p (.f64 p (fma.f64 #s(literal -10 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 5 binary64)))) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 (.f64 #s(literal -1/32 binary64) (.f64 x (.f64 x x))) (.f64 p p))) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (fma.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (.f64 #s(literal -1/32 binary64) (.f64 x (.f64 x x))) (.f64 p p)))) p))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
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#s(literal 1 binary64)
(+ 1 (* -1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) p))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) x (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) #s(literal 3/256 binary64)) (.f64 (.f64 p p) (*.f64 p p))))) p))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 p (.f64 p (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x))) x)
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 2 binary64) x)) x)
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (*.f64 p p))) #s(literal 2 binary64))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 p (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(neg.f64 (.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 p (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (*.f64 p p))) #s(literal 2 binary64)))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(neg.f64 (.f64 p (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64))))))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) p) (.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (.f64 p (.f64 p p))) #s(literal -1/64 binary64) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) (.f64 p #s(literal 2 binary64)))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) (*.f64 #s(literal 2 binary64) x) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (*.f64 x x)))) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(fma.f64 x (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (*.f64 x x)))) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) x))
(* 1/2 (/ x p))
(*.f64 #s(literal 1/2 binary64) (/.f64 x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(.f64 x (fma.f64 (/.f64 (.f64 x x) (.f64 p (.f64 p p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 #s(literal 3/256 binary64) (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (.f64 p (*.f64 p p)))) (/.f64 #s(literal 1/2 binary64) p)))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -5/2048 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 7 binary64))) (/.f64 #s(literal 3/256 binary64) (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (.f64 p (.f64 p p))))) (/.f64 #s(literal 1/2 binary64) p)))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 6 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 (+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 6 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64))) (/.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64) (neg.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (*.f64 p p))))) (pow.f64 x #s(literal 6 binary64))))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (/.f64 (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p)) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 6 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -2 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -20 binary64) (/.f64 #s(literal 6 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(* 1/2 (/ x p))
(*.f64 #s(literal 1/2 binary64) (/.f64 x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) #s(literal 3/256 binary64)) (.f64 (.f64 p p) (*.f64 p p))))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 x (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 p #s(literal 6 binary64))))) p)
(* -1/2 (/ x p))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) p)
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) #s(literal 3/256 binary64)) (.f64 (.f64 p p) (*.f64 p p))))) (neg.f64 p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 x (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 p #s(literal 6 binary64))))) (neg.f64 p))

eval74.0ms (0.8%)

Memory: -45.6MiB live, 152.6MiB allocated
Compiler: Compiled 16 829 to 2 161 computations (87.2% saved)

prune60.0ms (0.6%)

Memory

5.7MiB live, 166.6MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	433	11	444
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	434	11	445

Accuracy

99.8%

Counts

445 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.9%	(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
	80.9%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
▶	81.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	27.9%	(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
	52.6%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
▶	16.2%	(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
▶	16.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x))))
	78.1%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
▶	5.6%	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
	37.8%	(sqrt.f64 #s(literal 1 binary64))
▶	56.8%	(sqrt.f64 #s(literal 1/2 binary64))

Compiler

Compiled 252 to 188 computations (25.4% saved)

simplify696.0ms (7.2%)

Memory

-36.8MiB live, 202.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 p (.f64 p #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x))
✓	cost-diff	640	(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x)))
✓	cost-diff	1152	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	0	(/.f64 (.f64 p p) (.f64 x x))
✓	cost-diff	1152	(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
✓	cost-diff	192	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	320	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
✓	cost-diff	0	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
✓	cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Rules

4 318×	`associate-*r/`
3 982×	`lower-*.f32`
3 968×	`lower-*.f64`
1 724×	`associate-*l/`
904×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	149
0	50	141
1	79	133
2	138	133
3	260	133
4	401	133
5	1273	133
6	1605	133
7	1864	133
8	2348	133
9	2548	133
10	2587	133
11	2723	133
12	2777	133
13	2811	133
14	2855	133
15	3003	133
16	3021	133
17	3055	133
18	3097	133
19	3251	133
20	3269	133
21	3303	133
22	3347	133
23	3549	133
24	3567	133
25	3601	133
26	3647	133
27	3853	133
28	3871	133
29	3905	133
30	3947	133
31	4195	133
32	4213	133
33	4247	133
34	4293	133
35	4299	133
36	4299	133
37	4337	133
38	4355	133
39	4389	133
40	4435	133
41	4663	133
42	4681	133
43	4715	133
44	4757	133
45	5027	133
46	5045	133
47	5079	133
48	5121	133
49	5443	133
50	5461	133
51	5495	133
52	5537	133
53	5841	133
54	5859	133
55	5893	133
56	5937	133
57	6253	133
58	6271	133
59	6305	133
60	6349	133
61	6767	133
62	6785	133
63	6819	133
64	6861	133
65	7269	133
66	7287	133
67	7321	133
68	7365	133
69	7747	133
70	7765	133
71	7799	133
72	7843	133
0	8127	117

Stop Event

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

Calls

Call 1

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

Outputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))
x
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))
(fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))
(fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))
(.f64 p (.f64 #s(literal 4 binary64) p))
(.f64 p (.f64 p #s(literal 4 binary64)))
p
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
(sqrt.f64 #s(literal 0 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64)))
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
#s(literal 0 binary64)
#s(literal 1 binary64)
#s(literal -1 binary64)
(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
(fabs.f64 (/.f64 p x))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x))))
(fabs.f64 (/.f64 p x))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x)))
(/.f64 (.f64 p p) (.f64 x x))
#s(literal 1/2 binary64)
(/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x))
(.f64 p (.f64 p #s(literal 2 binary64)))
p
(*.f64 p #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x x)
x

localize106.0ms (1.1%)

Memory

3.2MiB live, 126.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 p #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x)))
✓	accuracy	91.5%	(/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x))
✓	accuracy	72.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	91.5%	(/.f64 (.f64 p p) (.f64 x x))
✓	accuracy	72.2%	(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
✓	accuracy	79.3%	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))

Samples

38.0ms	200×	0	valid
31.0ms	56×	1	exit

Compiler

Compiled 168 to 30 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 31.0ms (61% of total)

ival-sqrt: 9.0ms (17.7% of total)

ival-div: 5.0ms (9.8% of total)

ival-add: 3.0ms (5.9% of total)

adjust: 2.0ms (3.9% of total)

exact: 1.0ms (2% of total)

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

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

series16.0ms (0.2%)

Memory

21.7MiB live, 21.7MiB allocated

Counts

17 → 264

Calls

Call 1

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

Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt (* 1/2 (/ x p))>
#<alt (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt -1>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt (* 1/2 (/ x p))>
#<alt (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)>
#<alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)>
#<alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)>
#<alt (* -1/2 (/ x p))>
#<alt (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))>
#<alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))>
#<alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 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)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 (pow p 2))>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>
#<alt (* 2 p)>

Calls

66 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt (/ (* p p) (* x x)))
1.0ms	x	@	-inf	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
1.0ms	x	@	inf	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
1.0ms	x	@	0	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
1.0ms	p	@	inf	(sqrt (/ (* p p) (* x x)))

rewrite541.0ms (5.6%)

Memory

18.7MiB live, 442.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 562×	`lower-*.f32`
4 548×	`lower-*.f64`
4 286×	`lower-fma.f32`
4 282×	`lower-fma.f64`
2 926×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	116
0	50	107
1	138	95
2	760	91
3	6800	91
0	9186	91

Stop Event

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

Counts

17 → 732

Calls

Call 1

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

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

simplify596.0ms (6.1%)

Memory

18.3MiB live, 883.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 852×	`lower-fma.f64`
10 852×	`lower-fma.f32`
6 844×	`lower-*.f64`
6 844×	`lower-*.f32`
4 850×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	421	2950
1	1253	2905
2	4071	2840
0	8204	2694

