Metrics for Given's Rotation SVD example

analyze451.0ms (3.9%)

Memory

-14.7MiB live, 664.7MiB 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)

sample2.0s (17.6%)

Memory

12.1MiB live, 3 334.7MiB allocated

Samples

939.0ms	6 260×	0	valid
333.0ms	900×	2	valid
155.0ms	621×	1	valid
132.0ms	379×	3	valid
45.0ms	96×	4	valid
11.0ms	27×	5	exit

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-mult: 311.0ms (23.7% of total)

const: 297.0ms (22.6% of total)

ival-sqrt: 197.0ms (15% of total)

ival-add: 152.0ms (11.6% of total)

ival-div: 99.0ms (7.5% of total)

ival-<: 87.0ms (6.6% of total)

adjust: 75.0ms (5.7% of total)

ival-fabs: 66.0ms (5% of total)

exact: 13.0ms (1% of total)

ival-and: 11.0ms (0.8% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

preprocess64.0ms (0.6%)

Memory

1.7MiB live, 38.4MiB 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
1	29	17
2	36	17
3	38	17
4	39	17
0	39	15

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

Outputs

(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* 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)

explain257.0ms (2.2%)

Memory

10.2MiB live, 515.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
66	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
34	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
26	-	2	(9.335367285466494e-11 -1.3897946384413664e+145)	`(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)))))))`
1	-	0	-	`(/.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	-	`#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	66	0
↳	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	overflow	1
↳	`(*.f64 #s(literal 4 binary64) p)`	overflow	1
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	67
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	67
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	34	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	24	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	8
↳	`(.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	32
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	32
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	12
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	65

Confusion

	Predicted +	Predicted -
+	58	0
-	66	132

Precision

0.46774193548387094

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	58	0	0
-	66	0	132

Precision?

0.46774193548387094

Recall?

1.0

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

35.0ms	384×	0	valid
24.0ms	58×	2	valid
14.0ms	38×	1	valid
10.0ms	30×	3	valid
1.0ms	2×	4	valid

Compiler

Compiled 230 to 60 computations (73.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 22.0ms (39.7% of total)

ival-sqrt: 11.0ms (19.8% of total)

adjust: 8.0ms (14.4% of total)

ival-add: 7.0ms (12.6% of total)

ival-div: 6.0ms (10.8% of total)

exact: 1.0ms (1.8% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.2%	(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)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0%)

Memory

10.5MiB live, 10.5MiB 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×	`-lowering-.f32`
32×	`-lowering-.f64`
18×	`accelerator-lowering-fma.f32`
18×	`accelerator-lowering-fma.f64`
12×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	94
1	29	94
2	36	94
3	38	94
4	39	94
0	39	86

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1/2
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
1
(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
x
(sqrt (+ (* (* 4 p) p) (* x x)))
(+ (* (* 4 p) p) (* x x))
(* (* 4 p) p)
(* 4 p)
4
p
(* x x)

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

localize102.0ms (0.9%)

Memory

-28.6MiB live, 104.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
✓	accuracy	91.4%	(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	88.0%	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
✓	accuracy	76.0%	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

46.0ms	192×	0	valid
7.0ms	29×	2	valid
5.0ms	15×	3	valid
3.0ms	19×	1	valid
0.0ms	1×	4	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

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

ival-mult: 37.0ms (73.1% of total)

ival-sqrt: 5.0ms (9.9% of total)

ival-add: 4.0ms (7.9% of total)

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

adjust: 2.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series22.0ms (0.2%)

Memory

0.6MiB live, 38.1MiB allocated

Counts

6 → 144

Calls

Call 1

Inputs
#<alt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))>
#<alt (+ (* (* 4 p) p) (* x x))>
#<alt (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))>
#<alt (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))>
#<alt (sqrt (+ (* (* 4 p) p) (* x x)))>
#<alt (/ x (sqrt (+ (* (* 4 p) p) (* 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
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	p	@	0	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1.0ms	x	@	inf	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

rewrite346.0ms (3%)

Memory

45.8MiB live, 514.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 862×	`accelerator-lowering-fma.f32`
4 862×	`accelerator-lowering-fma.f64`
3 532×	`-lowering-.f32`
3 532×	`-lowering-.f64`
2 388×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
1	68	78
2	492	78
3	6948	78
0	8473	70

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 302

Calls

Call 1

Inputs
(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
(+ (* (* 4 p) p) (* x x))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
(sqrt (+ (* (* 4 p) p) (* x x)))
(/ x (sqrt (+ (* (* 4 p) p) (* 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 (neg.f64 x) (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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))))))) (sqrt.f64 (fma.f64 (.f64 x 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 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x))) #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 (+.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 1/4 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) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(/.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 (+.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 1/4 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)))))))))
(/.f64 (-.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 1/2 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 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))
(/.f64 (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 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 (neg.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))) (neg.f64 (-.f64 (+.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 1/4 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))))
(/.f64 (neg.f64 (-.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)))) (neg.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))))))))
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(/.f64 (neg.f64 (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))) (neg.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))))))))
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(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 (.f64 x 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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (*.f64 p p))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x))) (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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (sqrt.f64 (fma.f64 (.f64 x 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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x 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 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.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 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))))))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 x 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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))))))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 x 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 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))))
(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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x 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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x 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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x 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 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
(.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 (neg.f64 x) (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 (neg.f64 x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(neg.f64 (/.f64 (neg.f64 x) (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 (neg.f64 x) (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 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 (/.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 (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 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))))))) (sqrt.f64 (fma.f64 (.f64 x 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 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x))))

simplify503.0ms (4.4%)

Memory

-26.5MiB live, 846.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10 048×	`accelerator-lowering-fma.f32`
10 048×	`accelerator-lowering-fma.f64`
7 228×	`-lowering-.f32`
7 228×	`-lowering-.f64`
4 784×	`+-lowering-+.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 → 144

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)))))
(fma.f64 x (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (/.f64 (.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (*.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 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p)) (/.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -3/128 binary64)) (.f64 p (.f64 p p)))) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) 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)))
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(+ 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))

eval67.0ms (0.6%)

Memory: 23.1MiB live, 174.6MiB allocated
Compiler: Compiled 16 845 to 2 162 computations (87.2% saved)

prune73.0ms (0.6%)

Memory

14.7MiB live, 205.0MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	430	16	446
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	431	16	447

Accuracy

99.7%

Counts

447 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.8%	(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)))
	27.4%	(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
	79.2%	(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)))
	25.0%	(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
	51.8%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
	14.0%	(sqrt.f64 (/.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)))
▶	52.2%	(sqrt.f64 (/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))))
▶	16.4%	(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
▶	79.2%	(sqrt.f64 (/.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)))))))))
	55.8%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 (/.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 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (.f64 (/.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (/.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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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)))))))))
	52.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)) (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64))))))
▶	8.1%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64)))))
	74.6%	(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)))))
	6.9%	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))))
	35.0%	(sqrt.f64 #s(literal 1 binary64))
▶	55.7%	(sqrt.f64 #s(literal 1/2 binary64))

