Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze517.0ms (5.4%)

Memory

-19.3MiB live, 684.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.4s (24.7%)

Memory

65.2MiB live, 2 948.3MiB allocated

Samples

1.0s	6 255×	0	valid
370.0ms	418×	3	valid
268.0ms	996×	2	valid
171.0ms	587×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

const: 471.0ms (31.3% of total)

ival-mult: 336.0ms (22.3% of total)

ival-sqrt: 268.0ms (17.8% of total)

ival-add: 143.0ms (9.5% of total)

ival-div: 93.0ms (6.2% of total)

adjust: 79.0ms (5.3% of total)

ival-fabs: 52.0ms (3.5% of total)

ival-<: 38.0ms (2.5% of total)

ival-and: 11.0ms (0.7% of total)

exact: 10.0ms (0.7% of total)

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

Bogosity

explain231.0ms (2.4%)

Memory

-3.5MiB live, 461.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
56	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
36	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
25	-	2	(-3.273323260563821e-116 -5.144250708535805e+39)	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
0	-	0	-	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`p`
0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	-	0	-	`#s(literal 1/2 binary64)`
0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	oflow-rescue	56	0
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	56
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	56
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	36	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	uflow-rescue	23	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	7
↳	`(.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	30
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	30
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	10
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	63

Confusion

	Predicted +	Predicted -
+	59	0
-	56	141

Precision

0.5130434782608696

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	59	0	0
-	56	0	141

Precision?

0.5130434782608696

Recall?

1.0

Freqs

test

number	freq
0	141
1	115

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms	384×	0	valid
20.0ms	64×	2	valid
8.0ms	24×	3	valid
7.0ms	40×	1	valid

Compiler

Compiled 211 to 46 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 13.0ms (29% of total)

ival-sqrt: 11.0ms (24.5% of total)

ival-add: 10.0ms (22.3% of total)

ival-div: 5.0ms (11.1% of total)

adjust: 4.0ms (8.9% of total)

exact: 1.0ms (2.2% of total)

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

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

preprocess64.0ms (0.7%)

Memory

22.7MiB live, 58.2MiB 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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (*.f64 p #s(literal 4 binary64)) p (*.f64 x 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

2.3MiB live, 2.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.9%	(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)

simplify16.0ms (0.2%)

Memory

-22.5MiB live, 18.9MiB 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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x 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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x 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 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64))
#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 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
x
(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))
(.f64 (.f64 #s(literal 4 binary64) p) p)
(.f64 (.f64 p #s(literal 4 binary64)) p)
(*.f64 #s(literal 4 binary64) p)
(*.f64 p #s(literal 4 binary64))
#s(literal 4 binary64)
p
(*.f64 x x)

localize51.0ms (0.5%)

Memory

29.6MiB live, 135.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
accuracy	5.281224824933048	(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	8.020498944415017	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	13.037526786335997	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

21.0ms	192×	0	valid
8.0ms	20×	1	valid
8.0ms	32×	2	valid
4.0ms	12×	3	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sqrt: 13.0ms (45.3% of total)

ival-mult: 6.0ms (20.9% of total)

ival-add: 4.0ms (13.9% of total)

ival-div: 3.0ms (10.5% of total)

adjust: 2.0ms (7% of total)

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

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

exact: 0.0ms (0% of total)

series132.0ms (1.4%)

Memory

-30.2MiB live, 45.7MiB 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 (taylor 0 p) (#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 0 p) (#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 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#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 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#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 x 2) (taylor 0 p) (#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 (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#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 (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#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 (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#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 1/2) (sqrt 2)) (taylor 0 p) (#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 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#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 (+ (* (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)))))) (taylor 0 p) (#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 (+ (* (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)))))))) (taylor 0 p) (#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 2 (taylor 0 p) (#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>) () ())) ())
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#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 (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 (* -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 (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 (* 2 (/ (pow p 2) (pow x 2))) (taylor -inf x) (#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 (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2)) (taylor -inf x) (#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 (/ (+ (* 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)) (taylor -inf x) (#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 (/ (+ (* 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)) (taylor -inf x) (#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 (* -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

6 calls:

Time	Variable		Point	Expression
114.0ms	x	@	0	((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
4.0ms	x	@	-inf	((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
4.0ms	x	@	inf	((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
3.0ms	p	@	0	((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))
2.0ms	p	@	inf	((* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (* 4 p) p) (* x x)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (sqrt (+ (* (* 4 p) p) (* x x))))

simplify170.0ms (1.8%)

Memory

1.4MiB live, 228.1MiB 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	2486
1	1325	2377
2	4611	2304
0	8084	2141

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 118

Calls

Call 1

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

rewrite196.0ms (2.1%)

Memory

13.0MiB live, 209.1MiB 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
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(exp.f64 (.f64 (log.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/2 binary64)))

eval69.0ms (0.7%)

Memory: -11.8MiB live, 103.8MiB allocated
Compiler: Compiled 15 630 to 1 953 computations (87.5% saved)

prune109.0ms (1.1%)

Memory

-27.6MiB live, 85.9MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	378	16	394
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	379	16	395