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 262

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* -1/2 (/ x p))
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 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)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 (pow p 2))
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)

Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/64 binary64) (/.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 p p) (.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/128 binary64) (.f64 p (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 11/4 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 11/4 binary64)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 11/4 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 p p)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
(* -1 (/ p x))
(/.f64 p (neg.f64 x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x (.f64 x p)))) p) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 p (.f64 (.f64 x x) (.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x (.f64 x p)))) p)) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 p (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64))))) (.f64 #s(literal -256 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p)))))) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (fma.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))))) #s(literal -1/8 binary64)) (.f64 p p))) (.f64 p (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x (*.f64 x p)))) p)) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 #s(literal -69/16 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(fma.f64 x (fma.f64 #s(literal -1/64 binary64) (/.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/64 binary64) (/.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64)) (/.f64 (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (*.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64)) (/.f64 (.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 3/512 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))))))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 p p (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 x x)))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 p p (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 x x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64))))) (.f64 #s(literal -256 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p)))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 p p (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -10 binary64) (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
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(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
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(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 (pow p 2))
(.f64 #s(literal 2 binary64) (.f64 p p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* 2 p)
(*.f64 p #s(literal 2 binary64))

eval132.0ms (1.4%)

Memory: 14.1MiB live, 401.9MiB allocated
Compiler: Compiled 17 495 to 2 189 computations (87.5% saved)

prune99.0ms (1%)

Memory

-42.3MiB live, 312.4MiB allocated

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1 020	7	1 027
Fresh	6	0	6
Picked	3	2	5
Done	0	0	0
Total	1 029	9	1 038

Accuracy

100.0%

Counts

1 038 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	28.4%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
▶	24.1%	(/.f64 p (neg.f64 x))
▶	80.9%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
	78.1%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	81.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	52.6%	(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
✓	56.8%	(sqrt.f64 #s(literal 1/2 binary64))
▶	37.8%	#s(literal 1 binary64)
▶	5.6%	#s(literal 0 binary64)

Compiler

Compiled 157 to 113 computations (28% saved)

simplify12.0ms (0.1%)

Memory

-11.0MiB live, 29.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal 1/4 binary64) p)
✓	cost-diff	(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
✓	cost-diff	(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
✓	cost-diff	(neg.f64 x)
✓	cost-diff	(/.f64 p (neg.f64 x))
✓	cost-diff	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))
✓	cost-diff	(+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64))
✓	cost-diff	(sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64)))
✓	cost-diff	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))

Rules

84×	`lower-+.f32`
82×	`lower-+.f64`
62×	`lower-fma.f32`
58×	`lower-fma.f64`
48×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	117
0	37	117
1	53	117
2	66	117
3	75	117
4	84	117
5	94	117
6	120	117
7	154	117
8	189	117
9	198	117
10	199	117
0	199	117

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64)))
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))
x
(sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))
(fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))
(.f64 #s(literal 4 binary64) (.f64 p p))
#s(literal 4 binary64)
(*.f64 p p)
p
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)
#s(literal 1 binary64)
(/.f64 p (neg.f64 x))
p
(neg.f64 x)
x
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
x
(/.f64 #s(literal 1/4 binary64) p)
#s(literal 1/4 binary64)
p
#s(literal 1/2 binary64)

Outputs
(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64)))
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))
x
(sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))
(fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))
(.f64 #s(literal 4 binary64) (.f64 p p))
#s(literal 4 binary64)
(*.f64 p p)
p
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal 0 binary64)
#s(literal 1 binary64)
(/.f64 p (neg.f64 x))
p
(neg.f64 x)
x
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
x
(/.f64 #s(literal 1/4 binary64) p)
#s(literal 1/4 binary64)
p
#s(literal 1/2 binary64)

localize97.0ms (1%)

Memory

22.1MiB live, 180.8MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1/4 binary64) p)
✓	accuracy	99.9%	(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
✓	accuracy	97.3%	(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(/.f64 p (neg.f64 x))
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(.f64 #s(literal 4 binary64) (.f64 p p))
✓	accuracy	100.0%	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))
✓	accuracy	99.6%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	79.3%	(sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))

Samples

54.0ms	200×	0	valid
8.0ms	56×	0	invalid

Compiler

Compiled 127 to 25 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 7.0ms (27.5% of total)

ival-div: 6.0ms (23.6% of total)

ival-sqrt: 6.0ms (23.6% of total)

ival-add: 3.0ms (11.8% of total)

ival-neg: 2.0ms (7.9% of total)

exact: 1.0ms (3.9% of total)

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

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

series15.0ms (0.2%)

Memory

2.1MiB live, 41.1MiB allocated

Counts

11 → 228

Calls

Call 1

Inputs
#<alt (.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64)))>
#<alt (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64))>
#<alt (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))>
#<alt (/.f64 p (neg.f64 x))>
#<alt (neg.f64 x)>
#<alt (sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 1/4 binary64) p)>
#<alt (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))>
#<alt (.f64 #s(literal 4 binary64) (.f64 p p))>

Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))>
#<alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2))))))>
#<alt (+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow x 6) (sqrt 2)))))))>
#<alt (* -1 (/ (* p (sqrt 2)) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 4) (sqrt 2))))) (* p (sqrt 2)))) x))>
#<alt (* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 4) (sqrt 2))))) (* p (sqrt 2))))) x))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))>
#<alt (+ (sqrt 2) (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6))))) (sqrt 2))) (* 1/2 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (sqrt 2))))) (/ 1 (* (pow x 2) (sqrt 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (* 1/4 (/ x p))))>
#<alt (+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ x p)) (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (pow p 3))))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (/ x p)))>
#<alt (+ 1 (* -1 (/ (+ (* 1/32 (/ (pow x 2) p)) (* 1/4 x)) p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) p)) (* -1/32 (pow x 2))) p)) (* 1/4 x)) p)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))>
#<alt (+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))>
#<alt (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ x p)))>
#<alt (+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))>
#<alt (+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ x p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))>
#<alt (* 1/2 (/ x p))>
#<alt (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt -1>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 1)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt (* 1/2 (/ x p))>
#<alt (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)>
#<alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)>
#<alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)>
#<alt (* -1/2 (/ x p))>
#<alt (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))>
#<alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))>
#<alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))>
#<alt (* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>

Calls

57 calls:

Time	Variable		Point	Expression
1.0ms	p	@	0	(* (sqrt (+ (/ x (sqrt (+ (* x x) (* 4 (* p p))))) 1)) (sqrt 1/2))
1.0ms	x	@	-inf	(sqrt (+ (* x (/ 1/4 p)) 1/2))
1.0ms	x	@	inf	(sqrt (+ (* x (/ 1/4 p)) 1/2))
1.0ms	x	@	-inf	(sqrt (+ (/ x (sqrt (+ (* x x) (* 4 (* p p))))) 1))
1.0ms	p	@	0	(sqrt (+ (* x (/ 1/4 p)) 1/2))

rewrite245.0ms (2.5%)

Memory

8.1MiB live, 641.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 032×	`lower-fma.f32`
5 028×	`lower-fma.f64`
4 428×	`lower-*.f32`
4 422×	`lower-*.f64`
3 272×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	91
0	36	90
1	120	90
2	748	90
0	8699	89

Stop Event

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

Counts

11 → 304

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64)))
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))
(/.f64 p (neg.f64 x))
(neg.f64 x)
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/4 binary64) p)
(sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))
(.f64 #s(literal 4 binary64) (.f64 p p))