Compiler

Compiled 732 to 346 computations (52.7% saved)

simplify311.0ms (2.7%)

Memory

19.5MiB live, 513.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 (/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))))
✓	cost-diff	0	(fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
✓	cost-diff	256	(+.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)))
✓	cost-diff	640	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64))))
✓	cost-diff	1152	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64)))))
✓	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 #s(literal 1/2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
✓	cost-diff	0	(/.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)))))))
✓	cost-diff	0	(sqrt.f64 (/.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)))))))))
✓	cost-diff	1216	(/.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))))))))

Rules

7 380×	`accelerator-lowering-fma.f32`
7 380×	`accelerator-lowering-fma.f64`
3 838×	`-lowering-.f32`
3 838×	`-lowering-.f64`
1 698×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	355
1	74	345
2	138	343
3	231	343
4	417	343
5	748	343
6	1980	343
7	3534	343
8	3933	343
9	4610	343
10	5599	343
11	6791	343
0	8041	274

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))
(/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
1/2
(/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
1
(+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
x
(sqrt (+ (* x x) (* p (* 4 p))))
(+ (* x x) (* p (* 4 p)))
(* p (* 4 p))
p
(* 4 p)
4
(sqrt 1/2)
1/2
(sqrt (/ (* p p) (* x x)))
(/ (* p p) (* x x))
(* p p)
p
(* x x)
x
(sqrt (* 1/2 (+ 1 (+ (* (* p p) (/ 2 (* x x))) -1))))
(* 1/2 (+ 1 (+ (* (* p p) (/ 2 (* x x))) -1)))
1/2
(+ 1 (+ (* (* p p) (/ 2 (* x x))) -1))
1
(+ (* (* p p) (/ 2 (* x x))) -1)
(* p p)
p
(/ 2 (* x x))
2
(* x x)
x
-1
(sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)))
(/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1))
(* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2)
(+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1)
x
(/ x (+ (* x x) (* p (* 4 p))))
(+ (* x x) (* p (* 4 p)))
(* p (* 4 p))
p
(* 4 p)
4
-1
1/2
(+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
(sqrt (+ (* x x) (* p (* 4 p))))

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

localize454.0ms (3.9%)

Memory

-12.7MiB live, 437.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	89.3%	(+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))
✓	accuracy	89.0%	(/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)))
✓	accuracy	76.0%	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
✓	accuracy	53.6%	(fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 2 binary64) (*.f64 x x))
✓	accuracy	91.2%	(fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
✓	accuracy	77.4%	(+.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)))
✓	accuracy	66.3%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64)))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	84.3%	(/.f64 (.f64 p p) (.f64 x x))
✓	accuracy	66.3%	(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.5%	(/.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))))))))
✓	accuracy	91.8%	(sqrt.f64 (/.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)))))))))
✓	accuracy	88.0%	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
✓	accuracy	76.0%	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))

Samples

41.0ms	58×	2	valid
38.0ms	132×	0	valid
34.0ms	21×	3	valid
19.0ms	38×	1	valid
6.0ms	5×	4	valid
2.0ms	2×	5	exit

Compiler

Compiled 351 to 36 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-mult: 26.0ms (27.7% of total)

ival-div: 21.0ms (22.4% of total)

ival-sqrt: 20.0ms (21.3% of total)

ival-add: 16.0ms (17.1% of total)

adjust: 10.0ms (10.7% of total)

exact: 1.0ms (1.1% of total)

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

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

series54.0ms (0.5%)

Memory

19.6MiB live, 58.2MiB allocated

Counts

20 → 420

Calls

Call 1

Inputs
#<alt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))>
#<alt (sqrt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))>
#<alt (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))>
#<alt (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))>
#<alt (sqrt 1/2)>
#<alt (sqrt (/ (* p p) (* x x)))>
#<alt (/ (* p p) (* x x))>
#<alt (* p p)>
#<alt (* x x)>
#<alt (sqrt (* 1/2 (+ 1 (+ (* (* p p) (/ 2 (* x x))) -1))))>
#<alt (* 1/2 (+ 1 (+ (* (* p p) (/ 2 (* x x))) -1)))>
#<alt (+ 1 (+ (* (* p p) (/ 2 (* x x))) -1))>
#<alt (+ (* (* p p) (/ 2 (* x x))) -1)>
#<alt (sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)))>
#<alt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1))>
#<alt (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2)>
#<alt (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1)>
#<alt (sqrt (+ (* x x) (* p (* 4 p))))>
#<alt (/ 2 (* x x))>
#<alt (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)>

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 (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 (- (* 1/4 (/ x (pow p 2))) (* 1/2 (/ 1 p)))))>
#<alt (+ 1 (* x (- (* x (+ (* -1/16 (/ x (pow p 3))) (* 1/4 (/ 1 (pow p 2))))) (* 1/2 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (pow p 4) (pow x 4))) (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))>
#<alt (* 1/2 (/ (pow x 2) (pow p 2)))>
#<alt (* (pow x 2) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/2 (/ 1 (pow p 2)))))>
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#<alt (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 6)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))))) (pow p 2))) (+ (* 1/4 (/ (* (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/2 (/ (* (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (pow (sqrt 2) 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 p 2)))))))) (* (pow x 6) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))>
#<alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))>
#<alt (* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))>
#<alt (* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (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 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (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))) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* 1/2 (/ (* (- (* -8 (pow p 4)) (* -2 (pow p 4))) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (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) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (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))>
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#<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))))))))>
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#<alt 1/2>
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#<alt 1>
#<alt (+ 1 (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))))>
#<alt (+ 1 (+ (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))) (* 1/2 (/ (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))) (pow x 4)))))>
#<alt (+ 1 (+ (* 1/2 (/ (- (* -128 (pow p 6)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))))) (pow p 2))) (+ (* 1/4 (/ (* (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 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 p 2)))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))) (* 1/2 (/ (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))) (pow x 4))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/2 (/ (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (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))) (- (* -8 (pow p 4)) (* -2 (pow p 4)))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (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) (- (* 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>
#<alt (- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)>
#<alt (- (* (pow x 2) (+ (* -1/32 (/ (pow x 2) (pow p 4))) (* 1/8 (/ 1 (pow p 2))))) 1/2)>
#<alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/128 (/ (pow x 2) (pow p 6))) (* 1/32 (/ 1 (pow p 4))))) (* 1/8 (/ 1 (pow p 2))))) 1/2)>
#<alt (* -2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))>
#<alt (* -2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))>
#<alt (* -2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (* 8 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* (pow p 2) (+ (* -32 (/ (pow p 2) (pow x 6))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 8))) (* 32 (/ 1 (pow x 6))))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))>
#<alt -1/2>
#<alt (- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)>
#<alt (- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)>
#<alt (- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)>
#<alt -1/2>
#<alt (- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)>
#<alt (- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)>
#<alt (- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)>
#<alt -1>
#<alt (- (* 1/4 (/ (pow x 2) (pow p 2))) 1)>
#<alt (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))) 1)>
#<alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow p 6))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))) 1)>
#<alt (* -4 (/ (pow p 2) (pow x 2)))>
#<alt (/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))>
#<alt (/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))>
#<alt (/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))>
#<alt (* -4 (/ (pow p 2) (pow x 2)))>
#<alt (/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))>
#<alt (/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))>
#<alt (/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))>
#<alt (* -4 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))>
#<alt -1>
#<alt (- (* 1/4 (/ (pow x 2) (pow p 2))) 1)>
#<alt (- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)>
#<alt (- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))>
#<alt -1>
#<alt (- (* 1/4 (/ (pow x 2) (pow p 2))) 1)>
#<alt (- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)>
#<alt (- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))>
#<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 (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt (/ 2 (pow x 2))>
#<alt -1>
#<alt (- (* 1/2 (/ x p)) 1)>
#<alt (- (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))) 1)>
#<alt (- (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) 1)>
#<alt (* -2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -2 (pow p 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))))) (pow x 2))>
#<alt (/ (+ (* -2 (pow p 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)))))) (pow x 2))>
#<alt -2>
#<alt (- (* 2 (/ (pow p 2) (pow x 2))) 2)>
#<alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)>
#<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))))) 2)>
#<alt (* -2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))>
#<alt -1>
#<alt (- (* 1/2 (/ x p)) 1)>
#<alt (- (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))) 1)>
#<alt (- (+ (* -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)>
#<alt -1>
#<alt (- (* -1/2 (/ x p)) 1)>
#<alt (- (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)) 1)>
#<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)) 1)>