Accuracy

99.8%

Counts

395 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.5%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
	78.9%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	75.5%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64)))
▶	47.8%	(sqrt.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
	40.4%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (fma.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x #s(literal 1 binary64))))))
▶	78.9%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))))
	74.4%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))))))
	18.7%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
	47.3%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
▶	29.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
	15.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))))
	14.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 #s(literal -12 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p)) (.f64 x x))))
	21.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))))
	38.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	51.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	27.5%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x)))

Compiler

Compiled 668 to 368 computations (44.9% saved)

simplify140.0ms (1.5%)

Memory

10.3MiB live, 171.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

7 660×	`lower-fma.f32`
7 650×	`lower-fma.f64`
2 726×	`lower-*.f32`
2 716×	`lower-*.f64`
1 262×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	419
0	72	417
1	127	409
2	190	409
3	326	409
4	649	409
5	1182	409
6	2828	409
7	4984	409
8	5915	409
9	7125	409
0	8141	407

Stop Event

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

Calls

Call 1

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

localize205.0ms (2.1%)

Memory

9.9MiB live, 324.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	8.05868178362641	(.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
accuracy	9.355972900848178	(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
accuracy	13.037526786335997	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
accuracy	32.946972740644	(fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64))
accuracy	0.01171875	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
accuracy	5.281224824933048	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64)))
accuracy	13.037526786335997	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
accuracy	15.572755734820111	(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64))
accuracy	0.04296875	(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
accuracy	0.2109375	(/.f64 p (*.f64 x x))
accuracy	5.281224824933048	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
accuracy	44.88573978118283	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
accuracy	5.281224824933048	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	31.270204101857086	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.0078125	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))
accuracy	5.281224824933048	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))))
accuracy	8.020498944415017	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
accuracy	13.037526786335997	(sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))

Samples

55.0ms	68×	2	valid
44.0ms	46×	1	valid
35.0ms	119×	0	valid
26.0ms	23×	3	valid

Compiler

Compiled 425 to 43 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

adjust: 34.0ms (27.1% of total)

ival-mult: 23.0ms (18.3% of total)

ival-div: 21.0ms (16.7% of total)

ival-sqrt: 21.0ms (16.7% of total)

ival-add: 21.0ms (16.7% of total)

ival-neg: 3.0ms (2.4% of total)

ival-sub: 2.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series93.0ms (1%)

Memory

-18.5MiB live, 56.6MiB allocated

Counts

21 → 480

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) (patch (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) (patch (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) (patch (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) (patch (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#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 (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#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 (+ (* (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)))))) (taylor 0 p) (#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 (+ (* (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)))))))) (taylor 0 p) (#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 1 (taylor 0 p) (#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 (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#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 (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#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 (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#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 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4))))) (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #<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 (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) (patch (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) (patch (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) #<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 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) (patch (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) #<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 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) (patch (sqrt.f64 (fma.f64 x x (.f64 (.f64 p #s(literal 4 binary64)) p))) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 2 (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ 2 (* -1/2 (/ (+ (* 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 4))) (* 2 (/ (pow p 2) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	x	@	0	((* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))))) (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (sqrt (+ (* x x) (* (* p 4) p))) (/ p (* x x)) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
9.0ms	x	@	-inf	((* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))))) (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (sqrt (+ (* x x) (* (* p 4) p))) (/ p (* x x)) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
7.0ms	x	@	inf	((* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))))) (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (sqrt (+ (* x x) (* (* p 4) p))) (/ p (* x x)) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
6.0ms	p	@	inf	((* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))))) (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (sqrt (+ (* x x) (* (* p 4) p))) (/ p (* x x)) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
4.0ms	p	@	0	((* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))))) (+ 1 (/ x (sqrt (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (sqrt (+ (* x x) (* (* p 4) p))) (/ p (* x x)) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))

simplify316.0ms (3.3%)

Memory

6.8MiB live, 252.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 546×	`lower-fma.f64`
10 546×	`lower-fma.f32`
7 668×	`lower-*.f64`
7 668×	`lower-*.f32`
4 700×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	921	11095
1	2839	10559
0	8237	9916

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 476

Calls

Call 1

Inputs
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)))))
(* (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))))))))
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 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* (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))))))))
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)))))
(* (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))))))))
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
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
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))))))
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 x)
(+ (* -1 (/ (pow p 2) (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 5))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))
(+ (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 7))) (* 3 (/ 1 (pow x 5))))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))
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)))))
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)))))
(* (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))))))))
(* 4 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* -16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* 64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
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)))))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(* 2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* -6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* 20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
1/2
(+ 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)))))
(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))))))
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)))))
(* 1/2 (/ 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)
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1
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1
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1
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(sqrt 1/2)
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1/2
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(sqrt 1/2)
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1
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(/ p (pow x 2))
(/ p (pow x 2))
1
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1
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2
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1
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1
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(* -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))
(/ (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))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))) x))
(* -1 (/ (+ 1/2 (+ (* -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)))))) x))
(* -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))))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4)))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2)))) (pow x 2))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* 1/2 (/ (* (- (* -8 (pow p 4)) (* -2 (pow p 4))) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* (pow p 2) (pow (sqrt 2) 2))))))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* 4 (/ (pow p 2) (pow x 2)))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4))))) (pow x 2))
(/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -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))))))))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* 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 4))) (* 2 (/ (pow p 2) (pow x 2)))))

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

rewrite300.0ms (3.2%)