Outputs
(exp.f64 (.f64 (log.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 (log1p.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (log1p.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))) (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))))) #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal -1 binary64))))
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(/.f64 (-.f64 (.f64 (/.f64 (/.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal 16 binary64))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (/.f64 (/.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal 16 binary64))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal 16 binary64))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1/64 binary64) (.f64 p (.f64 p p))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1/16 binary64) (.f64 p p)) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal -1/2 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1/64 binary64) (.f64 p (.f64 p p))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))))
(.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1/64 binary64) (.f64 p (.f64 p p))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1/16 binary64) (.f64 p p)) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal -1/2 binary64))))))
(.f64 (neg.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) x) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal 16 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 4 binary64) p)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/4 binary64) p))
(neg.f64 (/.f64 #s(literal -1/4 binary64) p))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) p)))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal 4 binary64) p)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) p))
(/.f64 #s(literal 1/4 binary64) p)
(/.f64 #s(literal -1/4 binary64) (neg.f64 p))
(/.f64 #s(literal -1 binary64) (*.f64 p #s(literal -4 binary64)))
(pow.f64 (*.f64 #s(literal 4 binary64) p) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) p))
(*.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1 binary64) p))
(*.f64 (/.f64 #s(literal 1 binary64) p) #s(literal 1/4 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/4 binary64) p))
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) p) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 4 binary64) p) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))))
(sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))))
(/.f64 (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal -4 binary64))))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 p (.f64 p p)) p) #s(literal -16 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (fma.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)) (.f64 (.f64 x x) (fma.f64 x x (.f64 p (*.f64 p #s(literal -4 binary64))))))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 p (.f64 p p)) p) #s(literal -16 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal -4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 p (.f64 p p)) p) #s(literal -16 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal -4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 p (.f64 p p)) p) #s(literal -16 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal -4 binary64)))))))
(pow.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))) (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 p p)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 p (.f64 p p)) p) #s(literal -16 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 p (*.f64 p #s(literal -4 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 p (.f64 p p)) p) #s(literal -16 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 p (*.f64 p #s(literal -4 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 p (.f64 p p)) p) #s(literal -16 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal -4 binary64)))))))
(.f64 (pow.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))) #s(literal 1/4 binary64)))
(/.f64 p (/.f64 #s(literal 1/4 binary64) p))
(.f64 #s(literal 4 binary64) (.f64 p p))
(.f64 p (.f64 #s(literal 4 binary64) p))
(.f64 (.f64 p p) #s(literal 4 binary64))
(.f64 (.f64 #s(literal 4 binary64) p) p)

simplify381.0ms (3.9%)

Memory

-10.5MiB live, 745.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8 018×	`lower-fma.f64`
8 018×	`lower-fma.f32`
6 796×	`lower-*.f64`
6 796×	`lower-*.f32`
2 856×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	637	3953
1	1907	3762
2	6644	3711
0	8104	3476

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 226

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))
(+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2))))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow x 6) (sqrt 2)))))))
(* -1 (/ (* p (sqrt 2)) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 4) (sqrt 2))))) (* p (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 4) (sqrt 2))))) (* p (sqrt 2))))) x))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 2))))))
(+ (sqrt 2) (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6))))) (sqrt 2))) (* 1/2 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (sqrt 2))))) (/ 1 (* (pow x 2) (sqrt 2))))))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (* 1/4 (/ x p))))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ x p)) (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (pow p 3))))))
1
(+ 1 (* -1/4 (/ x p)))
(+ 1 (* -1 (/ (+ (* 1/32 (/ (pow x 2) p)) (* 1/4 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) p)) (* -1/32 (pow x 2))) p)) (* 1/4 x)) p)))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
1
(+ 1 (* -1/2 (/ x p)))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* -1/2 (/ x p))
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* 1/2 (sqrt (/ x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))
(* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))
(* 1/2 (sqrt (/ x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))

Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(fma.f64 x (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/32 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(fma.f64 x (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (.f64 x (fma.f64 x (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (.f64 p p))) #s(literal -3/128 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/32 binary64)) (.f64 p p))))) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 p (neg.f64 p)) (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 6 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 6 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 p p) (/.f64 (fma.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 6 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64))) #s(literal 2 binary64)) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64) (neg.f64 (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 p (.f64 x x))))) (neg.f64 x))
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#s(literal 2 binary64)
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#s(literal 1 binary64)
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#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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-1
#s(literal -1 binary64)
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1
#s(literal 1 binary64)
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(* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))
(.f64 (neg.f64 x) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/4 binary64))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))
(.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 (.f64 p (.f64 p p)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64)))) #s(literal -1/32 binary64)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/4 binary64)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))
(neg.f64 (.f64 x (fma.f64 #s(literal -1/32 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 p (.f64 p p)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64))))) (fma.f64 (sqrt.f64 (/.f64 (pow.f64 p #s(literal 5 binary64)) (pow.f64 x #s(literal 7 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (sqrt.f64 #s(literal -1/4 binary64)) #s(literal 5 binary64))) #s(literal 1/128 binary64)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/4 binary64)))))))))
(* 1/2 (sqrt (/ x p)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (.f64 x p)) (sqrt.f64 (/.f64 (.f64 p (.f64 p p)) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/.f64 (fma.f64 (.f64 p p) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x p)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x p)) (.f64 (.f64 p p) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (.f64 (.f64 p p) (fma.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 p (.f64 x (.f64 x x)))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 p (.f64 (.f64 (.f64 x x) (*.f64 x x)) x)))))))))) p)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 x (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/1024 binary64)) (.f64 (.f64 p p) (.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 x (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/128 binary64) (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (/.f64 (.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 #s(literal -1/64 binary64) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/1024 binary64)) (.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 x (/.f64 (.f64 #s(literal 1/4 binary64) x) p) (.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/64 binary64) (/.f64 (.f64 x x) (.f64 p (.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 p #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (*.f64 x x)))) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(fma.f64 x (fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (*.f64 x x))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal 4 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (*.f64 x x))))) x))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (.f64 p p) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)) x)
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 2 binary64) x)) x)
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(.f64 p (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (*.f64 p p)) #s(literal 2 binary64)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 p (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 p p)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (*.f64 p p))) #s(literal 2 binary64))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 p (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 p p)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (*.f64 p p)) #s(literal 2 binary64)) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 p p)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (*.f64 p p))) #s(literal 2 binary64))) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(.f64 p (neg.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (.f64 p p)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64))))))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))

eval75.0ms (0.8%)

Memory: 1.7MiB live, 198.7MiB allocated
Compiler: Compiled 13 008 to 1 844 computations (85.8% saved)

prune57.0ms (0.6%)

Memory

9.2MiB live, 169.0MiB allocated

Pruning

11 alts after pruning (4 fresh and 7 done)

	Pruned	Kept	Total
New	528	2	530
Fresh	0	2	2
Picked	0	5	5
Done	0	2	2
Total	528	11	539

Accuracy

100.0%

Counts

539 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	28.4%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
✓	24.1%	(/.f64 p (neg.f64 x))
▶	51.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
✓	80.9%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
▶	78.1%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	81.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	52.6%	(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
▶	52.6%	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
✓	56.8%	(sqrt.f64 #s(literal 1/2 binary64))
✓	37.8%	#s(literal 1 binary64)
✓	5.6%	#s(literal 0 binary64)

Compiler

Compiled 113 to 82 computations (27.4% saved)

simplify11.0ms (0.1%)

Memory

-20.7MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(*.f64 p p)
✓	cost-diff	(/.f64 (.f64 p p) (.f64 x x))
✓	cost-diff	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
✓	cost-diff	(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
✓	cost-diff	(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
✓	cost-diff	(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
✓	cost-diff	(fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	cost-diff	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	(*.f64 #s(literal 1/4 binary64) x)
✓	cost-diff	(fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x))
✓	cost-diff	(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
✓	cost-diff	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))