Calls

105 calls:

Time	Variable		Point	Expression
19.0ms	p	@	0	(sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)))
4.0ms	x	@	inf	(sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)))
3.0ms	x	@	-inf	(sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)))
2.0ms	x	@	inf	(sqrt (/ (* p p) (* x x)))
2.0ms	p	@	inf	(+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1)

rewrite400.0ms (3.5%)

Memory

-11.9MiB live, 656.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 682×	`/-lowering-/.f32`
4 682×	`/-lowering-/.f64`
4 606×	`-lowering-.f32`
4 606×	`-lowering-.f64`
3 944×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	235
1	205	215
2	1620	214
0	8895	194

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 769

Calls

Call 1

Inputs
(/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
(sqrt (/ 1/2 (/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))
(/ 1 (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))
(+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))
(sqrt 1/2)
(sqrt (/ (* p p) (* x x)))
(/ (* p p) (* x x))
(* p p)
(* x x)
(sqrt (* 1/2 (+ 1 (+ (* (* p p) (/ 2 (* x x))) -1))))
(* 1/2 (+ 1 (+ (* (* p p) (/ 2 (* x x))) -1)))
(+ 1 (+ (* (* p p) (/ 2 (* x x))) -1))
(+ (* (* p p) (/ 2 (* x x))) -1)
(sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)))
(/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) (+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1))
(* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2)
(+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1)
(sqrt (+ (* x x) (* p (* 4 p))))
(/ 2 (* x x))
(+ (/ x (sqrt (+ (* x x) (* p (* 4 p))))) -1)

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

simplify471.0ms (4.1%)

Memory

-26.7MiB live, 736.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 174×	`accelerator-lowering-fma.f32`
11 174×	`accelerator-lowering-fma.f64`
7 684×	`-lowering-.f32`
7 684×	`-lowering-.f64`
4 268×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	852	7631
1	2657	7336
0	8501	6926

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

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)))
(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 (- (* 1/4 (/ x (pow p 2))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (- (* x (+ (* -1/16 (/ x (pow p 3))) (* 1/4 (/ 1 (pow p 2))))) (* 1/2 (/ 1 p)))))
1/2
(+ 1/2 (* 1/2 (/ (pow p 2) (pow x 2))))
(- (+ 1/2 (* -1 (/ (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1/2 (/ (pow p 2) (pow x 2))))
(- (+ 1/2 (* -1 (/ (+ (* -1/8 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/8 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1/2 (pow p 4)) (* -1/8 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (pow p 4) (pow x 4))) (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/2 (/ 1 (pow p 2)))))
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1
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(+ 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
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(- (* (pow x 2) (+ (* -1/32 (/ (pow x 2) (pow p 4))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/128 (/ (pow x 2) (pow p 6))) (* 1/32 (/ 1 (pow p 4))))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(* -2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 8 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -32 (/ (pow p 2) (pow x 6))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 8))) (* 32 (/ 1 (pow x 6))))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
-1/2
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)
-1/2
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow p 6))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))) 1)
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
(* 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))))))))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
-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)))) 1)
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2))
(/ (+ (* -2 (pow p 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))))) (pow x 2))
(/ (+ (* -2 (pow p 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)))))) (pow x 2))
-2
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 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))))) 2)
(* -2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
-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)

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

eval262.0ms (2.3%)

Memory: 17.8MiB live, 452.4MiB allocated
Compiler: Compiled 39 218 to 3 832 computations (90.2% saved)

prune220.0ms (1.9%)

Memory

16.6MiB live, 397.6MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	1 270	8	1 278
Fresh	4	7	11
Picked	4	1	5
Done	0	0	0
Total	1 278	16	1 294

Accuracy

99.9%

Counts

1 294 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.0%	(/.f64 (sqrt.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p))))))))
	27.8%	(/.f64 p (neg.f64 x))
	7.1%	(/.f64 p x)
▶	8.4%	(sqrt.f64 (fma.f64 (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
▶	79.2%	(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)))
	25.0%	(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
▶	51.8%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
	14.0%	(sqrt.f64 (/.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)))
	3.1%	(sqrt.f64 (/.f64 (.f64 (fma.f64 x (/.f64 x (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 2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -2 binary64))))
▶	12.6%	(sqrt.f64 (/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)))
	55.2%	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	27.6%	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (.f64 p (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1/2 binary64))))
	55.8%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 (/.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 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (.f64 (/.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (/.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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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)))))))))
	74.6%	(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)))))
▶	35.0%	(sqrt.f64 #s(literal 1 binary64))
✓	55.7%	(sqrt.f64 #s(literal 1/2 binary64))

Compiler

Compiled 708 to 332 computations (53.1% saved)

simplify215.0ms (1.9%)

Memory

8.3MiB live, 320.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)))
✓	cost-diff	704	(/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64))
✓	cost-diff	0	(.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x)))
✓	cost-diff	0	(fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64))
✓	cost-diff	768	(fma.f64 (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	cost-diff	1152	(sqrt.f64 (fma.f64 (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
✓	cost-diff	0	(/.f64 x p)
✓	cost-diff	0	(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓	cost-diff	640	(sqrt.f64 #s(literal 1 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

3 952×	`accelerator-lowering-fma.f32`
3 952×	`accelerator-lowering-fma.f64`
3 526×	`-lowering-.f32`
3 526×	`-lowering-.f64`
2 618×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	264
1	71	264
2	119	260
3	206	252
4	351	248
5	539	244
6	1241	244
7	1981	244
8	4201	244
9	4607	244
10	5968	244
11	6396	244
12	6511	244
13	6582	244
14	7444	244
15	7460	244
0	8368	208