Memory

10.6MiB live, 241.3MiB allocated

Rules

4 656×	`lower-/.f32`
4 646×	`lower-/.f64`
4 310×	`lower-*.f32`
4 300×	`lower-*.f64`
3 336×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	309
0	72	277
1	294	267
2	1673	267
0	8258	267

Stop Event

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

Counts

21 → 912

Calls

Call 1

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

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

eval266.0ms (2.8%)

Memory: 20.2MiB live, 409.6MiB allocated
Compiler: Compiled 57 149 to 3 394 computations (94.1% saved)

prune162.0ms (1.7%)

Memory

12.9MiB live, 449.8MiB allocated

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	1 430	11	1 441
Fresh	7	4	11
Picked	2	3	5
Done	0	0	0
Total	1 439	18	1 457

Accuracy

100.0%

Counts

1 457 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.5%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
▶	78.9%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	75.5%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64)))
	74.4%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) x #s(literal 1/2 binary64)))
▶	47.3%	(sqrt.f64 (fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64)))
	24.9%	(sqrt.f64 (.f64 (fma.f64 (/.f64 (.f64 (neg.f64 x) x) (.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) (fma.f64 x x (.f64 #s(literal -4 binary64) (.f64 p p))))) (fma.f64 x x (.f64 #s(literal -4 binary64) (.f64 p p))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
▶	47.7%	(sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
	4.1%	(sqrt.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (/ x (sqrt (+ ( (* p 4) p) (* x x))))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64))))))
	45.3%	(sqrt.f64 (.f64 #s(approx (+ ( (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 x x) (.f64 p p)) #s(literal 1 binary64))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
	15.0%	(sqrt.f64 (.f64 #s(approx (+ ( (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -16 binary64)) (.f64 x x))) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
	13.4%	(sqrt.f64 (.f64 #s(approx (+ ( (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 8 binary64))) #s(literal -256 binary64) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x))) (.f64 p p))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
✓	78.9%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))))
▶	15.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))))
	14.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 #s(literal -12 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p)) (.f64 x x))))
✓	51.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	30.1%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
	27.8%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x))
▶	38.8%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 856 to 480 computations (43.9% saved)

simplify113.0ms (1.2%)

Memory

-60.6MiB live, 134.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
cost-diff	128	(.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))
cost-diff	320	(fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64))
cost-diff	0	(/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))))
cost-diff	640	(fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p))
cost-diff	0	(/.f64 #s(literal 1/4 binary64) p)
cost-diff	0	#s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p))
cost-diff	0	(fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
cost-diff	0	(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Rules

3 658×	`lower-fma.f32`
3 648×	`lower-fma.f64`
3 208×	`lower-*.f32`
3 192×	`lower-*.f64`
1 174×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	472
0	85	470
1	148	450
2	260	435
3	598	435
4	1661	435
5	2982	435
6	4174	435
7	6134	435
8	6988	435
0	8043	429

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

Outputs
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) x #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))
x
(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
(sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))
(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))
(fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)
p
#s(literal 4 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64)))
(fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
#s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p))
(/.f64 #s(literal 1/4 binary64) p)
#s(literal 1/4 binary64)
p
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 (fma.f64 (.f64 (/.f64 p (.f64 x x)) p) #s(literal -3 binary64) #s(literal 1 binary64)) (.f64 (/.f64 p (*.f64 x x)) p))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 (fma.f64 (.f64 (/.f64 p (.f64 x x)) p) #s(literal -3 binary64) #s(literal 1 binary64)) (.f64 (/.f64 p (*.f64 x x)) p)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))
(.f64 (fma.f64 (.f64 (/.f64 p (.f64 x x)) p) #s(literal -3 binary64) #s(literal 1 binary64)) (.f64 (/.f64 p (*.f64 x x)) p))
(fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p))
(.f64 (fma.f64 (.f64 (/.f64 p (.f64 x x)) p) #s(literal -3 binary64) #s(literal 1 binary64)) (.f64 p p))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)))
(.f64 (.f64 (.f64 (/.f64 p (.f64 x x)) p) p) (*.f64 #s(literal -12 binary64) p))
(.f64 (.f64 p p) (*.f64 p p))
(.f64 (.f64 (*.f64 p p) p) p)
(*.f64 p p)
p
(/.f64 #s(literal -12 binary64) (*.f64 x x))
#s(literal -12 binary64)
(*.f64 x x)
x
#s(literal 1/4 binary64)
(sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
(sqrt.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))))))
(.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))
(/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64))
(neg.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal -1 binary64)))
(*.f64 (neg.f64 x) x)
(neg.f64 x)
x
(/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))
#s(literal 1 binary64)
(fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))
(*.f64 #s(literal 4 binary64) p)
#s(literal 4 binary64)
p
(*.f64 x x)
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.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 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
(/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))
(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
(sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))
(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))
(fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))
(*.f64 p #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) p)

localize212.0ms (2.2%)

Memory

-6.2MiB live, 308.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	8.05868178362641	(.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))
accuracy	9.355972900848178	(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
accuracy	13.037526786335997	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
accuracy	32.94025206980416	(fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64))
accuracy	5.281224824933048	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))))
accuracy	6.221457806884081	(/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x))
accuracy	14.007696906491548	(fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p))
accuracy	46.49847722324663	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 p p)) (*.f64 x x)))
accuracy	0	(/.f64 #s(literal 1/4 binary64) p)
accuracy	5.281224824933048	(sqrt.f64 (fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64)))
accuracy	15.572755734820111	(fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
accuracy	33.181913888772655	#s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p))
accuracy	39.19126065170472	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))
accuracy	0.0078125	(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
accuracy	5.281224824933048	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	8.011728856390038	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	13.037526786335997	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))

