Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze502.0ms (5.8%)

Memory

-42.5MiB live, 738.8MiB 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)

sample2.2s (25.6%)

Memory

67.0MiB live, 3 204.6MiB allocated

Samples

1.1s	6 183×	0	valid
350.0ms	1 027×	2	valid
160.0ms	658×	1	valid
149.0ms	388×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

const: 412.0ms (29.4% of total)

ival-mult: 302.0ms (21.6% of total)

ival-sqrt: 202.0ms (14.4% of total)

ival-add: 137.0ms (9.8% of total)

ival-div: 127.0ms (9.1% of total)

adjust: 100.0ms (7.1% of total)

ival-fabs: 51.0ms (3.6% of total)

ival-<: 44.0ms (3.1% of total)

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

exact: 10.0ms (0.7% of total)

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

Bogosity

explain193.0ms (2.2%)

Memory

9.2MiB live, 326.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
66	0	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
25	0	-	1	(-7.724089295792843e-28 -3.0893618632483993e+134)	`(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)))))))`
22	1	(-7.724089295792843e-28 -3.0893618632483993e+134)	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
0	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	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	0	-	0	-	`#s(literal 4 binary64)`
0	0	-	0	-	`(*.f64 x x)`
0	0	-	0	-	`p`
0	0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	0	-	0	-	`#s(literal 1/2 binary64)`
0	0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	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
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	66
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	66
`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	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))))))`	underflow	25
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	25
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	15
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	57
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	23	0

Confusion

	Predicted +	Predicted -
+	47	0
-	66	143

Precision

0.415929203539823

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	47	0	0
-	66	0	143

Precision?

0.415929203539823

Recall?

1.0

Freqs

test

number	freq
0	143
1	113

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms	416×	0	valid
14.0ms	54×	2	valid
6.0ms	18×	3	valid
4.0ms	24×	1	valid

Compiler

Compiled 211 to 46 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 13.0ms (33.8% of total)

ival-sqrt: 9.0ms (23.4% of total)

ival-add: 7.0ms (18.2% of total)

ival-div: 5.0ms (13% of total)

adjust: 3.0ms (7.8% of total)

exact: 1.0ms (2.6% of total)

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

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

preprocess66.0ms (0.8%)

Memory

-1.2MiB live, 35.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs p)

Compiler

Compiled 19 to 14 computations (26.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	83.0%	(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)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0.1%)

Memory

7.6MiB live, 7.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize47.0ms (0.6%)

Memory

-4.8MiB live, 72.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.015625	(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
accuracy	5.200579817672857	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	5.538440216682749	(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	15.318429498080807	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

21.0ms	208×	0	valid
8.0ms	27×	2	valid
3.0ms	9×	3	valid
2.0ms	12×	1	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 7.0ms (36.2% of total)

ival-sqrt: 5.0ms (25.9% of total)

ival-add: 3.0ms (15.5% of total)

ival-div: 2.0ms (10.3% of total)

adjust: 2.0ms (10.3% of total)

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

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

exact: 0.0ms (0% of total)

series25.0ms (0.3%)

Memory

-20.3MiB live, 30.1MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/4 (/ x p))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(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))))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
#s(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)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.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)))))) #<representation binary64>) () ())) ())
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#s(alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -2 p) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(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)))))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(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))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())

Calls

30 calls:

Time	Variable		Point	Expression
6.0ms	p	@	inf	(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
3.0ms	x	@	-inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
1.0ms	x	@	inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
1.0ms	x	@	-inf	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1.0ms	p	@	0	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

simplify329.0ms (3.8%)

Memory

14.0MiB live, 324.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 590×	`lower-fma.f64`
9 590×	`lower-fma.f32`
6 900×	`lower-*.f64`
6 900×	`lower-*.f32`
4 472×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	2482
1	1325	2377
2	4606	2304
0	8075	2141

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 118

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))))))))