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
(+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
x
(sqrt (+ (* x x) (* p (* 4 p))))
(+ (* x x) (* p (* 4 p)))
(* p (* 4 p))
p
(* 4 p)
4
1/2
(sqrt 1)
1
(sqrt (+ (* 1/4 (/ x p)) 1/2))
(+ (* 1/4 (/ x p)) 1/2)
1/4
(/ x p)
x
p
1/2
(sqrt (+ (* (+ (* p (* p (/ 2 (* x x)))) 1) 1/2) -1/2))
(+ (* (+ (* p (* p (/ 2 (* x x)))) 1) 1/2) -1/2)
(+ (* p (* p (/ 2 (* x x)))) 1)
p
(* p (/ 2 (* x x)))
(/ 2 (* x x))
2
(* x x)
x
1
1/2
-1/2
(sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) -2))
(/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) -2)
(* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2)
(+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1)
x
(/ x (+ (* x x) (* p (* 4 p))))
(+ (* x x) (* p (* 4 p)))
(* p (* 4 p))
p
(* 4 p)
4
-1
1/2
-2

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

localize162.0ms (1.4%)

Memory

1.1MiB live, 407.8MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 4 binary64) p)
✓	accuracy	94.5%	(/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
✓	accuracy	90.6%	(sqrt.f64 (/.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)))
✓	accuracy	77.7%	(fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 2 binary64) (*.f64 x x))
✓	accuracy	99.7%	(.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x)))
✓	accuracy	89.3%	(fma.f64 (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	accuracy	74.5%	(sqrt.f64 (fma.f64 (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 x p)
✓	accuracy	98.1%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1 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	99.9%	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
✓	accuracy	76.0%	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))

Samples

32.0ms	130×	0	valid
25.0ms	66×	0	invalid
22.0ms	30×	2	valid
9.0ms	19×	1	valid
7.0ms	7×	3	valid
3.0ms	3×	4	valid
1.0ms	1×	5	exit

Compiler

Compiled 247 to 39 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-div: 21.0ms (29.7% of total)

ival-mult: 20.0ms (28.3% of total)

ival-sqrt: 13.0ms (18.4% of total)

ival-add: 10.0ms (14.1% of total)

adjust: 6.0ms (8.5% of total)

exact: 1.0ms (1.4% of total)

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

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

series41.0ms (0.4%)

Memory

-2.0MiB live, 109.1MiB allocated

Counts

19 → 408

Calls

Call 1

Inputs
#<alt (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))>
#<alt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)>
#<alt (/ x (sqrt (+ (* x x) (* p (* 4 p)))))>
#<alt (sqrt (+ (* x x) (* p (* 4 p))))>
#<alt (sqrt 1)>
#<alt (sqrt (+ (* 1/4 (/ x p)) 1/2))>
#<alt (+ (* 1/4 (/ x p)) 1/2)>
#<alt (/ x p)>
#<alt (sqrt (+ (* (+ (* p (* p (/ 2 (* x x)))) 1) 1/2) -1/2))>
#<alt (+ (* (+ (* p (* p (/ 2 (* x x)))) 1) 1/2) -1/2)>
#<alt (+ (* p (* p (/ 2 (* x x)))) 1)>
#<alt (* p (/ 2 (* x x)))>
#<alt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) -2)>
#<alt (sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) -2))>
#<alt (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2)>
#<alt (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1)>
#<alt (/ 2 (* x x))>
#<alt (/ x (+ (* x x) (* p (* 4 p))))>
#<alt (* 4 p)>

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

Calls

102 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(+ (* 1/4 (/ x p)) 1/2)
3.0ms	x	@	inf	(* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2)
3.0ms	x	@	0	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
2.0ms	x	@	0	(/ x p)
1.0ms	x	@	-inf	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))

rewrite405.0ms (3.5%)

Memory

-12.1MiB live, 718.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 708×	`accelerator-lowering-fma.f32`
5 708×	`accelerator-lowering-fma.f64`
4 098×	`-lowering-.f32`
4 098×	`-lowering-.f64`
3 816×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	209
1	186	209
2	1314	209
0	8293	187

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 565

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
(+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
(sqrt (+ (* x x) (* p (* 4 p))))
(sqrt 1)
(sqrt (+ (* 1/4 (/ x p)) 1/2))
(+ (* 1/4 (/ x p)) 1/2)
(/ x p)
(sqrt (+ (* (+ (* p (* p (/ 2 (* x x)))) 1) 1/2) -1/2))
(+ (* (+ (* p (* p (/ 2 (* x x)))) 1) 1/2) -1/2)
(+ (* p (* p (/ 2 (* x x)))) 1)
(* p (/ 2 (* x x)))
(/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) -2)
(sqrt (/ (* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2) -2))
(* (+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1) 1/2)
(+ (* x (/ x (+ (* x x) (* p (* 4 p))))) -1)
(/ 2 (* x x))
(/ x (+ (* x x) (* p (* 4 p))))
(* 4 p)

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

simplify480.0ms (4.2%)

Memory

26.3MiB live, 774.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 196×	`accelerator-lowering-fma.f32`
10 196×	`accelerator-lowering-fma.f64`
8 338×	`-lowering-.f32`
8 338×	`-lowering-.f64`
4 012×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	913	6621
1	2823	6485
0	8450	6104