Rules

154×	`lower-*.f32`
148×	`lower-*.f64`
64×	`lower-fma.f32`
62×	`*-commutative`
54×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	156
0	48	156
1	77	156
2	115	156
3	163	156
4	176	156
5	182	156
0	182	156

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
(fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x))
#s(literal 1/2 binary64)
p
(*.f64 #s(literal 1/4 binary64) x)
#s(literal 1/4 binary64)
x
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
x
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
#s(literal 2 binary64)
(/.f64 (*.f64 p p) x)
(*.f64 p p)
p
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
x
(/.f64 #s(literal 1/4 binary64) p)
#s(literal 1/4 binary64)
p
#s(literal 1/2 binary64)
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
#s(literal 1 binary64)

Outputs
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
(fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x))
#s(literal 1/2 binary64)
p
(*.f64 #s(literal 1/4 binary64) x)
#s(literal 1/4 binary64)
x
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64))
(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
(/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x))
x
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)
#s(literal 2 binary64)
(/.f64 (*.f64 p p) x)
(*.f64 p p)
p
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
x
(/.f64 #s(literal 1/4 binary64) p)
#s(literal 1/4 binary64)
p
#s(literal 1/2 binary64)
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal -1/2 binary64)) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
p
(*.f64 x x)
x
#s(literal 1 binary64)

localize115.0ms (1.2%)

Memory

17.7MiB live, 134.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	91.5%	(/.f64 (.f64 p p) (.f64 x x))
✓	accuracy	99.9%	(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
✓	accuracy	97.6%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	96.5%	(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
✓	accuracy	96.3%	(/.f64 (*.f64 p p) x)
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/4 binary64) x)
✓	accuracy	100.0%	(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
✓	accuracy	97.3%	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))

Samples

63.0ms	200×	0	valid
11.0ms	56×	0	invalid

Compiler

Compiled 172 to 32 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 35.0ms (61.3% of total)

ival-div: 11.0ms (19.3% of total)

ival-add: 6.0ms (10.5% of total)

ival-sqrt: 5.0ms (8.8% of total)

exact: 1.0ms (1.8% of total)

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

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

series34.0ms (0.3%)

Memory

-14.7MiB live, 61.2MiB allocated

Counts

17 → 372

Calls

Call 1

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

Outputs
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (* (sqrt -1) (sqrt -1/2))>
#<alt (+ (* -1/8 (/ (* x (sqrt -1)) (* p (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/128 (/ (* (pow x 2) (sqrt -1)) (* p (pow (sqrt -1/2) 3)))) (* 1/8 (/ (* x (sqrt -1)) (sqrt -1/2)))) p)) (* (sqrt -1) (sqrt -1/2)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (* (pow x 2) (sqrt -1)) (pow (sqrt -1/2) 3))) (* -1/1024 (/ (* (pow x 3) (sqrt -1)) (* p (pow (sqrt -1/2) 5))))) p)) (* 1/8 (/ (* x (sqrt -1)) (sqrt -1/2)))) p)) (* (sqrt -1) (sqrt -1/2)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))>
#<alt (* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 x)>
#<alt (+ (* 1/4 x) (* 1/2 p))>
#<alt (+ (* 1/4 x) (* 1/2 p))>
#<alt (+ (* 1/4 x) (* 1/2 p))>
#<alt (* 1/2 p)>
#<alt (* p (+ 1/2 (* 1/4 (/ x p))))>
#<alt (* p (+ 1/2 (* 1/4 (/ x p))))>
#<alt (* p (+ 1/2 (* 1/4 (/ x p))))>
#<alt (* 1/2 p)>
#<alt (* -1 (* p (- (* -1/4 (/ x p)) 1/2)))>
#<alt (* -1 (* p (- (* -1/4 (/ x p)) 1/2)))>
#<alt (* -1 (* p (- (* -1/4 (/ x p)) 1/2)))>
#<alt (* 1/2 p)>
#<alt (+ (* 1/4 x) (* 1/2 p))>
#<alt (+ (* 1/4 x) (* 1/2 p))>
#<alt (+ (* 1/4 x) (* 1/2 p))>
#<alt (* 1/4 x)>
#<alt (* x (+ 1/4 (* 1/2 (/ p x))))>
#<alt (* x (+ 1/4 (* 1/2 (/ p x))))>
#<alt (* x (+ 1/4 (* 1/2 (/ p x))))>
#<alt (* 1/4 x)>
#<alt (* -1 (* x (- (* -1/2 (/ p x)) 1/4)))>
#<alt (* -1 (* x (- (* -1/2 (/ p x)) 1/4)))>
#<alt (* -1 (* x (- (* -1/2 (/ p x)) 1/4)))>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* -1/2 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow x 2) (- (* 1/16 (/ 1 (pow p 6))) (* -1/8 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -4 (pow p 6)) (* -1/2 (* (pow p 2) (- (* 2 (pow p 4)) (* 1/4 (pow p 4)))))) (pow x 6))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (+ (* -1/2 (/ (+ (* 1/2 (* (pow p 2) (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))) (* -1/2 (/ (pow p 2) (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 7/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -25/16 (/ (pow p 2) (pow x 6))) (* 7/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1/2 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))>
#<alt (+ 1/2 (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -4 (/ (pow p 6) (pow x 6))) (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 2 (/ (pow p 4) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* -4 (/ (pow p 6) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 8))) (* 1/8 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))>
#<alt (/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))>
#<alt (/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (/ (+ (* 2 (pow p 2)) (pow x 2)) x)>
#<alt (/ (+ (* 2 (pow p 2)) (pow x 2)) x)>
#<alt (/ (+ (* 2 (pow p 2)) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))>
#<alt (* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/4 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (* 2 (sqrt (/ p x)))>
#<alt (+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (* 2 (sqrt (/ p x))))>
#<alt (+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (+ (* 2 (sqrt (/ p x))) (* 4 (sqrt (/ (pow p 5) (pow x 5))))))>
#<alt (+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (+ (* -1/4 (* (sqrt (/ 1 (* p (pow x 7)))) (+ (* 4 (* (pow p 3) x)) (* 32 (pow p 4))))) (+ (* 2 (sqrt (/ p x))) (* 4 (sqrt (/ (pow p 5) (pow x 5)))))))>
#<alt (* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1)))>
#<alt (+ (* -4 (* (sqrt (/ (pow p 3) (pow x 3))) (/ (sqrt -1) (sqrt -4)))) (* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ (pow p 3) (pow x 3))) (/ (sqrt -1) (sqrt -4)))) (+ (* 8 (* (sqrt (/ (pow p 5) (pow x 5))) (/ (sqrt -1) (sqrt -4)))) (* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1)))))>
#<alt (+ (* -4 (* (sqrt (/ (pow p 3) (pow x 3))) (/ (sqrt -1) (sqrt -4)))) (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow p 5) x)) (/ (sqrt -1) (sqrt -4)))) (* 1/2 (* (sqrt (/ 1 (* p x))) (/ (* (sqrt -1) (+ (* -16 (/ (* (pow p 3) x) (pow (sqrt -4) 2))) (* 32 (pow p 4)))) (sqrt -4))))) (pow x 3))) (* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1)))))>
#<alt (* 2 (sqrt (/ p x)))>
#<alt (+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (* 2 (sqrt (/ p x))))>
#<alt (+ (* 2 (sqrt (/ p x))) (* (pow p 2) (+ (* -2 (sqrt (/ 1 (* p (pow x 3))))) (* 4 (sqrt (/ p (pow x 5)))))))>
#<alt (+ (* 2 (sqrt (/ p x))) (* (pow p 2) (+ (* -2 (sqrt (/ 1 (* p (pow x 3))))) (* p (+ (* -1/4 (* (sqrt (* p x)) (+ (* 4 (/ 1 (* p (pow x 3)))) (* 32 (/ 1 (pow x 4)))))) (* 4 (sqrt (/ 1 (* p (pow x 5))))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2))))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2)))) (* (pow p 3) (sqrt 2)))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* 1/2 (/ x (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* p (sqrt 2))))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))) (* -1/4 (pow x 3))) (* p (sqrt 2))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))>
#<alt (+ 2 (* x (- (* x (+ (* -1/4 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))>
#<alt (* 4 (/ p x))>
#<alt (/ (+ (* -8 (/ (pow p 2) x)) (* 4 p)) x)>
#<alt (/ (- (+ (* 4 p) (* 16 (/ (pow p 3) (pow x 2)))) (* 8 (/ (pow p 2) x))) x)>
#<alt (/ (- (+ (* -32 (/ (pow p 4) (pow x 3))) (* 4 p)) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 8 (/ (pow p 2) x)))) x)>
#<alt (* 4 (/ p x))>
#<alt (* -1 (/ (+ (* -4 p) (* 8 (/ (pow p 2) x))) x))>
#<alt (* -1 (/ (+ (* -4 p) (* -1 (/ (- (* 16 (/ (pow p 3) x)) (* 8 (pow p 2))) x))) x))>
#<alt (* -1 (/ (+ (* -4 p) (* -1 (/ (- (* -1 (/ (- (* 32 (/ (pow p 4) x)) (* 16 (pow p 3))) x)) (* 8 (pow p 2))) x))) x))>
#<alt (* 4 (/ p x))>
#<alt (* p (+ (* -8 (/ p (pow x 2))) (* 4 (/ 1 x))))>
#<alt (* p (+ (* p (- (* 16 (/ p (pow x 3))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))>
#<alt (* p (+ (* p (- (* p (+ (* -32 (/ p (pow x 4))) (* 16 (/ 1 (pow x 3))))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))>
#<alt (- (+ 2 (* -1/4 (/ (pow x 3) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) (* -1 x)) p)))>
#<alt (+ 2 (* -1 (/ (- (* -1 (/ (- (* -1/4 (/ (pow x 3) p)) (* -1/2 (pow x 2))) p)) (* -1 x)) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 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)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>