Samples

58.0ms	68×	2	valid
36.0ms	46×	1	valid
34.0ms	119×	0	valid
26.0ms	23×	3	valid

Compiler

Compiled 446 to 47 computations (89.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-mult: 43.0ms (37.2% of total)

ival-div: 21.0ms (18.2% of total)

ival-sqrt: 19.0ms (16.4% of total)

ival-add: 15.0ms (13% of total)

adjust: 14.0ms (12.1% of total)

ival-sub: 2.0ms (1.7% of total)

exact: 1.0ms (0.9% of total)

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

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

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

series35.0ms (0.4%)

Memory

4.5MiB live, 46.6MiB allocated

Counts

18 → 408

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #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 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (patch (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4))))) (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (patch (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (patch (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) (patch (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) (patch (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2))) (pow x 2)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) (patch (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4)))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2)))) (pow x 2)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) (patch (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* 1/2 (/ (* (- (* -8 (pow p 4)) (* -2 (pow p 4))) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* (pow p 2) (pow (sqrt 2) 2))))))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt 2 (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ 2 (* -1/2 (/ (+ (* 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 4))) (* 2 (/ (pow p 2) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/ 1/4 p) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (* (neg x) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
2.0ms	p	@	0	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/ 1/4 p) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (* (neg x) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
2.0ms	x	@	-inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/ 1/4 p) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (* (neg x) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
2.0ms	p	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/ 1/4 p) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (* (neg x) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
2.0ms	x	@	0	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2) (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/ 1/4 p) (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (* x x)) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (* (neg x) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))

simplify296.0ms (3.1%)

Memory

24.0MiB live, 219.5MiB allocated

Algorithm

1×	egg-herbie

Rules

10 258×	`lower-fma.f64`
10 258×	`lower-fma.f32`
7 820×	`lower-*.f64`
7 820×	`lower-*.f32`
4 526×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	917	9677
1	2846	9303
0	8234	8730