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

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)))))
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-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow p 6))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))) 1)
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(/ 2 (pow x 2))
(* 1/4 (/ x (pow p 2)))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2)))))
(* x (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow p 6))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2)))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/256 (/ (pow x 2) (pow p 8))) (* 1/64 (/ 1 (pow p 6))))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2)))))
(/ 1 x)
(/ (+ 1 (* -4 (/ (pow p 2) (pow x 2)))) x)
(/ (- (+ 1 (* 16 (/ (pow p 4) (pow x 4)))) (* 4 (/ (pow p 2) (pow x 2)))) x)
(/ (- (+ 1 (* -64 (/ (pow p 6) (pow x 6)))) (+ (* -16 (/ (pow p 4) (pow x 4))) (* 4 (/ (pow p 2) (pow x 2))))) x)
(/ 1 x)
(* -1 (/ (- (* 4 (/ (pow p 2) (pow x 2))) 1) x))
(* -1 (/ (- (* -16 (/ (pow p 4) (pow x 4))) (+ 1 (* -4 (/ (pow p 2) (pow x 2))))) x))
(* -1 (/ (- (* 64 (/ (pow p 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow p 2) (pow x 2))) (* 16 (/ (pow p 4) (pow x 4)))))) x))
(/ 1 x)
(+ (* -4 (/ (pow p 2) (pow x 3))) (/ 1 x))
(+ (* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 5))) (* 4 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 7))) (* 16 (/ 1 (pow x 5))))) (* 4 (/ 1 (pow x 3))))) (/ 1 x))
(* 1/4 (/ x (pow p 2)))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/4 x)) (pow p 2))
(/ (- (+ (* 1/64 (/ (pow x 5) (pow p 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/256 (/ (pow x 7) (pow p 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow p 4))) (* 1/16 (/ (pow x 3) (pow p 2))))) (pow p 2))
(* 1/4 (/ x (pow p 2)))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/4 x)) (pow p 2))
(/ (- (+ (* 1/64 (/ (pow x 5) (pow p 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/256 (/ (pow x 7) (pow p 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow p 4))) (* 1/16 (/ (pow x 3) (pow p 2))))) (pow p 2))
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 p)
(* 4 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 -1/128 binary64) (/.f64 x (.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)))
(+ (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 (.f64 #s(literal 1/2 binary64) x) (/.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)))) (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 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) (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 (fma.f64 #s(literal -1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (fma.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 p p)) (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64))))))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 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 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (*.f64 x x))) 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 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (fma.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)) (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 4 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) 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 #s(literal 1/4 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 2 binary64) (.f64 p p)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 8 binary64))))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (fma.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)) (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (.f64 p p)))))) (.f64 p p))) (.f64 p (pow.f64 x #s(literal 6 binary64)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (fma.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)) (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 4 binary64))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (*.f64 x x))) 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 p (.f64 p (fma.f64 (.f64 (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.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) (pow.f64 x #s(literal 4 binary64)))) (/.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 -1/128 binary64) (/.f64 x (.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)))
(+ (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 -1/128 binary64) (/.f64 x (.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))) (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 1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/128 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) 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 -1/2 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)) (.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) 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))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 p p) (*.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 (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 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 (pow.f64 p #s(literal 4 binary64)) #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) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) (fma.f64 p p (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))) (*.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 (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 2 binary64) (.f64 p p)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 8 binary64))))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x))) (fma.f64 p p (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
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(/.f64 (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -4 binary64) #s(literal 1 binary64)) x)
(* -1 (/ (- (* -16 (/ (pow p 4) (pow x 4))) (+ 1 (* -4 (/ (pow p 2) (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -4 binary64) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (/ (- (* 64 (/ (pow p 6) (pow x 6))) (+ 1 (+ (* -4 (/ (pow p 2) (pow x 2))) (* 16 (/ (pow p 4) (pow x 4)))))) x))
(/.f64 (-.f64 (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (fma.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -4 binary64) #s(literal 1 binary64)))) (neg.f64 x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -4 (/ (pow p 2) (pow x 3))) (/ 1 x))
(fma.f64 (/.f64 (.f64 p p) (.f64 x (*.f64 x x))) #s(literal -4 binary64) (/.f64 #s(literal 1 binary64) x))
(+ (* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 5))) (* 4 (/ 1 (pow x 3))))) (/ 1 x))
(fma.f64 (.f64 p p) (fma.f64 p (.f64 p (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(+ (* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 7))) (* 16 (/ 1 (pow x 5))))) (* 4 (/ 1 (pow x 3))))) (/ 1 x))
(fma.f64 p (.f64 p (fma.f64 (.f64 p p) (fma.f64 #s(literal -64 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) x))
(* 1/4 (/ x (pow p 2)))
(/.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 p p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/4 x)) (pow p 2))
(/.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) #s(literal -1/16 binary64) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p))
(/ (- (+ (* 1/64 (/ (pow x 5) (pow p 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) #s(literal -1/16 binary64) (.f64 x #s(literal 1/4 binary64)))) (*.f64 p p))
(/ (- (+ (* -1/256 (/ (pow x 7) (pow p 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow p 4))) (* 1/16 (/ (pow x 3) (pow p 2))))) (pow p 2))
(/.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal -1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 #s(literal -1/64 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 p #s(literal 4 binary64))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)))) (.f64 p p))
(* 1/4 (/ x (pow p 2)))
(/.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 p p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/4 x)) (pow p 2))
(/.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) #s(literal -1/16 binary64) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p))
(/ (- (+ (* 1/64 (/ (pow x 5) (pow p 4))) (* 1/4 x)) (* 1/16 (/ (pow x 3) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) #s(literal -1/16 binary64) (.f64 x #s(literal 1/4 binary64)))) (*.f64 p p))
(/ (- (+ (* -1/256 (/ (pow x 7) (pow p 6))) (* 1/4 x)) (+ (* -1/64 (/ (pow x 5) (pow p 4))) (* 1/16 (/ (pow x 3) (pow p 2))))) (pow p 2))
(/.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal -1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 #s(literal -1/64 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 p #s(literal 4 binary64))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)))) (.f64 p p))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))
(* 4 p)
(*.f64 p #s(literal 4 binary64))

eval264.0ms (2.3%)

Memory: 5.2MiB live, 231.0MiB allocated
Compiler: Compiled 26 773 to 3 125 computations (88.3% saved)

prune284.0ms (2.5%)

Memory

-1.9MiB live, 204.4MiB allocated

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	980	7	987
Fresh	4	6	10
Picked	2	3	5
Done	0	1	1
Total	986	17	1 003

Accuracy

99.9%

Counts

1 003 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.4%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
▶	27.8%	(/.f64 p (neg.f64 x))
	7.1%	(/.f64 p x)
✓	8.4%	(sqrt.f64 (fma.f64 (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
▶	74.6%	(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)))
✓	79.2%	(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)))
✓	51.8%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
	14.0%	(sqrt.f64 (/.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)))
▶	13.1%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)))
	55.2%	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	27.6%	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (.f64 p (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1/2 binary64))))
▶	12.6%	(sqrt.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (*.f64 x x))) #s(literal -1 binary64)) #s(literal -1/4 binary64)))
	14.9%	(sqrt.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
	55.8%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 (/.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 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (.f64 (/.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (/.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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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)))))))))
✓	55.7%	(sqrt.f64 #s(literal 1/2 binary64))
	16.3%	(sqrt.f64 #s(literal 1/4 binary64))
▶	35.0%	#s(literal 1 binary64)

Compiler

Compiled 626 to 282 computations (55% saved)

simplify405.0ms (3.5%)

Memory

1.8MiB live, 158.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (/.f64 (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)))
✓	cost-diff	320	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (*.f64 x x) #s(literal -1 binary64))
✓	cost-diff	704	(/.f64 (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64))
✓	cost-diff	0	(/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))
✓	cost-diff	0	(fma.f64 x (/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 (fma.f64 x (/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (*.f64 x x))) #s(literal -1 binary64)) #s(literal -1/4 binary64))
✓	cost-diff	0	(sqrt.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (*.f64 x x))) #s(literal -1 binary64)) #s(literal -1/4 binary64)))
✓	cost-diff	0	(neg.f64 x)
✓	cost-diff	0	(/.f64 p (neg.f64 x))
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
✓	cost-diff	0	(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
✓	cost-diff	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))
✓	cost-diff	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)))