Calls

93 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
1.0ms	x	@	0	(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
1.0ms	x	@	-inf	(sqrt (/ 1 (+ (* x (/ 1/4 p)) 1/2)))
1.0ms	p	@	inf	(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
1.0ms	x	@	inf	(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))

rewrite328.0ms (3.4%)

Memory

12.5MiB live, 524.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 014×	`lower-fma.f32`
6 004×	`lower-fma.f64`
4 318×	`lower-*.f32`
4 312×	`lower-*.f64`
3 774×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	133
0	48	133
1	193	124
2	1285	124
0	8245	124

Stop Event

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

Counts

17 → 583

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
(fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x))
(*.f64 #s(literal 1/4 binary64) x)
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 p p)
(*.f64 x x)
(/.f64 (*.f64 p p) x)

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) p)) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))) (sqrt.f64 p))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (sqrt.f64 (.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (sqrt.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))) p)))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64)))) (sqrt.f64 (.f64 p (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64)))) (sqrt.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64))) p)))
(/.f64 (sqrt.f64 (fma.f64 p #s(literal -1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) (sqrt.f64 (neg.f64 p)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))) (neg.f64 (sqrt.f64 p)))
(/.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) p)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 p #s(literal -1/2 binary64)))))))
(/.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) p)) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 p #s(literal -1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))) (neg.f64 (sqrt.f64 (neg.f64 p))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))))) (neg.f64 (neg.f64 (sqrt.f64 p))))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p) #s(literal 1/2 binary64))
(pow.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) p) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) p)))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p))) (/.f64 #s(literal 1 binary64) (sqrt.f64 p)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 p)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p))))
(.f64 (sqrt.f64 (fma.f64 p #s(literal -1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) p) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 p #s(literal -1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) p)))
(.f64 (sqrt.f64 (fma.f64 p #s(literal -1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 p))))
(.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 p))))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) p) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 p #s(literal -1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) p))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))) p) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))) p))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 p)) (/.f64 (fma.f64 p #s(literal -1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) p))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 p (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (.f64 p (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))))))
(neg.f64 (/.f64 (fma.f64 p #s(literal -1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) p))
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)
(/.f64 #s(literal 1 binary64) (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64)))))) (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 p (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))) (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (*.f64 x x) #s(literal -1/16 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))) p) (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))) p) (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (*.f64 x x) #s(literal -1/16 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/64 binary64))) p)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) p)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))))
(/.f64 (fma.f64 p #s(literal -1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) (neg.f64 p))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))) p))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64)))))))
(/.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64))) p))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (.f64 p (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (neg.f64 (.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))) p)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64)))) (neg.f64 (.f64 p (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64)))) (neg.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64))) p)))
(/.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) p) (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 p #s(literal -1/2 binary64))))))
(/.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) p) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) p)) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 p #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) p)) (neg.f64 (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))))
(pow.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))) #s(literal -1 binary64))
(.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) (/.f64 #s(literal 1 binary64) p))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) p) (/.f64 (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) p)) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)))
(.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) p))
(.f64 #s(literal -1 binary64) (/.f64 (fma.f64 p #s(literal -1/2 binary64) (.f64 x #s(literal -1/4 binary64))) p))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p))))))
(.f64 (fma.f64 p #s(literal -1/2 binary64) (.f64 x #s(literal -1/4 binary64))) (/.f64 #s(literal -1 binary64) p))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 p #s(literal -1/2 binary64))))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 p #s(literal -1/2 binary64))))) p)))
(.f64 (/.f64 #s(literal 1 binary64) p) (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (/.f64 #s(literal 1 binary64) (.f64 p (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))))))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))) p)))
(.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) p) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64)))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64))) p) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (/.f64 p (fma.f64 #s(literal 1/8 binary64) (.f64 p (.f64 p p)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64)))))))
(.f64 (pow.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 x x) #s(literal -1/16 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64))))) p) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/2 binary64) p)) (fma.f64 #s(literal 1/4 binary64) (.f64 p p) (.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64)))))))
(+.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 #s(literal 1/2 binary64) p))
(+.f64 (.f64 #s(literal 1/2 binary64) p) (.f64 #s(literal 1/4 binary64) x))
(+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64))))))
(-.f64 #s(literal 0 binary64) (fma.f64 p #s(literal -1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/2 binary64) p (.f64 x #s(literal -1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (fma.f64 #s(literal 1/4 binary64) x (.f64 p #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x))
(fma.f64 p #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) x))
(fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p))
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(.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 p p) (.f64 p p)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x))))))))
(.f64 (neg.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 p #s(literal -1/2 binary64)) (/.f64 p (.f64 x x)) #s(literal -1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x))))))
(exp.f64 (*.f64 (log.f64 (/.f64 p x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 p) #s(literal 2 binary64)) (.f64 (log.f64 x) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (.f64 p p) (neg.f64 (.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 x x))) (/.f64 (.f64 p p) (neg.f64 (*.f64 x x))))
(neg.f64 (/.f64 (.f64 p p) (neg.f64 (.f64 x x))))
(neg.f64 (.f64 (neg.f64 (/.f64 (.f64 p p) x)) (/.f64 #s(literal 1 binary64) x)))
(neg.f64 (.f64 (/.f64 (.f64 p p) (neg.f64 (*.f64 x x))) #s(literal 1 binary64)))
(/.f64 p (/.f64 (*.f64 x x) p))
(/.f64 (.f64 p p) (.f64 x x))
(/.f64 (/.f64 (*.f64 p p) x) x)
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 p p)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (.f64 x x) (.f64 p p)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 p p))))
(/.f64 (neg.f64 (.f64 p p)) (neg.f64 (.f64 x x)))
(/.f64 (/.f64 p x) (/.f64 x p))
(/.f64 (neg.f64 (/.f64 (*.f64 p p) x)) (neg.f64 x))
(pow.f64 (/.f64 p x) #s(literal 2 binary64))
(pow.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 x (.f64 p p)) x) #s(literal -1 binary64))
(.f64 p (/.f64 p (.f64 x x)))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (.f64 p p) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 p p) x) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 p p) (neg.f64 (*.f64 x x))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (.f64 x x) (*.f64 p p)))))
(.f64 (neg.f64 (.f64 p p)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(*.f64 (/.f64 p x) (/.f64 p x))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 p p) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 p p))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) #s(literal -1 binary64)))
(.f64 (/.f64 p (.f64 x x)) p)
(.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (.f64 p p) x)))
(.f64 (neg.f64 (/.f64 (.f64 p p) x)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p (neg.f64 x)) (/.f64 (neg.f64 p) x))
(*.f64 (/.f64 (neg.f64 p) x) (/.f64 p (neg.f64 x)))
(.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 (neg.f64 p) (.f64 x x)))
(*.f64 (pow.f64 (/.f64 p x) #s(literal 1 binary64)) (pow.f64 (/.f64 p x) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 x x) (*.f64 p p)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 p) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (*.f64 p p)))
(neg.f64 (neg.f64 (*.f64 p p)))
(pow.f64 p #s(literal 2 binary64))
(pow.f64 (*.f64 p p) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 p)) #s(literal 2 binary64))
(*.f64 p p)
(.f64 (.f64 p p) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 p p))
(.f64 #s(literal -1 binary64) (neg.f64 (.f64 p p)))
(*.f64 (neg.f64 p) (neg.f64 p))
(*.f64 (exp.f64 (log.f64 p)) (exp.f64 (log.f64 p)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (*.f64 x x)))
(neg.f64 (neg.f64 (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 x 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 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (.f64 x x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(exp.f64 (.f64 (log.f64 (/.f64 x (.f64 p p))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (*.f64 p p) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (neg.f64 (/.f64 (*.f64 p p) x)))
(neg.f64 (neg.f64 (/.f64 (*.f64 p p) x)))
(/.f64 p (/.f64 x p))
(/.f64 (*.f64 p p) x)
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 p p)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (*.f64 p p)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (*.f64 p p))))
(/.f64 (neg.f64 (*.f64 p p)) (neg.f64 x))
(pow.f64 (/.f64 x (*.f64 p p)) #s(literal -1 binary64))
(*.f64 p (/.f64 p x))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) x))
(.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 p p) x)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x (.f64 p p)))))
(.f64 (neg.f64 (.f64 p p)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p x) p)
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 p p))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) #s(literal -1 binary64)))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 (neg.f64 p) x))
(.f64 (pow.f64 (/.f64 x (.f64 p p)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x (*.f64 p p)) #s(literal -1/2 binary64)))