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

rewrite311.0ms (3.6%)

Memory

4.0MiB live, 232.9MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	66
0	23	66
1	77	66
2	501	66
3	6967	66
0	8492	59

Stop Event

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

Counts

5 → 276

Calls

Call 1

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

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))
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(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 9 binary64))) (/.f64 #s(literal 1 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)))))))) (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)))))) (-.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 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.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 #s(literal 1 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 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.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 #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)))))))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.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 #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)))))))) (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)))
(pow.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))))))) #s(literal -1 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 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (/.f64 #s(literal 1 binary64) (-.f64 (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 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))))
(.f64 (+.f64 #s(literal -1 binary64) (neg.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)))))))) (/.f64 #s(literal 1 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)))))))))
(.f64 (+.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 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (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))))))) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 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 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (+.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 3 binary64)))) (fma.f64 (-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (-.f64 (-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)))))) (+.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (+.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (*.f64 p p)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p)))) (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (*.f64 #s(literal 4 binary64) p)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))))) (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 p p) #s(literal -4 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 #s(literal -16 binary64) (.f64 p (.f64 p (.f64 p p)))))) (sqrt.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))))) (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))
(.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (neg.f64 x) (.f64 p (.f64 #s(literal 4 binary64) p))))))
(.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))

eval135.0ms (1.6%)

Memory: 20.0MiB live, 148.6MiB allocated
Compiler: Compiled 15 630 to 1 955 computations (87.5% saved)

prune101.0ms (1.2%)

Memory

-12.6MiB live, 109.1MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	386	8	394
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	387	8	395

Accuracy

99.8%

Counts

395 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	83.0%	(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)))
▶	7.9%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))))
▶	54.3%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
	13.3%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
	40.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	58.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	54.0%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))))
	20.9%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x)))

Compiler

Compiled 260 to 148 computations (43.1% saved)

simplify684.0ms (7.9%)

Memory

35.7MiB live, 296.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))))
cost-diff	1984	(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)))
cost-diff	2240	(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))
cost-diff	4864	(pow.f64 p #s(literal 6 binary64))
cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p)
cost-diff	0	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	640	(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #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	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
cost-diff	0	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Rules

28 176×	`lower-fma.f32`
28 162×	`lower-fma.f64`
3 278×	`lower-*.f32`
3 254×	`lower-*.f64`
2 852×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	663
0	93	650
1	166	602
2	294	540
3	549	524
4	1115	476
5	1445	476
6	1562	476
7	1647	476
8	1759	476
9	1853	476
10	1866	476
11	1866	476
12	2455	471
13	3298	471
14	4674	471
15	5810	471
16	6814	471
17	6846	471
18	6894	471
19	6912	471
20	6912	471
21	7408	471
22	7632	471
23	7632	471
0	8445	458

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
x
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
(fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))
(.f64 p (.f64 #s(literal 4 binary64) p))
p
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
#s(literal 1/4 binary64)
(/.f64 x p)
x
p
#s(literal 1/2 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1/4 binary64)
(/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p)
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
p
(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))))
(.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))))
#s(literal 1/2 binary64)
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))
(/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
(fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (*.f64 x x)))))
p
(*.f64 p #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)))
(.f64 (.f64 p p) (*.f64 p p))
(*.f64 p p)
(/.f64 #s(literal -12 binary64) (*.f64 x x))
#s(literal -12 binary64)
(*.f64 x x)
x
(/.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))) (.f64 (.f64 x x) (*.f64 x x)))
(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)))
(.f64 #s(literal -12 binary64) (.f64 p p))
(*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))
(pow.f64 p #s(literal 6 binary64))
#s(literal 6 binary64)
#s(literal 32 binary64)
(.f64 (.f64 x x) (*.f64 x x))

Outputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))))
x
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
(sqrt.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))
(fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))
(fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))
(.f64 p (.f64 #s(literal 4 binary64) p))
(.f64 #s(literal 4 binary64) (.f64 p p))
p
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
#s(literal 1/4 binary64)
(/.f64 x p)
x
p
#s(literal 1/2 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1 binary64)))
#s(literal 1/4 binary64)
(/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p)
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
p
(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 (.f64 (.f64 p (.f64 p p)) (/.f64 p (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 20 binary64) (.f64 x x)) #s(literal -6 binary64)) (.f64 p (.f64 p #s(literal 2 binary64)))) (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))))
(.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 (.f64 (.f64 p (.f64 p p)) (/.f64 p (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 20 binary64) (.f64 x x)) #s(literal -6 binary64)) (.f64 p (.f64 p #s(literal 2 binary64)))) (*.f64 x x))))
#s(literal 1/2 binary64)
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 (.f64 (.f64 p (.f64 p p)) (/.f64 p (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 20 binary64) (.f64 x x)) #s(literal -6 binary64)) (.f64 p (.f64 p #s(literal 2 binary64)))) (*.f64 x x)))
(/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
(/.f64 (fma.f64 (.f64 (.f64 p (.f64 p p)) (/.f64 p (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 20 binary64) (.f64 x x)) #s(literal -6 binary64)) (.f64 p (.f64 p #s(literal 2 binary64)))) (*.f64 x x))
(fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (*.f64 x x)))))
(fma.f64 (.f64 (.f64 p (.f64 p p)) (/.f64 p (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 20 binary64) (.f64 x x)) #s(literal -6 binary64)) (.f64 p (.f64 p #s(literal 2 binary64))))
p
(*.f64 p #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))
(.f64 (.f64 (.f64 p (.f64 p p)) (/.f64 p (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 20 binary64) (*.f64 x x)) #s(literal -6 binary64)))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)))
(/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p #s(literal -12 binary64)))) (*.f64 x x))
(.f64 (.f64 p p) (*.f64 p p))
(.f64 p (.f64 p (*.f64 p p)))
(*.f64 p p)
(/.f64 #s(literal -12 binary64) (*.f64 x x))
#s(literal -12 binary64)
(*.f64 x x)
x
(/.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))) (.f64 (.f64 x x) (*.f64 x x)))
(.f64 (.f64 p p) (.f64 (.f64 (.f64 p (.f64 p p)) (/.f64 p (.f64 x (.f64 x (*.f64 x x))))) #s(literal 20 binary64)))
(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)))
(.f64 p (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p p))) #s(literal 20 binary64)))
(.f64 #s(literal -12 binary64) (.f64 p p))
(.f64 p (.f64 p #s(literal -12 binary64)))
(*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))
(.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p (.f64 p p)) #s(literal 32 binary64)))
(pow.f64 p #s(literal 6 binary64))
(.f64 p (.f64 (.f64 p p) (.f64 p (*.f64 p p))))
#s(literal 6 binary64)
#s(literal 32 binary64)
(.f64 (.f64 x x) (*.f64 x x))
(.f64 x (.f64 x (*.f64 x x)))

localize456.0ms (5.3%)

Memory

-24.3MiB live, 359.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	15.877332328284554	(/.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))) (.f64 (.f64 x x) (*.f64 x x)))
accuracy	18.335937500000004	(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))
accuracy	19.628906250000004	(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)))
accuracy	50.04734863530351	#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))
accuracy	0.015625	(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0.19140625	(/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p)
accuracy	0.41015625	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	29.444759099193163	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0	(/.f64 x p)
accuracy	0.20701848760924468	(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
accuracy	5.538440216682749	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
accuracy	29.283694284489084	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
accuracy	5.538440216682749	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	27.20066917309791	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.01171875	(fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))
accuracy	5.1958640970505465	(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	5.538440216682749	(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	15.318429498080807	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))