Rules

2 560×	`accelerator-lowering-fma.f32`
2 560×	`accelerator-lowering-fma.f64`
1 968×	`-lowering-.f32`
1 968×	`-lowering-.f64`
1 380×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	255
1	67	253
2	124	253
3	210	253
4	345	253
5	376	253
6	463	253
7	618	253
8	765	253
9	954	253
10	1195	253
11	1415	253
12	2170	253
13	2899	253
14	3265	253
15	3494	253
16	3710	253
17	3808	253
18	3824	253
19	3989	253
20	4533	253
21	4803	253
22	4803	253
23	4803	253
24	5126	253
25	6150	253
26	6392	253
27	7087	253
28	7179	253
29	7311	253
30	7626	253
31	7694	253
0	8074	229

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
(+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2)
(/ x (+ (* 2 (/ (* p p) x)) x))
x
(+ (* 2 (/ (* p p) x)) x)
2
(/ (* p p) x)
(* p p)
p
1/2
1
(/ p (neg x))
p
(neg x)
x
(sqrt (* (+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1) -1/4))
(* (+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1) -1/4)
(+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1)
x
(/ x (+ (* 4 (* p p)) (* x x)))
(+ (* 4 (* p p)) (* x x))
4
(* p p)
p
(* x x)
-1
-1/4
(sqrt (/ (* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2) -2))
(/ (* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2) -2)
(* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2)
(+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1)
(/ 1 (+ (* 4 (* p p)) (* x x)))
1
(+ (* 4 (* p p)) (* x x))
4
(* p p)
p
(* x x)
x
-1
1/2
-2

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

localize257.0ms (2.2%)

Memory

-6.1MiB live, 192.0MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))
✓	accuracy	82.1%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)))
✓	accuracy	53.4%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) (*.f64 x x) #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	94.4%	(/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x)))
✓	accuracy	82.1%	(sqrt.f64 (.f64 (fma.f64 x (/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (*.f64 x x))) #s(literal -1 binary64)) #s(literal -1/4 binary64)))
✓	accuracy	53.3%	(fma.f64 x (/.f64 x (fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))) #s(literal -1 binary64))
✓	accuracy	100.0%	(/.f64 p (neg.f64 x))
✓	accuracy	100.0%	(neg.f64 x)
✓	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	100.0%	(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
✓	accuracy	95.9%	(/.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x))
✓	accuracy	91.8%	(/.f64 (*.f64 p p) x)

Samples

61.0ms	132×	0	valid
59.0ms	59×	2	valid
32.0ms	22×	3	valid
15.0ms	38×	1	valid
4.0ms	4×	4	valid
1.0ms	1×	5	exit

Compiler

Compiled 243 to 35 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 107.0ms

ival-div: 40.0ms (37.4% of total)

ival-add: 26.0ms (24.3% of total)

ival-mult: 21.0ms (19.6% of total)

ival-sqrt: 9.0ms (8.4% of total)

adjust: 8.0ms (7.5% of total)

exact: 1.0ms (0.9% of total)

ival-neg: 1.0ms (0.9% of total)

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

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

series39.0ms (0.3%)

Memory

-3.9MiB live, 33.3MiB allocated

Counts

17 → 384

Calls

Call 1

Inputs
#<alt (sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))>
#<alt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2)>
#<alt (/ x (+ (* 2 (/ (* p p) x)) x))>
#<alt (+ (* 2 (/ (* p p) x)) x)>
#<alt (/ p (neg x))>
#<alt (neg x)>
#<alt (sqrt (* (+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1) -1/4))>
#<alt (* (+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1) -1/4)>
#<alt (+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1)>
#<alt (/ x (+ (* 4 (* p p)) (* x x)))>
#<alt (/ (* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2) -2)>
#<alt (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1)>
#<alt (sqrt (/ (* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2) -2))>
#<alt (* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2)>
#<alt (/ (* p p) x)>
#<alt (* p p)>
#<alt (/ 1 (+ (* 4 (* p p)) (* x x)))>

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

Calls

96 calls:

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

rewrite814.0ms (7.1%)

Memory

-169.7MiB live, 1 010.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 610×	`accelerator-lowering-fma.f32`
9 610×	`accelerator-lowering-fma.f64`
5 518×	`-lowering-.f32`
5 518×	`-lowering-.f64`
3 486×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	206
1	176	204
2	1290	204
0	8894	182

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 803

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2))
(+ (* (/ x (+ (* 2 (/ (* p p) x)) x)) 1/2) 1/2)
(/ x (+ (* 2 (/ (* p p) x)) x))
(+ (* 2 (/ (* p p) x)) x)
(/ p (neg x))
(neg x)
(sqrt (* (+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1) -1/4))
(* (+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1) -1/4)
(+ (* x (/ x (+ (* 4 (* p p)) (* x x)))) -1)
(/ x (+ (* 4 (* p p)) (* x x)))
(/ (* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2) -2)
(+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1)
(sqrt (/ (* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2) -2))
(* (+ (* (/ 1 (+ (* 4 (* p p)) (* x x))) (* x x)) -1) 1/2)
(/ (* p p) x)
(* p p)
(/ 1 (+ (* 4 (* p p)) (* x x)))

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

simplify385.0ms (3.3%)

Memory

18.1MiB live, 923.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 608×	`accelerator-lowering-fma.f32`
7 608×	`accelerator-lowering-fma.f64`
6 934×	`-lowering-.f32`
6 934×	`-lowering-.f64`
2 472×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	668	7525
1	2105	7280
2	6908	7272
0	8267	6792