simplify355.0ms (3.7%)

Memory

12.8MiB live, 562.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 048×	`lower-fma.f64`
7 048×	`lower-fma.f32`
6 990×	`lower-*.f64`
6 990×	`lower-*.f32`
2 448×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	721	5138
1	2115	4993
2	6559	4958
0	8276	4644

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 369

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(* (sqrt -1) (sqrt -1/2))
(+ (* -1/8 (/ (* x (sqrt -1)) (* p (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))
(+ (* -1 (/ (+ (* 1/128 (/ (* (pow x 2) (sqrt -1)) (* p (pow (sqrt -1/2) 3)))) (* 1/8 (/ (* x (sqrt -1)) (sqrt -1/2)))) p)) (* (sqrt -1) (sqrt -1/2)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (* (pow x 2) (sqrt -1)) (pow (sqrt -1/2) 3))) (* -1/1024 (/ (* (pow x 3) (sqrt -1)) (* p (pow (sqrt -1/2) 5))))) p)) (* 1/8 (/ (* x (sqrt -1)) (sqrt -1/2)))) p)) (* (sqrt -1) (sqrt -1/2)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* 1/2 (sqrt (/ x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))
(* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 x)
(+ (* 1/4 x) (* 1/2 p))
(+ (* 1/4 x) (* 1/2 p))
(+ (* 1/4 x) (* 1/2 p))
(* 1/2 p)
(* p (+ 1/2 (* 1/4 (/ x p))))
(* p (+ 1/2 (* 1/4 (/ x p))))
(* p (+ 1/2 (* 1/4 (/ x p))))
(* 1/2 p)
(* -1 (* p (- (* -1/4 (/ x p)) 1/2)))
(* -1 (* p (- (* -1/4 (/ x p)) 1/2)))
(* -1 (* p (- (* -1/4 (/ x p)) 1/2)))
(* 1/2 p)
(+ (* 1/4 x) (* 1/2 p))
(+ (* 1/4 x) (* 1/2 p))
(+ (* 1/4 x) (* 1/2 p))
(* 1/4 x)
(* x (+ 1/4 (* 1/2 (/ p x))))
(* x (+ 1/4 (* 1/2 (/ p x))))
(* x (+ 1/4 (* 1/2 (/ p x))))
(* 1/4 x)
(* -1 (* x (- (* -1/2 (/ p x)) 1/4)))
(* -1 (* x (- (* -1/2 (/ p x)) 1/4)))
(* -1 (* x (- (* -1/2 (/ p x)) 1/4)))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* -1/2 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow x 2) (- (* 1/16 (/ 1 (pow p 6))) (* -1/8 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -4 (pow p 6)) (* -1/2 (* (pow p 2) (- (* 2 (pow p 4)) (* 1/4 (pow p 4)))))) (pow x 6))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (+ (* -1/2 (/ (+ (* 1/2 (* (pow p 2) (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))) (* -1/2 (/ (pow p 2) (pow x 2))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 7/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -25/16 (/ (pow p 2) (pow x 6))) (* 7/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))
(+ 1/2 (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -4 (/ (pow p 6) (pow x 6))) (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 2 (/ (pow p 4) (pow x 4)))) (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -4 (/ (pow p 6) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 8))) (* 1/8 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* 2 (/ (pow p 2) x)))
(* 2 (/ (pow p 2) x))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* 2 (/ (pow p 2) x))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* 2 (/ (pow p 2) x))
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
x
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* 1/2 (sqrt (/ x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))
(* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))
(* 1/2 (sqrt (/ x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/4 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(* 2 (sqrt (/ p x)))
(+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (* 2 (sqrt (/ p x))))
(+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (+ (* 2 (sqrt (/ p x))) (* 4 (sqrt (/ (pow p 5) (pow x 5))))))
(+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (+ (* -1/4 (* (sqrt (/ 1 (* p (pow x 7)))) (+ (* 4 (* (pow p 3) x)) (* 32 (pow p 4))))) (+ (* 2 (sqrt (/ p x))) (* 4 (sqrt (/ (pow p 5) (pow x 5)))))))
(* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1)))
(+ (* -4 (* (sqrt (/ (pow p 3) (pow x 3))) (/ (sqrt -1) (sqrt -4)))) (* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1))))
(+ (* -4 (* (sqrt (/ (pow p 3) (pow x 3))) (/ (sqrt -1) (sqrt -4)))) (+ (* 8 (* (sqrt (/ (pow p 5) (pow x 5))) (/ (sqrt -1) (sqrt -4)))) (* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1)))))
(+ (* -4 (* (sqrt (/ (pow p 3) (pow x 3))) (/ (sqrt -1) (sqrt -4)))) (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow p 5) x)) (/ (sqrt -1) (sqrt -4)))) (* 1/2 (* (sqrt (/ 1 (* p x))) (/ (* (sqrt -1) (+ (* -16 (/ (* (pow p 3) x) (pow (sqrt -4) 2))) (* 32 (pow p 4)))) (sqrt -4))))) (pow x 3))) (* (sqrt (/ p x)) (* (sqrt -4) (sqrt -1)))))
(* 2 (sqrt (/ p x)))
(+ (* -2 (sqrt (/ (pow p 3) (pow x 3)))) (* 2 (sqrt (/ p x))))
(+ (* 2 (sqrt (/ p x))) (* (pow p 2) (+ (* -2 (sqrt (/ 1 (* p (pow x 3))))) (* 4 (sqrt (/ p (pow x 5)))))))
(+ (* 2 (sqrt (/ p x))) (* (pow p 2) (+ (* -2 (sqrt (/ 1 (* p (pow x 3))))) (* p (+ (* -1/4 (* (sqrt (* p x)) (+ (* 4 (/ 1 (* p (pow x 3)))) (* 32 (/ 1 (pow x 4)))))) (* 4 (sqrt (/ 1 (* p (pow x 5))))))))))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2))))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2)))) (* (pow p 3) (sqrt 2)))))))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* -1 (/ (+ (* 1/2 (/ x (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* p (sqrt 2))))) p)))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))) (* -1/4 (pow x 3))) (* p (sqrt 2))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))
(+ 2 (* x (- (* x (+ (* -1/4 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))
(* 4 (/ p x))
(/ (+ (* -8 (/ (pow p 2) x)) (* 4 p)) x)
(/ (- (+ (* 4 p) (* 16 (/ (pow p 3) (pow x 2)))) (* 8 (/ (pow p 2) x))) x)
(/ (- (+ (* -32 (/ (pow p 4) (pow x 3))) (* 4 p)) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 8 (/ (pow p 2) x)))) x)
(* 4 (/ p x))
(* -1 (/ (+ (* -4 p) (* 8 (/ (pow p 2) x))) x))
(* -1 (/ (+ (* -4 p) (* -1 (/ (- (* 16 (/ (pow p 3) x)) (* 8 (pow p 2))) x))) x))
(* -1 (/ (+ (* -4 p) (* -1 (/ (- (* -1 (/ (- (* 32 (/ (pow p 4) x)) (* 16 (pow p 3))) x)) (* 8 (pow p 2))) x))) x))
(* 4 (/ p x))
(* p (+ (* -8 (/ p (pow x 2))) (* 4 (/ 1 x))))
(* p (+ (* p (- (* 16 (/ p (pow x 3))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))
(* p (+ (* p (- (* p (+ (* -32 (/ p (pow x 4))) (* 16 (/ 1 (pow x 3))))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))
2
(+ 2 (* -1 (/ x p)))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
(- (+ 2 (* -1/4 (/ (pow x 3) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) (* -1 x)) p)))
(+ 2 (* -1 (/ (- (* -1 (/ (- (* -1/4 (/ (pow x 3) p)) (* -1/2 (pow x 2))) p)) (* -1 x)) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 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)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)