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 406

Calls

Call 1

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

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 11/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 p p) #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 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.f64 p p) #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 (fma.f64 (fma.f64 #s(literal -10 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 6 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -2 binary64) (.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -20 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -2 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (/.f64 (.f64 p p) (.f64 (.f64 x x) x)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (.f64 p p) 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 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 5 binary64))) #s(literal 4 binary64) (/.f64 #s(literal -2 binary64) (.f64 (.f64 x x) x))) (.f64 p p) (/.f64 #s(literal 2 binary64) x)) (*.f64 p p) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 11/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 p p) #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 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) #s(literal 11/8 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 p p) #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 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.f64 p p) #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 (fma.f64 (fma.f64 #s(literal -10 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* -1 (/ (pow p 2) (pow x 3))) (* 1/2 (/ 1 x)))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 p p) (.f64 (*.f64 x x) x)))
(+ (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 5))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))
(fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 5 binary64))) #s(literal 3 binary64) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) x))) (.f64 p p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 7))) (* 3 (/ 1 (pow x 5))))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 7 binary64))) #s(literal -10 binary64) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 p p) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) x))) (*.f64 p p) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(pow p 2)
(*.f64 p p)
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)) (.f64 p p))
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)) (.f64 p p))
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)) (.f64 p p))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (.f64 (neg.f64 p) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (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))))))
(fma.f64 (fma.f64 (.f64 (.f64 p p) #s(literal 1/2 binary64)) (/.f64 (.f64 (-.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) x))) (.f64 p p) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 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 (fma.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))) (.f64 x x)) (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 p p)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (.f64 p p) (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) x))) (.f64 p p) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.f64 p p) #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 (fma.f64 (fma.f64 #s(literal -10 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 p p))
(* 4 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))
(* (pow p 2) (+ (* -16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal -16 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 4 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* 64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (fma.f64 #s(literal 64 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x))) (*.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 8 binary64))) #s(literal -256 binary64) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x))) (.f64 p p))
1
#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
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1
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1/2
#s(literal 1/2 binary64)
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(* -2 p)
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(sqrt 1/2)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (.f64 (.f64 x x) x) (.f64 p p)) #s(literal -1/32 binary64) (.f64 #s(literal 1/4 binary64) x)) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/256 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) x) (.f64 p p)) #s(literal -1/32 binary64) (.f64 #s(literal 1/4 binary64) x))) p))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) 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 (.f64 x (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p)) #s(literal 1/32 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/4 binary64))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/32 (* (pow x 2) (sqrt 1/2))) (* 1/2 (/ (* (sqrt 1/2) (+ (* -1/64 (pow x 3)) (* 1/16 (pow x 3)))) p))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x (/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 3/64 binary64)) p) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) #s(literal -1/32 binary64))) (neg.f64 p))) p))
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 #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 x x) x) (.f64 p p)) (.f64 x #s(literal -1/2 binary64))) p))
(+ 1 (* -1 (/ (- (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4)) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
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(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) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
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(+ (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 (fma.f64 (fma.f64 (/.f64 (.f64 (-.f64 (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)) p) (.f64 p p))) (/.f64 #s(literal 1/32 binary64) (.f64 (.f64 p p) p))) x) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal -1/128 binary64) (.f64 (.f64 (.f64 p p) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) x (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) x (sqrt.f64 #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) p)) #s(literal -1/32 binary64) (/.f64 #s(literal 1/4 binary64) p)) x #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 (fma.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 3/512 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 (.f64 p p) p))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
(* 1/2 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (.f64 p p) p)) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)) x)
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/256 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 p p) p))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) p)) x)
(* 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))))
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(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64) (.f64 #s(literal 2 binary64) p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (.f64 p p) p)) #s(literal -1/64 binary64) (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x) (*.f64 #s(literal 2 binary64) 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)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) p))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x) (.f64 #s(literal 2 binary64) p))
(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) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 (fma.f64 (/.f64 x (.f64 (.f64 (.f64 p p) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -1/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) x (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 (fma.f64 (fma.f64 (/.f64 (.f64 (-.f64 (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)) p) (.f64 p p))) (/.f64 #s(literal 1/32 binary64) (.f64 (.f64 p p) p))) x) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal -1/128 binary64) (.f64 (.f64 (.f64 p p) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) x (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) x (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) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 (fma.f64 (/.f64 x (.f64 (.f64 (.f64 p p) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -1/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) x (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 (fma.f64 (fma.f64 (/.f64 (.f64 (-.f64 (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)) p) (.f64 p p))) (/.f64 #s(literal 1/32 binary64) (.f64 (.f64 p p) p))) x) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal -1/128 binary64) (.f64 (.f64 (.f64 p p) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) x (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) x (sqrt.f64 #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) p)) #s(literal -1/32 binary64) (/.f64 #s(literal 1/4 binary64) p)) x #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 (fma.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 3/512 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 (.f64 p p) p))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))
(fma.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) p)) #s(literal -1/32 binary64) (/.f64 #s(literal 1/4 binary64) p))
(+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))
(fma.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 3/512 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 (.f64 p p) p))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) p))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/4096 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 7 binary64))) (/.f64 #s(literal 3/512 binary64) (pow.f64 p #s(literal 5 binary64)))) (.f64 x x) (/.f64 #s(literal -1/32 binary64) (.f64 (.f64 p p) p))) (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p))
(* -3 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (.f64 x x))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 2))
(/.f64 (fma.f64 (.f64 (.f64 p p) x) x (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (.f64 x x))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 2))
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(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 2))
(/.f64 (fma.f64 (.f64 (.f64 p p) x) x (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (.f64 x x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) p) #s(literal 1/4 binary64) (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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(+ (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))))))))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
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(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
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(* -3 (/ (pow p 4) (pow x 4)))
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(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
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(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
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(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
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1
#s(literal 1 binary64)
(+ 1 (* -1/4 (/ (pow x 2) (pow p 2))))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
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(sqrt 1/2)
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(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
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(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))
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(* -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))
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) p) p) #s(literal 1 binary64) (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (.f64 x x))) (.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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))
(/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (fma.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64)))) #s(literal 1/2 binary64) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) p) p) #s(literal 1 binary64) (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 (.f64 #s(literal 2 binary64) p) p)))) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 6 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) p) p) #s(literal 1 binary64) (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (.f64 p p)) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x)) #s(literal 1/4 binary64) (fma.f64 p p (/.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) p) p) #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64))))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (fma.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64)))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x x))) (fma.f64 p p (/.f64 (fma.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) p) p) #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64))))) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (.f64 x x)) #s(literal -3 binary64) (.f64 p p)) (*.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (.f64 x x)) #s(literal -3 binary64) (.f64 p p)) (*.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (.f64 x x)) #s(literal -3 binary64) (.f64 p p)) (*.f64 x x))
(* 4 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -16 binary64)) (.f64 x x))) (.f64 x x))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 64 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -16 binary64)) (.f64 x x)))) (.f64 x x))
(/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 8 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -256 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 64 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -16 binary64)) (.f64 x x))))) (.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 x x)) #s(literal 1/2 binary64) (.f64 p p)) (.f64 x x))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 x x)) (/.f64 (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (fma.f64 (.f64 (neg.f64 p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p)) (.f64 x x))
(/ (+ (* 1/2 (/ (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4)))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal -128 binary64) (pow.f64 p #s(literal 8 binary64))) (fma.f64 (.f64 (neg.f64 p) p) (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (fma.f64 (.f64 (neg.f64 p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 p p)))) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64))) (.f64 p p))))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 x x)) (/.f64 (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (fma.f64 (.f64 (neg.f64 p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p))) (.f64 x x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(/.f64 (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (.f64 x x))) (.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (.f64 x x))) (/.f64 (.f64 (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (fma.f64 (.f64 (.f64 (neg.f64 p) p) (pow.f64 p #s(literal 4 binary64))) #s(literal -6 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 p p) (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) #s(literal 2 binary64)) (.f64 p p)))))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) (.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* 1/2 (/ (* (- (* -8 (pow p 4)) (* -2 (pow p 4))) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* (pow p 2) (pow (sqrt 2) 2))))))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 #s(literal -128 binary64) (pow.f64 p #s(literal 8 binary64))) (fma.f64 (neg.f64 (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (fma.f64 (.f64 (neg.f64 p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 p p))))) (.f64 p p) (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal -6 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (fma.f64 (.f64 (.f64 (neg.f64 p) p) (pow.f64 p #s(literal 4 binary64))) #s(literal -6 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 p p) (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) #s(literal 2 binary64)) (.f64 p p)))))) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64))) (.f64 p p)) (.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64))) (.f64 p p)))))) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (.f64 x x))) (/.f64 (.f64 (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (fma.f64 (.f64 (.f64 (neg.f64 p) p) (pow.f64 p #s(literal 4 binary64))) #s(literal -6 binary64) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 p p) (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64)) #s(literal 2 binary64)) (.f64 p p)))))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) (.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 2 binary64)))
(- (+ 2 (* -1/2 (/ (+ (* 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 4))) (* 2 (/ (pow p 2) (pow x 2)))))
(-.f64 (+.f64 (+.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 x x)))