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

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

Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (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)))))))
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (.f64 (.f64 p p) (.f64 p p))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 p p) (.f64 p p)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (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)))))))
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#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
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1
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(fma.f64 (.f64 x x) (/.f64 #s(literal 1/8 binary64) (.f64 p p)) #s(literal -1/2 binary64))
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 p p) (.f64 p p))) #s(literal -1/32 binary64) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/8 binary64) (.f64 p p)) #s(literal -1/2 binary64)))
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 p p) (.f64 p p))) #s(literal -1/32 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal 1/128 binary64) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/8 binary64) (.f64 p p)) #s(literal -1/2 binary64))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(fma.f64 (.f64 x x) (/.f64 #s(literal 1/8 binary64) (.f64 p p)) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ (* -1/32 (/ (pow x 2) (pow p 4))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (.f64 (.f64 p p) (.f64 p p))) #s(literal -1/32 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 p p))) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/128 (/ (pow x 2) (pow p 6))) (* 1/32 (/ 1 (pow p 4))))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 6 binary64))) #s(literal 1/128 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 (.f64 p p) (.f64 p p)))) (/.f64 #s(literal 1/8 binary64) (*.f64 p p))) #s(literal -1/2 binary64))
(* -2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (*.f64 x x))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 8 binary64)) (.f64 x x))) (*.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/.f64 (fma.f64 #s(literal 8 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 x x) (.f64 x x))) #s(literal -32 binary64) (fma.f64 p (.f64 p #s(literal -2 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) (/.f64 (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal 128 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (.f64 x x))
(* -2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (*.f64 x x))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 8 binary64)) (.f64 x x))) (*.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/.f64 (fma.f64 #s(literal 8 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 x x) (.f64 x x))) #s(literal -32 binary64) (fma.f64 p (.f64 p #s(literal -2 binary64)) (fma.f64 #s(literal 8 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) (/.f64 (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal 128 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (.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)
(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)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(+ (* -4 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))
(fma.f64 #s(literal -4 binary64) (/.f64 (.f64 p p) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(+ (* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(fma.f64 (.f64 p p) (fma.f64 p (.f64 p (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(+ (* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 8))) (* 16 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 #s(literal -64 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 8 binary64))) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/ 1/4 (pow p 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 p p))
(/ (+ 1/4 (* -1/16 (/ (pow x 2) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/16 binary64) #s(literal 1/4 binary64)) (*.f64 p p))
(/ (- (+ 1/4 (* 1/64 (/ (pow x 4) (pow p 4)))) (* 1/16 (/ (pow x 2) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 p p) (.f64 p p))) (fma.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/16 binary64) #s(literal 1/4 binary64))) (*.f64 p p))
(/ (- (+ 1/4 (* -1/256 (/ (pow x 6) (pow p 6)))) (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/16 (/ (pow x 2) (pow p 2))))) (pow p 2))
(/.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal -1/256 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 1/4 binary64)))) (*.f64 p p))
(/ 1/4 (pow p 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 p p))
(/ (+ 1/4 (* -1/16 (/ (pow x 2) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/16 binary64) #s(literal 1/4 binary64)) (*.f64 p p))
(/ (- (+ 1/4 (* 1/64 (/ (pow x 4) (pow p 4)))) (* 1/16 (/ (pow x 2) (pow p 2)))) (pow p 2))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 p p) (.f64 p p))) (fma.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/16 binary64) #s(literal 1/4 binary64))) (*.f64 p p))
(/ (- (+ 1/4 (* -1/256 (/ (pow x 6) (pow p 6)))) (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/16 (/ (pow x 2) (pow p 2))))) (pow p 2))
(/.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal -1/256 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 1/4 binary64)))) (*.f64 p p))
(/ 1/4 (pow p 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 p p))
(+ (* -1/16 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (.f64 p p) (.f64 p p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 p p)))
(+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow p 6))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (/.f64 #s(literal 1/64 binary64) (pow.f64 p #s(literal 6 binary64)))) (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 p p) (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) (.f64 p p)))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/256 (/ (pow x 2) (pow p 8))) (* 1/64 (/ 1 (pow p 6))))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 8 binary64))) #s(literal -1/256 binary64) (/.f64 #s(literal 1/64 binary64) (pow.f64 p #s(literal 6 binary64)))) (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 p p) (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) (*.f64 p p)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* -4 (/ (pow p 2) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal -4 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(/ (- (+ 1 (* 16 (/ (pow p 4) (pow x 4)))) (* 4 (/ (pow p 2) (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) #s(literal 16 binary64) (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (* -64 (/ (pow p 6) (pow x 6)))) (+ (* -16 (/ (pow p 4) (pow x 4))) (* 4 (/ (pow p 2) (pow x 2))))) (pow x 2))
(/.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) #s(literal 1 binary64)) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) #s(literal 16 binary64) (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 x x))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* -4 (/ (pow p 2) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal -4 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))
(/ (- (+ 1 (* 16 (/ (pow p 4) (pow x 4)))) (* 4 (/ (pow p 2) (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) #s(literal 16 binary64) (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (* -64 (/ (pow p 6) (pow x 6)))) (+ (* -16 (/ (pow p 4) (pow x 4))) (* 4 (/ (pow p 2) (pow x 2))))) (pow x 2))
(/.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -64 binary64) #s(literal 1 binary64)) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) #s(literal 16 binary64) (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 x x))) (.f64 x x))

eval171.0ms (1.5%)

Memory: 15.5MiB live, 432.2MiB allocated
Compiler: Compiled 38 476 to 3 429 computations (91.1% saved)

prune157.0ms (1.4%)

Memory

-1.0MiB live, 321.4MiB allocated

Pruning

17 alts after pruning (10 fresh and 7 done)

	Pruned	Kept	Total
New	1 232	3	1 235
Fresh	1	7	8
Picked	2	3	5
Done	0	4	4
Total	1 235	17	1 252

Accuracy

99.9%

Counts

1 252 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.4%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
✓	27.8%	(/.f64 p (neg.f64 x))
	7.1%	(/.f64 p x)
✓	8.4%	(sqrt.f64 (fma.f64 (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
	16.2%	(sqrt.f64 (fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 x x))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
✓	74.6%	(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)))
✓	79.2%	(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)))
	13.1%	(sqrt.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x)))) (.f64 x x) #s(literal 1/4 binary64)))
✓	51.8%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
	14.0%	(sqrt.f64 (/.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)))
	13.9%	(sqrt.f64 (/.f64 (fma.f64 #s(literal -4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 x x)) (.f64 p p)) (.f64 x x)))
	55.2%	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	27.6%	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (.f64 p (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1/2 binary64))))
	55.8%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 (/.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 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (.f64 (/.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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 (/.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 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 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)))))))))
✓	55.7%	(sqrt.f64 #s(literal 1/2 binary64))
	16.3%	(sqrt.f64 #s(literal 1/4 binary64))
✓	35.0%	#s(literal 1 binary64)

Compiler

Compiled 945 to 309 computations (67.3% saved)

regimes88.0ms (0.8%)

Memory

22.7MiB live, 165.3MiB allocated

Counts

35 → 2

Calls

Call 1

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

Outputs

(/.f64 p (neg.f64 x))

(sqrt.f64 (/.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)))))))))

Calls

7 calls:

22.0ms	x
13.0ms	(.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))))))
13.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
12.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
10.0ms	p

Results

Accuracy	Segments	Branch
79.2%	1	`p`
84.7%	4	`x`
99.8%	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)))))))`
99.8%	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))))))`
99.8%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.8%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
79.2%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes31.0ms (0.3%)

Memory

-18.2MiB live, 57.8MiB allocated

Counts

28 → 2

Calls

Call 1

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

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

4 calls:

9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
7.0ms	(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)))))))
7.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
6.0ms	(.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
99.7%	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)))))))`
99.7%	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))))))`
99.7%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.7%	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)

regimes25.0ms (0.2%)

Memory

20.5MiB live, 58.2MiB allocated

Counts

23 → 2

Calls

Call 1

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

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:

7.0ms	(.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))))))
6.0ms	(/.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)))))
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)))))))

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)

regimes22.0ms (0.2%)

Memory

-3.4MiB live, 39.2MiB allocated

Counts

19 → 3

Calls

Call 1

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

Outputs

(/.f64 p (neg.f64 x))

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

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

Calls

4 calls:

7.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
5.0ms	(/.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	(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
99.4%	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)))))))`
99.4%	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))))))`
99.4%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.4%	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)

regimes19.0ms (0.2%)