Outputs
(* 1/2 (sqrt (/ x p)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (.f64 x p)) (sqrt.f64 (/.f64 (.f64 p (.f64 p p)) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x p)) (.f64 (.f64 p p) (fma.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x p))))))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(/.f64 (fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 p (pow.f64 x #s(literal 5 binary64))))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x p)))) p)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/8 binary64) (.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/8 binary64) (.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/1024 binary64)) (.f64 (.f64 p (.f64 p p)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))))))
(* (sqrt -1) (sqrt -1/2))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))
(+ (* -1/8 (/ (* x (sqrt -1)) (* p (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 p (sqrt.f64 #s(literal -1/2 binary64)))))
(+ (* -1 (/ (+ (* 1/128 (/ (* (pow x 2) (sqrt -1)) (* p (pow (sqrt -1/2) 3)))) (* 1/8 (/ (* x (sqrt -1)) (sqrt -1/2)))) p)) (* (sqrt -1) (sqrt -1/2)))
(-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64))) (/.f64 (.f64 #s(literal 1/128 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 #s(literal -1/2 binary64)) (*.f64 p #s(literal -1/2 binary64))))) p))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (* (pow x 2) (sqrt -1)) (pow (sqrt -1/2) 3))) (* -1/1024 (/ (* (pow x 3) (sqrt -1)) (* p (pow (sqrt -1/2) 5))))) p)) (* 1/8 (/ (* x (sqrt -1)) (sqrt -1/2)))) p)) (* (sqrt -1) (sqrt -1/2)))
(-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1/2 binary64))) (/.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 #s(literal -1/1024 binary64) (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (.f64 p (pow.f64 (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 5 binary64))))) p)) p))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/8 binary64) (.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/1024 binary64) (/.f64 x (.f64 (.f64 p (.f64 p p)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/128 binary64) (.f64 #s(literal -1/2 binary64) (.f64 p (.f64 p (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))
(* 1/2 (sqrt (/ x p)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x p)))))
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(* -1 (/ (+ (* -4 p) (* -1 (/ (- (* -1 (/ (- (* 32 (/ (pow p 4) x)) (* 16 (pow p 3))) x)) (* 8 (pow p 2))) x))) x))
(/.f64 (fma.f64 p #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal 32 binary64) x) (.f64 (.f64 p (.f64 p p)) #s(literal -16 binary64))) x) (.f64 p (.f64 p #s(literal 8 binary64)))) x)) (neg.f64 x))
(* 4 (/ p x))
(/.f64 (*.f64 p #s(literal 4 binary64)) x)
(* p (+ (* -8 (/ p (pow x 2))) (* 4 (/ 1 x))))
(.f64 p (fma.f64 #s(literal -8 binary64) (/.f64 p (.f64 x x)) (/.f64 #s(literal 4 binary64) x)))
(* p (+ (* p (- (* 16 (/ p (pow x 3))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))
(.f64 p (fma.f64 p (fma.f64 p (/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -8 binary64) (.f64 x x))) (/.f64 #s(literal 4 binary64) x)))
(* p (+ (* p (- (* p (+ (* -32 (/ p (pow x 4))) (* 16 (/ 1 (pow x 3))))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))
(.f64 p (fma.f64 p (fma.f64 p (fma.f64 #s(literal -32 binary64) (/.f64 p (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -8 binary64) (*.f64 x x))) (/.f64 #s(literal 4 binary64) x)))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
(-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (*.f64 x x) (/.f64 #s(literal -1/2 binary64) p) x) p))
(- (+ 2 (* -1/4 (/ (pow x 3) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
(+.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 x (.f64 x x)) p) (.f64 #s(literal 1/2 binary64) (.f64 x x))) p) x) p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) (* -1 x)) p)))
(-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (*.f64 x x) (/.f64 #s(literal -1/2 binary64) p) x) p))
(+ 2 (* -1 (/ (- (* -1 (/ (- (* -1/4 (/ (pow x 3) p)) (* -1/2 (pow x 2))) p)) (* -1 x)) p)))
(+.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 x (.f64 x x)) p) (.f64 #s(literal 1/2 binary64) (.f64 x x))) p) x) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal 1/4 binary64))) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal 1/4 binary64))) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 x #s(literal 1/4 binary64))) p)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(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)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)
(/ (pow p 2) x)
(/.f64 (*.f64 p p) x)

eval128.0ms (1.3%)

Memory: 14.0MiB live, 315.0MiB allocated
Compiler: Compiled 21 434 to 2 670 computations (87.5% saved)

prune108.0ms (1.1%)