rewrite282.0ms (3%)

Memory

1.2MiB live, 229.6MiB allocated

Rules

4 822×	`lower-/.f32`
4 810×	`lower-/.f64`
4 552×	`lower-*.f32`
4 536×	`lower-*.f64`
3 298×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	337
0	85	290
1	322	277
2	1974	276
0	8470	272

Stop Event

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

Counts

18 → 711

Calls

Call 1

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

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

eval291.0ms (3.1%)

Memory: 11.7MiB live, 239.1MiB allocated
Compiler: Compiled 50 968 to 3 362 computations (93.4% saved)

prune358.0ms (3.8%)

Memory

-12.5MiB live, 311.3MiB allocated

Pruning

18 alts after pruning (11 fresh and 7 done)

	Pruned	Kept	Total
New	1 222	8	1 230
Fresh	7	3	10
Picked	1	4	5
Done	0	3	3
Total	1 230	18	1 248

Accuracy

100.0%

Counts

1 248 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.5%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	78.9%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	74.4%	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	75.5%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64)))
✓	47.3%	(sqrt.f64 (fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64)))
✓	47.7%	(sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
▶	47.8%	(sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (neg.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 p p) (*.f64 x x)) x))))))))
▶	4.1%	(sqrt.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (/ x (sqrt (+ ( (* p 4) p) (* x x))))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64))))))
	45.3%	(sqrt.f64 (.f64 #s(approx (+ ( (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 x x) (.f64 p p)) #s(literal 1 binary64))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
	15.0%	(sqrt.f64 (.f64 #s(approx (+ ( (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -16 binary64)) (.f64 x x))) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
	13.4%	(sqrt.f64 (.f64 #s(approx (+ ( (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 8 binary64))) #s(literal -256 binary64) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x))) (.f64 p p))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
✓	78.9%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))))
	14.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 #s(literal -12 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p)) (.f64 x x))))
	16.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)) (.f64 p p))) (*.f64 x x))))
✓	51.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	30.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	27.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
✓	38.8%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 762 to 433 computations (43.2% saved)

simplify192.0ms (2%)

Memory

29.4MiB live, 148.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (neg.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 p p) (*.f64 x x)) x))))))))
cost-diff	128	(.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (neg.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 p p) (*.f64 x x)) x)))))))
cost-diff	320	(fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64))
cost-diff	640	(fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 p p) (*.f64 x x)) x)
cost-diff	0	(neg.f64 x)
cost-diff	0	(fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (/ x (sqrt (+ ( (* p 4) p) (* x x))))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64))))))
cost-diff	128	(.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (/ x (sqrt (+ ( (* p 4) p) (* x x))))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64)))))
cost-diff	0	#s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))
cost-diff	0	(/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)))
cost-diff	0	(fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(neg.f64 p)
cost-diff	0	(/.f64 (neg.f64 p) x)
cost-diff	0	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
cost-diff	0	(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
cost-diff	0	(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))

Rules

3 482×	`lower-fma.f32`
3 468×	`lower-fma.f64`
2 940×	`lower-*.f32`
2 922×	`lower-*.f64`
1 782×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	706
0	106	700
1	182	696
2	372	696
3	1064	668
4	3790	668
5	5268	668
6	7202	668
0	8208	663

Stop Event

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

Calls

Call 1

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

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

localize535.0ms (5.6%)

Memory

-28.4MiB live, 456.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	8.05868178362641	(.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (neg.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 p p) (*.f64 x x)) x)))))))
accuracy	9.355972900848178	(-.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (neg.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 p p) (*.f64 x x)) x)))))
accuracy	32.94025206980416	(fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64))
accuracy	46.118344247316095	#s(approx (sqrt (+ (* (* p 4) p) (* x x))) (neg.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 p p) (*.f64 x x)) x)))
accuracy	6.936180528859655	(/.f64 (.f64 p p) (.f64 x x))
accuracy	8.05868178362641	(.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (/ x (sqrt (+ ( (* p 4) p) (* x x))))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64)))))
accuracy	32.946972740644	(fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64))
accuracy	46.450503110468674	#s(approx (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64)))
accuracy	4.011773073978981	(/.f64 (*.f64 p p) x)
accuracy	5.281224824933048	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	8.011728856390038	(fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	44.577976714436396	#s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))
accuracy	0	(/.f64 (neg.f64 p) x)
accuracy	0	(neg.f64 p)
accuracy	46.22945026127714	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
accuracy	0.390625	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	5.254279927640047	(sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64)))
accuracy	8.020498944415017	(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64))
accuracy	13.037526786335997	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))