Samples

94.0ms	208×	0	valid
57.0ms	26×	2	valid
24.0ms	10×	3	valid
8.0ms	12×	1	valid

Compiler

Compiled 502 to 53 computations (89.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-mult: 30.0ms (38.3% of total)

ival-div: 14.0ms (17.9% of total)

ival-add: 12.0ms (15.3% of total)

ival-sqrt: 11.0ms (14.1% of total)

adjust: 6.0ms (7.7% of total)

ival-pow: 3.0ms (3.8% of total)

exact: 1.0ms (1.3% of total)

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

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

series118.0ms (1.4%)

Memory

-1.6MiB live, 109.0MiB allocated

Counts

21 → 468

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (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)) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (patch (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x p) (patch (/.f64 x p) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))) (patch (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (patch (/.f64 (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 p #s(literal 6 binary64)) (patch (pow.f64 p #s(literal 6 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x)))) (patch (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())
#s(alt (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))) (patch (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))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))))) #<representation binary64>) () ())
#s(alt (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (patch (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #<representation binary64>) () ())
#s(alt #s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))) (patch #s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.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))) (.f64 (.f64 x x) (.f64 x x))) (patch (/.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))) (.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())

Outputs
#s(alt (sqrt 1/2) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(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))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(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)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(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)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (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))) #<representation binary64>) () ())) ())
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Calls

117 calls:

Time	Variable		Point	Expression
21.0ms	x	@	inf	(* x (sqrt 1/2))
2.0ms	p	@	0	(+ (* 1/4 (/ x p)) 1/2)
1.0ms	x	@	0	(+ (* 1/2 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (/ (+ (* (* (* p p) (* p p)) (* -12 (* p p))) (* (pow p 6) 32)) (* (* x x) (* x x))))
1.0ms	x	@	0	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
1.0ms	p	@	0	(+ (* 1/2 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (/ (+ (* (* (* p p) (* p p)) (* -12 (* p p))) (* (pow p 6) 32)) (* (* x x) (* x x))))

simplify357.0ms (4.1%)

Memory

-38.0MiB live, 422.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 026×	`lower-fma.f64`
8 026×	`lower-fma.f32`
6 882×	`lower-*.f64`
6 882×	`lower-*.f32`
2 722×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	654	8696
1	1990	8250
2	6776	8140
0	8099	7649

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 466

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)))))
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(* -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
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(sqrt 1/2)
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(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
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(+ (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
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1
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(/ (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
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1/2
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1/2
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(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
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(* 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
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-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
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(* 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))
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(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(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)))
1/2
(+ 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)))
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(sqrt 1/2)
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(* 20 (pow p 6))
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(+ (* 4 (pow p 2)) (pow x 2))
(pow x 2)
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(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
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(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(pow x 2)
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(+ (* 4 (pow p 2)) (pow x 2))
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1
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(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
2
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(* 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)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(* 20 (/ (pow p 6) (pow x 4)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))

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 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 p p) (.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/128 binary64) (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
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 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)))) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (fma.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)))))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
(* -1 (/ p x))
(/.f64 p (neg.f64 x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) p) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 p (.f64 (.f64 x x) (.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #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 (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 p (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #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) (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.f64 #s(literal -256 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p)))))) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.f64 p p)) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #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 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 #s(literal -69/16 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ 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 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (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 p (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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 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)))))
(+.f64 (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 (+.f64 (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64)) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 p p (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) #s(literal 1/4 binary64)) (.f64 x x))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 x x)) (fma.f64 p p (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #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) (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 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))) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 x x))) (fma.f64 p p (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (.f64 (.f64 x x) (.f64 x x))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 p (.f64 p (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -10 binary64) (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(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)))
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(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(* 20 (/ (pow p 6) (pow x 4)))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(* 20 (/ (pow p 6) (pow x 4)))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(* 20 (/ (pow p 6) (pow x 4)))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(* 20 (/ (pow p 6) (pow x 4)))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ (* -12 (pow p 6)) (* 32 (pow p 6))) (pow x 4))
(/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 20 binary64)) (.f64 (.f64 x x) (.f64 x x)))

rewrite442.0ms (5.1%)