Memory

-1.3MiB live, 212.6MiB allocated

Pruning

13 alts after pruning (3 fresh and 10 done)

	Pruned	Kept	Total
New	973	3	976
Fresh	0	0	0
Picked	1	3	4
Done	0	7	7
Total	974	13	987

Accuracy

100.0%

Counts

987 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	28.4%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
	28.4%	(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
✓	24.1%	(/.f64 p (neg.f64 x))
	51.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))))
	56.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	80.9%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	78.1%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	81.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	52.6%	(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
✓	52.6%	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
✓	56.8%	(sqrt.f64 #s(literal 1/2 binary64))
✓	37.8%	#s(literal 1 binary64)
✓	5.6%	#s(literal 0 binary64)

Compiler

Compiled 357 to 189 computations (47.1% saved)

regimes66.0ms (0.7%)

Memory

-12.7MiB live, 69.2MiB allocated

Counts

24 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p (neg.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))

Outputs
(/.f64 p (neg.f64 x))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Calls

7 calls:

24.0ms	p
10.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
7.0ms	x
7.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
6.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
81.3%	1	`p`
87.0%	2	`x`
100.0%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
100.0%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
100.0%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
81.3%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes21.0ms (0.2%)

Memory

30.1MiB live, 30.1MiB allocated

Counts

20 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p (neg.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))

Outputs
(/.f64 p (neg.f64 x))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Calls

4 calls:

5.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
5.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
5.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
5.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
98.8%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
98.8%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.8%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.8%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes37.0ms (0.4%)

Memory

-6.2MiB live, 31.8MiB allocated

Counts

17 → 3

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p (neg.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p))
(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) (*.f64 x x))
(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 p (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))

Outputs
(/.f64 p (neg.f64 x))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))

Calls

4 calls:

23.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
4.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
99.3%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.3%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.3%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.3%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes15.0ms (0.2%)

Memory

-23.4MiB live, 14.8MiB allocated

Counts

9 → 3

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p (neg.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))

Outputs
(/.f64 p (neg.f64 x))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
#s(literal 1 binary64)

Calls

4 calls:

6.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
3.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
3.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
99.0%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.0%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.0%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.0%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes10.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Counts

7 → 3

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p (neg.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))

Outputs
(/.f64 p (neg.f64 x))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1 binary64)

Calls

4 calls:

2.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
2.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
2.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
98.4%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
98.4%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.4%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.4%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes16.0ms (0.2%)

Memory

-10.2MiB live, 33.3MiB allocated

Counts

4 → 3

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))

Outputs
#s(literal 0 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1 binary64)

Calls

7 calls:

4.0ms	x
2.0ms	p
2.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
2.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
72.2%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
72.2%	2	`p`
61.9%	2	`x`
79.7%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
79.7%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
79.7%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
79.7%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes11.0ms (0.1%)

Memory

21.8MiB live, 21.8MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)

Outputs
#s(literal 0 binary64)
#s(literal 1 binary64)

Calls

7 calls:

2.0ms	p
2.0ms	x
1.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
1.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
1.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
39.4%	2	`x`
37.8%	1	`p`
37.8%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
39.8%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
39.8%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
39.8%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
39.8%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes10.0ms (0.1%)

Memory

-19.2MiB live, 18.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

7 calls:

2.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
1.0ms	x
1.0ms	p
1.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
1.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)

Results

Accuracy	Segments	Branch
5.6%	1	`p`
5.6%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
5.6%	1	`x`
5.6%	1	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
5.6%	1	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
5.6%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
5.6%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-2.5097321523774297e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-2.5097321523774297e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5823415665660194	0.9068213610446434
0.0ms	-1.0	-2.5097321523774297e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5823415665660194	0.9068213610446434
0.0ms	-1.0	-2.5097321523774297e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0002059913796127285	0.5823415665660194
0.0ms	-1.0	-2.5097321523774297e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch23.0ms (0.2%)

Memory

4.1MiB live, 41.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.0002059913796127285	0.5823415665660194
10.0ms	-1.0	-2.5097321523774297e-5

Samples

11.0ms

256×

valid

Compiler

Compiled 166 to 163 computations (1.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 3.0ms (47.9% of total)

ival-mult: 2.0ms (31.9% of total)

ival-sqrt: 2.0ms (31.9% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.0	-2.5097321523774297e-5

Compiler

Compiled 86 to 83 computations (3.5% saved)

simplify9.0ms (0.1%)

Memory

16.5MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	249
1	63	249
2	69	249
3	74	249
4	77	249
5	78	249

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(literal 0 binary64) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 0 binary64) #s(literal 1 binary64))
#s(literal 0 binary64)

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(literal 0 binary64) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) #s(literal 0 binary64) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 0 binary64) #s(literal 1 binary64))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal 0 binary64) #s(literal 1 binary64))
#s(literal 0 binary64)

soundness670.0ms (6.9%)

Memory

-8.1MiB live, 626.7MiB allocated

Rules

10 852×	`lower-fma.f64`
10 852×	`lower-fma.f32`
10 048×	`lower-fma.f64`
10 048×	`lower-fma.f32`
7 228×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	116
0	50	107
1	138	95
2	760	91
3	6800	91
0	9186	91
0	14	78
0	23	78
1	77	78
2	501	78
3	6967	78
0	8492	70
0	421	2950
1	1253	2905
2	4071	2840
0	8204	2694
0	472	2993
1	1444	2876
2	4985	2834
0	8534	2634

Stop Event

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

Compiler

Compiled 596 to 302 computations (49.3% saved)

preprocess106.0ms (1.1%)

Memory: -13.0MiB live, 142.5MiB allocated
Compiler: Compiled 644 to 198 computations (69.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	117
0	37	117
1	53	117
2	66	117
3	75	117
4	84	117
5	94	117
6	120	117
7	154	117
8	189	117
9	198	117
10	199	117
0	199	117

Iter	Nodes	Cost
0	21	117
0	37	117
1	53	117
2	66	117
3	75	117
4	84	117
5	94	117
6	120	117
7	154	117
8	189	117
9	198	117
10	199	117
0	199	117

analyze529.0ms (5.4%)

sample2.4s (25.1%)

preprocess65.0ms (0.7%)

explain330.0ms (3.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize65.0ms (0.7%)

series46.0ms (0.5%)

rewrite414.0ms (4.3%)

simplify534.0ms (5.5%)

eval74.0ms (0.8%)

prune60.0ms (0.6%)

simplify696.0ms (7.2%)

localize106.0ms (1.1%)

series16.0ms (0.2%)

rewrite541.0ms (5.6%)

simplify596.0ms (6.1%)

eval132.0ms (1.4%)

prune99.0ms (1%)

simplify12.0ms (0.1%)

localize97.0ms (1%)

series15.0ms (0.2%)

rewrite245.0ms (2.5%)

simplify381.0ms (3.9%)

eval75.0ms (0.8%)

prune57.0ms (0.6%)

simplify11.0ms (0.1%)

localize115.0ms (1.2%)

series34.0ms (0.3%)

rewrite328.0ms (3.4%)

simplify355.0ms (3.7%)

eval128.0ms (1.3%)

prune108.0ms (1.1%)

regimes66.0ms (0.7%)

regimes21.0ms (0.2%)

regimes37.0ms (0.4%)

regimes15.0ms (0.2%)

regimes10.0ms (0.1%)

regimes16.0ms (0.2%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch23.0ms (0.2%)

bsearch1.0ms (0%)

simplify9.0ms (0.1%)

soundness670.0ms (6.9%)

preprocess106.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	117
0	37	117
1	53	117
2	66	117
3	75	117
4	84	117
5	94	117
6	120	117
7	154	117
8	189	117
9	198	117
10	199	117
0	199	117