Samples

167.0ms	68×	2	valid
162.0ms	46×	1	valid
84.0ms	119×	0	valid
27.0ms	23×	3	valid

Compiler

Compiled 582 to 52 computations (91.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 308.0ms

adjust: 110.0ms (35.7% of total)

ival-mult: 85.0ms (27.6% of total)

ival-div: 72.0ms (23.4% of total)

ival-sqrt: 18.0ms (5.8% of total)

ival-add: 17.0ms (5.5% of total)

ival-neg: 3.0ms (1% of total)

ival-sub: 2.0ms (0.6% of total)

exact: 1.0ms (0.3% of total)

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

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

series81.0ms (0.8%)

Memory

28.3MiB live, 105.2MiB allocated

Counts

25 → 576

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	((* (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (sqrt 1/2)) (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (+ (* (* x 2) (/ (* p p) (* x x))) x) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (sqrt (+ (* (* p 4) p) (* x x))) (/ (* p p) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (sqrt (+ (* (* p 4) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
7.0ms	p	@	inf	((* (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (sqrt 1/2)) (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (+ (* (* x 2) (/ (* p p) (* x x))) x) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (sqrt (+ (* (* p 4) p) (* x x))) (/ (* p p) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (sqrt (+ (* (* p 4) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
3.0ms	x	@	-inf	((* (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (sqrt 1/2)) (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (+ (* (* x 2) (/ (* p p) (* x x))) x) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (sqrt (+ (* (* p 4) p) (* x x))) (/ (* p p) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (sqrt (+ (* (* p 4) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
3.0ms	p	@	0	((* (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (sqrt 1/2)) (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (+ (* (* x 2) (/ (* p p) (* x x))) x) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (sqrt (+ (* (* p 4) p) (* x x))) (/ (* p p) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (sqrt (+ (* (* p 4) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))
2.0ms	p	@	-inf	((* (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (sqrt 1/2)) (sqrt (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1)) (+ (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (+ (* (neg x) (/ x (+ (* (* p 4) p) (* x x)))) 1) (neg x) (+ (* (* x 2) (/ (* p p) (* x x))) x) (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))) (sqrt (* (+ (* (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x)))))))) (sqrt (+ (* (* p 4) p) (* x x))) (/ (* p p) x) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (/ (* p p) (* x x)) (sqrt (+ (* (* p 4) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))))

simplify233.0ms (2.4%)

Memory

-5.0MiB live, 341.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 050×	`lower-fma.f64`
11 050×	`lower-fma.f32`
7 968×	`lower-*.f64`
7 968×	`lower-*.f32`
4 902×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	954	13202
1	2971	12668
0	8577	11890

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 567

Calls

Call 1

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

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

rewrite232.0ms (2.4%)

Memory

-3.2MiB live, 296.1MiB allocated

Rules

5 560×	`lower-*.f32`
5 542×	`lower-*.f64`
3 564×	`lower-/.f32`
3 544×	`lower-/.f64`
2 666×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	482
0	106	475
1	405	457
2	2578	457
0	8608	455

Stop Event

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

Counts

25 → 566

Calls

Call 1

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

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

eval199.0ms (2.1%)

Memory: 2.0MiB live, 307.3MiB allocated
Compiler: Compiled 46 176 to 3 658 computations (92.1% saved)

prune230.0ms (2.4%)

Memory

6.6MiB live, 414.2MiB allocated

Pruning

17 alts after pruning (8 fresh and 9 done)

	Pruned	Kept	Total
New	1 205	3	1 208
Fresh	1	5	6
Picked	2	3	5
Done	1	6	7
Total	1 209	17	1 226

Accuracy

100.0%

Counts

1 226 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	78.5%	(.f64 (sqrt.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
	45.9%	(.f64 #s(approx (sqrt (+ (/ x (sqrt (+ ( (* p 4) p) (* x x)))) 1)) (fma.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/32 binary64) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	78.9%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	74.4%	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	75.5%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64)))
✓	47.3%	(sqrt.f64 (fma.f64 #s(approx (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) (/.f64 #s(literal 1/4 binary64) p)) x #s(literal 1/2 binary64)))
	47.8%	(sqrt.f64 (.f64 (fma.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (neg.f64 #s(approx (+ (* (* x 2) (/ (* p p) (* x x))) x) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)))))))))
	6.8%	(sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) (/.f64 #s(literal 1/2 binary64) #s(approx (- 1 (/ x (sqrt (+ (* (* p 4) p) (* x x))))) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 2 binary64))))))
	15.0%	(sqrt.f64 (.f64 #s(approx (+ ( (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -16 binary64)) (.f64 x x))) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
	13.4%	(sqrt.f64 (.f64 #s(approx (+ ( (* (neg x) x) (/ 1 (+ (* (* 4 p) p) (* x x)))) 1) (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 8 binary64))) #s(literal -256 binary64) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x))) (.f64 p p))) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))))))
✓	78.9%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))))
	14.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 #s(literal -12 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p)) (.f64 x x))))
	16.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (* (* (* p p) (* p p)) (/ -12 (* x x))) 1/4) (* p p)) (.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)) (.f64 p p))) (*.f64 x x))))
✓	51.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	30.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	27.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
✓	38.8%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 1 269 to 416 computations (67.2% saved)

regimes79.0ms (0.8%)