Memory

12.9MiB live, 608.4MiB allocated

Rules

5 946×	`lower-*.f32`
5 922×	`lower-*.f64`
4 252×	`lower-/.f32`
4 240×	`lower-/.f64`
3 962×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	419
0	93	383
1	342	359
2	2299	344
0	9314	339

Stop Event

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

Counts

21 → 636

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(/.f64 x p)
(fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p)
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(pow.f64 p #s(literal 6 binary64))
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))
(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)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))))
(fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))
#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))
(/.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))) (.f64 (.f64 x x) (*.f64 x x)))

Outputs
(exp.f64 (.f64 (log.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))) #s(literal 1/2 binary64)))
(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)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.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)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64))))) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64))) (sqrt.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal -1/4 binary64))) (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))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal -1/4 binary64)))) (sqrt.f64 (neg.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)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))))))) (sqrt.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))))) #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))))))
(pow.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)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)) (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))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64))))))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal -1/2 binary64)))))
(.f64 (pow.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)) #s(literal 1/4 binary64)) (pow.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)) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))))
(+.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) (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))) (/.f64 #s(literal 1/4 binary64) (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))))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 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))
(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))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.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)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64))))) #s(literal -1/4 binary64))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))))) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) (.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64)))))) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 p #s(literal 4 binary64))))) #s(literal -1/4 binary64)) (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)))
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eval177.0ms (2.1%)

Memory: 10.2MiB live, 354.5MiB allocated
Compiler: Compiled 63 870 to 4 402 computations (93.1% saved)

prune133.0ms (1.5%)

Memory

-21.6MiB live, 269.9MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 099	3	1 102
Fresh	3	0	3
Picked	2	3	5
Done	0	0	0
Total	1 104	6	1 110

Accuracy

100.0%

Counts

1 110 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	83.0%	(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)))
✓	54.3%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
✓	58.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	21.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
▶	40.0%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))
▶	53.9%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p)))

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify129.0ms (1.5%)

Memory

42.5MiB live, 197.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

5 012×	`lower-fma.f32`
5 010×	`lower-fma.f64`
4 448×	`lower-*.f32`
4 446×	`lower-*.f64`
1 422×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	136
0	45	138
1	91	138
2	122	138
3	148	138
4	172	135
5	191	135
6	244	132
7	313	132
8	356	132
9	603	132
10	1489	132
11	4518	132
12	5682	132
0	8021	126

Stop Event

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

Calls

Call 1

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

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

localize92.0ms (1.1%)

Memory

-1.5MiB live, 157.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 p (neg.f64 x))
accuracy	0	(neg.f64 x)
accuracy	50.464453534935195	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
accuracy	38.40814974417546	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))
accuracy	0	#s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))
accuracy	0.30859375	(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p)
accuracy	0.41796875	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p))
accuracy	29.444759099193163	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p)))

Samples

43.0ms	208×	0	valid
14.0ms	26×	2	valid
9.0ms	10×	3	valid
4.0ms	12×	1	valid

Compiler

Compiled 102 to 35 computations (65.7% saved)

Precisions

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

ival-mult: 17.0ms (30.8% of total)

ival-div: 12.0ms (21.7% of total)

ival-sqrt: 12.0ms (21.7% of total)

ival-add: 9.0ms (16.3% of total)

adjust: 4.0ms (7.2% of total)

ival-neg: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.2%)

Memory

-13.2MiB live, 24.8MiB allocated

Counts

8 → 180

Calls

Call 1

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

Outputs
#s(alt (sqrt 1/2) (taylor 0 x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p))) (taylor 0 x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p))))) (taylor 0 x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(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)))))))) (taylor 0 x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(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)))) (taylor inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(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))))) (taylor inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x)) (taylor -inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(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)) (taylor -inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(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)) (taylor -inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
#s(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)) (taylor -inf x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ p x)) (taylor -inf x) (#s(alt (/.f64 p (neg.f64 x)) (patch (/.f64 p (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor -inf x) (#s(alt (/.f64 p (neg.f64 x)) (patch (/.f64 p (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())