Memory

0.8MiB live, 39.2MiB allocated

Counts

17 → 3

Calls

Call 1

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

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:

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

Results

Accuracy	Segments	Branch
99.4%	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)))))))`
99.4%	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))))))`
99.4%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.4%	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)

regimes12.0ms (0.1%)

Memory

-17.7MiB live, 21.3MiB allocated

Counts

8 → 3

Calls

Call 1

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

3.0ms	(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))))
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
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)

regimes10.0ms (0.1%)

Memory

30.4MiB live, 30.4MiB allocated

Counts

7 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/4 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))
(/.f64 p x)
(/.f64 p (neg.f64 x))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(literal -1 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
98.7%	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)))))))`
98.7%	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))))))`
98.7%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.7%	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 (0.1%)

Memory

-8.4MiB live, 30.0MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

Calls

7 calls:

3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
2.0ms	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))))

Results

Accuracy	Segments	Branch
69.2%	2	`p`
69.2%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
60.5%	2	`x`
77.5%	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)))))))`
77.5%	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))))))`
77.5%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
77.5%	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)

regimes7.0ms (0.1%)

Memory

15.3MiB live, 15.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs
(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
74.6%	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)))))))`
74.6%	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))))))`
74.6%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
74.6%	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)

regimes12.0ms (0.1%)

Memory

-13.9MiB live, 28.0MiB allocated

Accuracy

Total -12.2b remaining (-29.4%)

Threshold costs -12.2b (-29.4%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/4 binary64))

Outputs
#s(literal 1 binary64)

Calls

7 calls:

3.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	x
1.0ms	p
1.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
1.0ms	(.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
35.0%	1	`x`
35.0%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
35.0%	1	`p`
35.0%	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)))))))`
35.0%	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))))))`
35.0%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
35.0%	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)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999959828	-0.9999999933427183

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	-0.9999999999959828	-0.9999999933427183

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	-0.9999999933427183	-1.6697919389601797e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0031618130617433256	0.9965799057555172
0.0ms	-0.9999999933427183	-1.6697919389601797e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0031618130617433256	0.9965799057555172
0.0ms	-0.9999999933427183	-1.6697919389601797e-6

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	0.0031618130617433256	0.9965799057555172
0.0ms	-0.9999999933427183	-1.6697919389601797e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0031618130617433256	0.9965799057555172
0.0ms	-0.9999999933427183	-1.6697919389601797e-6

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	0.0031618130617433256	0.9965799057555172
0.0ms	-1.0	-0.9999999999959828

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch11.0ms (0.1%)

Memory

-22.8MiB live, 15.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.0031618130617433256	0.9965799057555172

Samples

6.0ms

128×

valid

Compiler

Compiled 94 to 91 computations (3.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (57.4% of total)

ival-add: 1.0ms (28.7% of total)

ival-mult: 1.0ms (28.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify11.0ms (0.1%)

Memory

27.4MiB live, 27.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
10×	`+-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	66	343
1	77	343
2	83	343
3	88	343
4	91	343
5	92	343

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 -2251799802426249/2251799813685248 binary64)) (/.f64 p (neg.f64 x)) (sqrt.f64 (/.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))))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -2251799802426249/2251799813685248 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 -1/2 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 -1/2 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 5764607523034235/1152921504606846976 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (.f64 p (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #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 -1/2 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 5764607523034235/1152921504606846976 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 -1/2 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 5764607523034235/1152921504606846976 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 -1/2 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 5764607523034235/1152921504606846976 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)) (/.f64 p x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5764607523034235/1152921504606846976 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 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -2251799802426249/2251799813685248 binary64)) (/.f64 p (neg.f64 x)) (sqrt.f64 (/.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))))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -2251799802426249/2251799813685248 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (/.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))))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -2251799802426249/2251799813685248 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 -2251799802426249/2251799813685248 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 -1/2 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 -1/2 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 -1/2 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 5764607523034235/1152921504606846976 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (.f64 p (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #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 -1/2 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 5764607523034235/1152921504606846976 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 p (.f64 p (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #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 -1/2 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 5764607523034235/1152921504606846976 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 -1/2 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 5764607523034235/1152921504606846976 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 -1/2 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 5764607523034235/1152921504606846976 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 -1/2 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 5764607523034235/1152921504606846976 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 -1/2 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 5764607523034235/1152921504606846976 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 -1/2 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 5764607523034235/1152921504606846976 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)) (/.f64 p x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5764607523034235/1152921504606846976 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)) (/.f64 p x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 5764607523034235/1152921504606846976 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 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 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness952.0ms (8.3%)

Memory

-34.1MiB live, 925.7MiB allocated

Rules

11 174×	`accelerator-lowering-fma.f32`
11 174×	`accelerator-lowering-fma.f64`
10 196×	`accelerator-lowering-fma.f32`
10 196×	`accelerator-lowering-fma.f64`
10 048×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	209
1	186	209
2	1314	209
0	8293	187
0	14	78
1	68	78
2	492	78
3	6948	78
0	8473	70
0	913	6621
1	2823	6485
0	8450	6104
0	852	7631
1	2657	7336
0	8501	6926
0	472	2993
1	1444	2876
2	4985	2834
0	8534	2634
0	34	235
1	205	215
2	1620	214
0	8895	194

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

Compiler

Compiled 644 to 275 computations (57.3% saved)

preprocess138.0ms (1.2%)

Memory: -10.6MiB live, 148.0MiB allocated
Compiler: Compiled 838 to 226 computations (73% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze451.0ms (3.9%)

sample2.0s (17.6%)

preprocess64.0ms (0.6%)

explain257.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

localize102.0ms (0.9%)

series22.0ms (0.2%)

rewrite346.0ms (3%)

simplify503.0ms (4.4%)

eval67.0ms (0.6%)

prune73.0ms (0.6%)

simplify311.0ms (2.7%)

localize454.0ms (3.9%)

series54.0ms (0.5%)

rewrite400.0ms (3.5%)

simplify471.0ms (4.1%)

eval262.0ms (2.3%)

prune220.0ms (1.9%)

simplify215.0ms (1.9%)

localize162.0ms (1.4%)

series41.0ms (0.4%)

rewrite405.0ms (3.5%)

simplify480.0ms (4.2%)

eval264.0ms (2.3%)

prune284.0ms (2.5%)

simplify405.0ms (3.5%)

localize257.0ms (2.2%)

series39.0ms (0.3%)

rewrite814.0ms (7.1%)

simplify385.0ms (3.3%)

eval171.0ms (1.5%)

prune157.0ms (1.4%)

regimes88.0ms (0.8%)

regimes31.0ms (0.3%)

regimes25.0ms (0.2%)

regimes22.0ms (0.2%)

regimes19.0ms (0.2%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes16.0ms (0.1%)

regimes7.0ms (0.1%)

regimes12.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch11.0ms (0.1%)

simplify11.0ms (0.1%)

soundness952.0ms (8.3%)

preprocess138.0ms (1.2%)

end0.0ms (0%)

Profiling