Memory

-3.2MiB live, 155.3MiB allocated

Counts

39 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

13.0ms	x
13.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
11.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
11.0ms	p
10.0ms	(.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
78.9%	1	`p`
84.1%	2	`x`
99.8%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.8%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.8%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.8%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
78.9%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes21.0ms (0.2%)

Memory

-27.2MiB live, 51.0MiB allocated

Counts

18 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

6.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
4.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

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

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes18.0ms (0.2%)

Memory

19.8MiB live, 59.2MiB allocated

Counts

16 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

5.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
4.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
98.5%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
98.5%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.5%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.5%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes18.0ms (0.2%)

Memory

-4.5MiB live, 45.5MiB allocated

Counts

13 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

6.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
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)))))))

Results

Accuracy	Segments	Branch
99.2%	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)))))))`
99.2%	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))))))`
99.2%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.2%	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)

regimes11.0ms (0.1%)

Memory

-10.4MiB live, 29.0MiB allocated

Counts

7 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

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))))))
3.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
2.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
98.5%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
98.5%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.5%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.5%	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)

regimes9.0ms (0.1%)

Memory

-10.7MiB live, 28.7MiB allocated

Counts

5 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes12.0ms (0.1%)

Memory

33.7MiB live, 33.7MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
68.7%	2	`p`
68.7%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
61.7%	2	`x`
74.3%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
74.3%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
74.3%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
74.3%	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)

regimes11.0ms (0.1%)

Memory

-11.5MiB live, 27.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
38.8%	1	`x`
38.8%	1	`p`
38.8%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
38.8%	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)))))))`
38.8%	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))))))`
38.8%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
38.8%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.99999999999702	-0.9999966728704456

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.99999999999702	-0.9999966728704456

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.8943051315439732	-3.520516672665684e-9

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.719814362276471e-6	0.9871685472251505
0.0ms	-0.8943051315439732	-3.520516672665684e-9

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.719814362276471e-6	0.9871685472251505
0.0ms	-0.8943051315439732	-3.520516672665684e-9

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.719814362276471e-6	0.9871685472251505
0.0ms	-0.8943051315439732	-3.520516672665684e-9

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch13.0ms (0.1%)

Memory

-17.8MiB live, 23.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	5.719814362276471e-6	0.9871685472251505

Samples

6.0ms

144×

valid

Compiler

Compiled 121 to 100 computations (17.4% saved)

Precisions

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

ival-add: 1.0ms (34.9% of total)

ival-mult: 1.0ms (34.9% of total)

ival-sqrt: 1.0ms (34.9% of total)

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

exact: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Memory

16.7MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	532
1	93	532
2	99	532
3	104	532
4	107	532
5	108	532

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 -9007181240342483/9007199254740992 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -9007181240342483/9007199254740992 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 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 (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 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 -9007181240342483/9007199254740992 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -9007181240342483/9007199254740992 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p #s(literal 4 binary64)) p)))) #s(literal 1 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 -9007181240342483/9007199254740992 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -9007181240342483/9007199254740992 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x))) x #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 5902958103587057/590295810358705651712 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 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 (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #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 (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

soundness578.0ms (6.1%)

Memory

16.5MiB live, 565.3MiB allocated

Rules

10 546×	`lower-fma.f64`
10 546×	`lower-fma.f32`
9 590×	`lower-fma.f64`
9 590×	`lower-fma.f32`
7 668×	`lower-*.f64`

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
0	434	2486
1	1325	2377
2	4611	2304
0	8084	2141
0	921	11095
1	2839	10559
0	8237	9916

Stop Event

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

Compiler

Compiled 677 to 344 computations (49.2% saved)

preprocess68.0ms (0.7%)

Memory: -8.0MiB live, 185.2MiB allocated
Compiler: Compiled 692 to 208 computations (69.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze517.0ms (5.4%)

sample2.4s (24.7%)

explain231.0ms (2.4%)

preprocess64.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify16.0ms (0.2%)

localize51.0ms (0.5%)

series132.0ms (1.4%)

simplify170.0ms (1.8%)

rewrite196.0ms (2.1%)

eval69.0ms (0.7%)

prune109.0ms (1.1%)

simplify140.0ms (1.5%)

localize205.0ms (2.1%)

series93.0ms (1%)

simplify316.0ms (3.3%)

rewrite300.0ms (3.2%)

eval266.0ms (2.8%)

prune162.0ms (1.7%)

simplify113.0ms (1.2%)

localize212.0ms (2.2%)

series35.0ms (0.4%)

simplify296.0ms (3.1%)

rewrite282.0ms (3%)

eval291.0ms (3.1%)

prune358.0ms (3.8%)

simplify192.0ms (2%)

localize535.0ms (5.6%)

series81.0ms (0.8%)

simplify233.0ms (2.4%)

rewrite232.0ms (2.4%)

eval199.0ms (2.1%)

prune230.0ms (2.4%)

regimes79.0ms (0.8%)

regimes21.0ms (0.2%)

regimes18.0ms (0.2%)

regimes18.0ms (0.2%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

regimes12.0ms (0.1%)

regimes11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch13.0ms (0.1%)

simplify9.0ms (0.1%)

soundness578.0ms (6.1%)

preprocess68.0ms (0.7%)

end0.0ms (0%)

Profiling