Calls

45 calls:

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

simplify260.0ms (3%)

Memory

17.4MiB live, 370.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 652×	`lower-fma.f64`
7 652×	`lower-fma.f32`
7 086×	`lower-*.f64`
7 086×	`lower-*.f32`
3 548×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	362	3107
1	1154	2948
2	4369	2831
0	8059	2652

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

rewrite225.0ms (2.6%)

Memory

-20.0MiB live, 341.7MiB allocated

Rules

7 396×	`lower-fma.f32`
7 394×	`lower-fma.f64`
4 180×	`lower-*.f32`
4 178×	`lower-*.f64`
3 850×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	123
0	45	123
1	206	123
2	1308	123
0	8509	115

Stop Event

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

Counts

8 → 121

Calls

Call 1

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

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

eval35.0ms (0.4%)

Memory: -4.0MiB live, 71.4MiB allocated
Compiler: Compiled 5 417 to 586 computations (89.2% saved)

prune32.0ms (0.4%)

Memory

36.2MiB live, 73.0MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	300	7	307

Accuracy

100.0%

Counts

307 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	83.0%	(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)))
✓	54.3%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
✓	58.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	21.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
✓	40.0%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))
✓	53.9%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p)))
▶	58.0%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) p)))

Compiler

Compiled 67 to 43 computations (35.8% saved)

simplify58.0ms (0.7%)

Memory

-36.7MiB live, 50.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

300×	`lower-*.f32`
298×	`lower-*.f64`
136×	`associate-l`
130×	`lower-fma.f64`
130×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	108
0	33	108
1	64	108
2	87	108
3	106	108
4	117	106
5	125	106
6	127	106
7	133	106
8	133	106
9	189	106
10	205	106
11	321	106
12	330	106
13	353	106
14	370	106
15	371	106
16	375	106
17	379	106
18	382	106
19	383	106
0	383	98

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize73.0ms (0.8%)

Memory

0.4MiB live, 121.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.30859375	(/.f64 #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) p)
accuracy	0.42578125	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
accuracy	29.444759099193163	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) p)))
accuracy	29.88056985365916	#s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))

Samples

35.0ms	208×	0	valid
9.0ms	27×	2	valid
4.0ms	9×	3	valid
3.0ms	12×	1	valid

Compiler

Compiled 56 to 27 computations (51.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 14.0ms (33.6% of total)

ival-add: 12.0ms (28.8% of total)

ival-div: 6.0ms (14.4% of total)

ival-sqrt: 6.0ms (14.4% of total)

adjust: 3.0ms (7.2% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

12.0MiB live, 12.1MiB allocated

Counts

5 → 108

Calls

Call 1

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

Outputs
#s(alt (sqrt 1/2) (taylor 0 x) (#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) p))) (patch #s(approx (sqrt ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) p))) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) (taylor 0 x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) (taylor 0 x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) (taylor 0 x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* x (sqrt 1/2))) (taylor inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/4 (sqrt 1/2)) (/ (* p (sqrt 1/2)) x))) (taylor inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/4 (sqrt 1/2)) (/ (* p (sqrt 1/2)) x))) (taylor inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/4 (sqrt 1/2)) (/ (* p (sqrt 1/2)) x))) (taylor inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* x (sqrt 1/2))) (taylor -inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (* p (sqrt 1/2)) x)) (* -1/4 (sqrt 1/2))))) (taylor -inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (* p (sqrt 1/2)) x)) (* -1/4 (sqrt 1/2))))) (taylor -inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (* p (sqrt 1/2)) x)) (* -1/4 (sqrt 1/2))))) (taylor -inf x) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (* x (sqrt 1/2))) (taylor 0 p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) (taylor 0 p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) (taylor 0 p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) (taylor 0 p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))) (taylor inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))) (taylor inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))) (taylor inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor -inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ (* -1 (sqrt 1/2)) (* -1/4 (/ (* x (sqrt 1/2)) p))))) (taylor -inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ (* -1 (sqrt 1/2)) (* -1/4 (/ (* x (sqrt 1/2)) p))))) (taylor -inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ (* -1 (sqrt 1/2)) (* -1/4 (/ (* x (sqrt 1/2)) p))))) (taylor -inf p) (#s(alt #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (patch #s(approx ( (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 1/2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #<representation binary64>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
0.0ms	p	@	inf	(* (sqrt 1/2) p)
0.0ms	p	@	0	(* (sqrt 1/2) p)
0.0ms	p	@	-inf	(* (sqrt 1/2) p)
0.0ms	x	@	-inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
0.0ms	x	@	inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

simplify284.0ms (3.3%)

Memory

24.7MiB live, 374.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 222×	`lower-fma.f64`
10 222×	`lower-fma.f32`
7 426×	`lower-*.f64`
7 426×	`lower-*.f32`
3 428×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	221	1675
1	713	1558
2	2783	1475
0	8185	1386

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite256.0ms (3%)

Memory

-22.3MiB live, 380.3MiB allocated

Rules

5 432×	`lower-fma.f64`
5 432×	`lower-fma.f32`
4 504×	`lower-*.f32`
4 502×	`lower-*.f64`
4 010×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	104
0	33	104
1	138	104
2	963	104
0	8648	96

Stop Event

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

Counts

5 → 27

Calls

Call 1

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

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

eval17.0ms (0.2%)

Memory: -7.4MiB live, 39.5MiB allocated
Compiler: Compiled 2 189 to 220 computations (89.9% saved)

prune16.0ms (0.2%)

Memory

0.9MiB live, 38.4MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	135	7	142

Accuracy

100.0%

Counts

142 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	83.0%	(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)))
✓	54.3%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
✓	58.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	21.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
✓	40.0%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))
✓	53.9%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p)))
✓	58.0%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) p)))

Compiler

Compiled 227 to 105 computations (53.7% saved)

regimes32.0ms (0.4%)

Memory

1.0MiB live, 77.8MiB allocated

Counts

13 → 2

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 #s(approx (* (sqrt 1/2) (+ (* x 1/4) p)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) p)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) #s(approx (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (sqrt 1/2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) p)) p)))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x)))
(sqrt.f64 (fma.f64 (/.f64 x (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 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (fma.f64 p (.f64 p #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (/.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))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x)))))

Outputs

#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))

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

Calls

7 calls:

6.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
5.0ms	p
4.0ms	x
4.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
4.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Results

Accuracy	Segments	Branch
83.0%	1	`p`
86.7%	2	`x`
100.0%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
100.0%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
100.0%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
83.0%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes13.0ms (0.1%)

Memory

30.7MiB live, 30.7MiB allocated

Counts

10 → 3

Calls

Call 1

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

Outputs

#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))

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

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

Calls

4 calls:

3.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
3.0ms	(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 #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%	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)))))))`
99.7%	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))))))`
99.7%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.7%	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)

regimes10.0ms (0.1%)

Memory

-20.3MiB live, 26.6MiB allocated

Counts

5 → 3

Calls

Call 1

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

Outputs

#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))

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

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

Results

Accuracy	Segments	Branch
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)

regimes15.0ms (0.2%)

Memory

-10.3MiB live, 28.5MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
72.7%	2	`p`
72.7%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
66.6%	2	`x`
80.9%	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)))))))`
80.9%	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))))))`
80.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
80.9%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes8.0ms (0.1%)

Memory

18.9MiB live, 18.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
40.0%	1	`x`
40.0%	1	`p`
40.0%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
40.0%	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)))))))`
40.0%	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))))))`
40.0%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
40.0%	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)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-2.3739628964313172e-5

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	0.25191374253336507	1.0
0.0ms	-1.0	-2.3739628964313172e-5

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	0.25191374253336507	1.0
0.0ms	-1.0	-2.3739628964313172e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch28.0ms (0.3%)

Memory

-25.0MiB live, 14.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
28.0ms	0.25191374253336507	1.0

Samples

24.0ms

80×

valid

Compiler

Compiled 77 to 64 computations (16.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-add: 21.0ms (92.9% of total)

ival-sqrt: 1.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Memory

20.5MiB live, 20.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	309
1	64	309
2	70	309
3	75	309
4	78	309
5	79	309

Stop Event

1×

saturated

Calls

Call 1

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

soundness552.0ms (6.4%)

Memory

-3.1MiB live, 478.1MiB allocated

Rules

9 590×	`lower-fma.f64`
9 590×	`lower-fma.f32`
8 026×	`lower-fma.f64`
8 026×	`lower-fma.f32`
6 900×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	654	8696
1	1990	8250
2	6776	8140
0	8099	7649
0	434	2482
1	1325	2377
2	4606	2304
0	8075	2141
0	14	66
0	23	66
1	77	66
2	501	66
3	6967	66
0	8492	59

Stop Event

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

Compiler

Compiled 711 to 289 computations (59.4% saved)

preprocess155.0ms (1.8%)

Memory: -9.8MiB live, 142.8MiB allocated
Compiler: Compiled 432 to 160 computations (63% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	29	108
0	33	108
1	64	108
2	87	108
3	106	108
4	117	106
5	125	106
6	127	106
7	133	106
8	133	106
9	189	106
10	205	106
11	321	106
12	330	106
13	353	106
14	370	106
15	371	106
16	375	106
17	379	106
18	382	106
19	383	106
0	383	98

Iter	Nodes	Cost
0	29	108
0	33	108
1	64	108
2	87	108
3	106	108
4	117	106
5	125	106
6	127	106
7	133	106
8	133	106
9	189	106
10	205	106
11	321	106
12	330	106
13	353	106
14	370	106
15	371	106
16	375	106
17	379	106
18	382	106
19	383	106
0	383	98

start0.0ms (0%)

analyze502.0ms (5.8%)

sample2.2s (25.6%)

explain193.0ms (2.2%)

preprocess66.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize47.0ms (0.6%)

series25.0ms (0.3%)

simplify329.0ms (3.8%)

rewrite311.0ms (3.6%)

eval135.0ms (1.6%)

prune101.0ms (1.2%)

simplify684.0ms (7.9%)

localize456.0ms (5.3%)

series118.0ms (1.4%)

simplify357.0ms (4.1%)

rewrite442.0ms (5.1%)

eval177.0ms (2.1%)

prune133.0ms (1.5%)

simplify129.0ms (1.5%)

localize92.0ms (1.1%)

series20.0ms (0.2%)

simplify260.0ms (3%)

rewrite225.0ms (2.6%)

eval35.0ms (0.4%)

prune32.0ms (0.4%)

simplify58.0ms (0.7%)

localize73.0ms (0.8%)

series6.0ms (0.1%)

simplify284.0ms (3.3%)

rewrite256.0ms (3%)

eval17.0ms (0.2%)

prune16.0ms (0.2%)

regimes32.0ms (0.4%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes15.0ms (0.2%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch28.0ms (0.3%)

simplify9.0ms (0.1%)

soundness552.0ms (6.4%)

preprocess155.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	29	108
0	33	108
1	64	108
2	87	108
3	106	108
4	117	106
5	125	106
6	127	106
7	133	106
8	133	106
9	189	106
10	205	106
11	321	106
12	330	106
13	353	106
14	370	106
15	371	106
16	375	106
17	379	106
18	382	106
19	383	106
0	383	98