Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze466.0ms (6.5%)

Memory

1.3MiB live, 774.0MiB 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 (33.9%)

Memory

23.6MiB live, 2 210.4MiB allocated

Samples

1.2s	6 246×	0	valid
312.0ms	1 007×	2	valid
194.0ms	378×	3	valid
170.0ms	625×	1	valid

Precisions

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

ival-mult: 365.0ms (24.1% of total)

ival-sqrt: 294.0ms (19.5% of total)

const: 286.0ms (18.9% of total)

ival-add: 255.0ms (16.9% of total)

ival-div: 107.0ms (7.1% of total)

adjust: 91.0ms (6% of total)

ival-fabs: 50.0ms (3.3% 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

explain261.0ms (3.6%)

Memory

-20.5MiB live, 180.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
58	0	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
32	1	(-3.8676353892311794e-113 -1.04304462886882e+49)	1	(-1.3045673878903597e-92 -1.1594339644146317e-91)	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
18	0	-	2	(-6.360472554743305e-149 -4403814239207.889)	`(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	-	0	-	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	0	-	0	-	`#s(literal 4 binary64)`
0	0	-	0	-	`(*.f64 x x)`
0	0	-	0	-	`p`
0	0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	0	-	0	-	`#s(literal 1/2 binary64)`
0	0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	oflow-rescue	58	0
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	58
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	58
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	32	1
`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	16	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	11
↳	`(.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	27
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	27
↳	`(/.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	65

Confusion

	Predicted +	Predicted -
+	48	0
-	58	150

Precision

0.4528301886792453

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	48	0	0
-	58	1	149

Precision?

0.4485981308411215

Recall?

1.0

Freqs

test

number	freq
0	150
1	106

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms	60×	2	valid
35.0ms	394×	0	valid
28.0ms	34×	1	valid
7.0ms	24×	3	valid

Compiler

Compiled 209 to 46 computations (78% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-add: 38.0ms (54.1% of total)

ival-mult: 13.0ms (18.5% of total)

ival-sqrt: 10.0ms (14.2% of total)

ival-div: 5.0ms (7.1% of total)

adjust: 4.0ms (5.7% of total)

exact: 1.0ms (1.4% of total)

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

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

preprocess80.0ms (1.1%)

Memory

-0.1MiB live, 39.1MiB 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 17 to 14 computations (17.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	82.1%	(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)))))))

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify4.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB 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)

localize68.0ms (0.9%)

Memory

0.3MiB live, 48.4MiB 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	4.1408506181828635	(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	7.143118033037141	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	13.469552762971226	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

41.0ms	197×	0	valid
7.0ms	30×	2	valid
7.0ms	12×	3	valid
3.0ms	17×	1	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

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

ival-mult: 30.0ms (68.8% of total)

ival-sqrt: 5.0ms (11.5% of total)

ival-add: 4.0ms (9.2% of total)

ival-div: 3.0ms (6.9% of total)

adjust: 2.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.4%)

Memory

-7.1MiB live, 32.3MiB 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>) () ())) ())
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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))))) (* 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 (+ (* 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
8.0ms	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))))
3.0ms	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))))

simplify221.0ms (3.1%)

Memory

3.8MiB live, 192.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	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))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.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 p (/.f64 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))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (neg.f64 x)) (/.f64 (.f64 p p) (sqrt.f64 #s(literal 2 binary64))) (.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 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (neg.f64 x)) (sqrt.f64 #s(literal 2 binary64)))) (.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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.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 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x)) (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 p p) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 p p) (/.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (neg.f64 x)) (sqrt.f64 #s(literal 2 binary64)))) (.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 (/.f64 #s(literal -2 binary64) x) (/.f64 (*.f64 p p) 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 (.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.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 p (/.f64 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))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 3 binary64)))) #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 (pow.f64 p #s(literal 4 binary64)) (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 5 binary64)))) #s(literal 4 binary64) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal -1/32 binary64) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(+.f64 (fma.f64 x (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 5 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) p)) (.f64 (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal -1/32 binary64))) #s(literal 1/2 binary64))
(* 4 (pow p 2))
(.f64 #s(literal 4 binary64) (.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 (.f64 (fma.f64 (/.f64 x p) (/.f64 x p) #s(literal 4 binary64)) p) p)
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 (.f64 (fma.f64 (/.f64 x p) (/.f64 x p) #s(literal 4 binary64)) p) p)
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 (.f64 (fma.f64 (/.f64 x p) (/.f64 x p) #s(literal 4 binary64)) p) p)
(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) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(fma.f64 (fma.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) p) #s(literal -1/32 binary64)) x (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(fma.f64 (fma.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) p) #s(literal -1/32 binary64)) x (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal -3/64 binary64) (pow.f64 p #s(literal 3 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(fma.f64 #s(literal -1/16 binary64) (pow.f64 (/.f64 x p) #s(literal 3 binary64)) (fma.f64 (/.f64 x p) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
(+.f64 (fma.f64 x (fma.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal 1/2 binary64) p)) (*.f64 #s(literal -1/16 binary64) (pow.f64 (/.f64 x p) #s(literal 3 binary64)))) #s(literal 1 binary64))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x (/.f64 x p)) #s(literal 2 binary64)) p)
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/64 binary64) (pow.f64 p #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x (/.f64 x p)) #s(literal 2 binary64))) p)
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/64 binary64) (pow.f64 p #s(literal 4 binary64))) (/.f64 (.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x (/.f64 x p)) #s(literal 2 binary64))) p)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/32 binary64) p) (/.f64 (pow.f64 x #s(literal 3 binary64)) p) (*.f64 #s(literal 1/4 binary64) x)) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 4 binary64)))) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal -1/32 binary64) p) (/.f64 (pow.f64 x #s(literal 3 binary64)) p))) p))
(* 4 (pow p 2))
(.f64 #s(literal 4 binary64) (.f64 p p))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 (.f64 (fma.f64 (/.f64 x p) (/.f64 x p) #s(literal 4 binary64)) p) p)
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 (.f64 (fma.f64 (/.f64 x p) (/.f64 x p) #s(literal 4 binary64)) p) p)
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 (.f64 (fma.f64 (/.f64 x p) (/.f64 x p) #s(literal 4 binary64)) p) p)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.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 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal -1/32 binary64) x) x (.f64 (/.f64 (*.f64 #s(literal -3/64 binary64) (pow.f64 x #s(literal 3 binary64))) p) #s(literal -1/2 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 (/.f64 #s(literal -1/16 binary64) p) (/.f64 (pow.f64 x #s(literal 3 binary64)) p) (*.f64 #s(literal 1/2 binary64) x)) p))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (fma.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal -1/16 binary64) p) (/.f64 (pow.f64 x #s(literal 3 binary64)) p))) p))
(* -2 p)
(*.f64 #s(literal -2 binary64) p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 (neg.f64 p) (fma.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x (/.f64 x p)) #s(literal 2 binary64)))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 (neg.f64 p) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/64 binary64) (pow.f64 p #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x (/.f64 x p)) #s(literal 2 binary64))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/64 binary64) (pow.f64 p #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x (/.f64 x p)) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64))))) #s(literal -1 binary64) #s(literal -2 binary64)) p)
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 (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal -1/32 binary64) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #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 (*.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal 3/512 binary64) (/.f64 #s(literal -1/32 binary64) (pow.f64 p #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
(* 4 (pow p 2))
(.f64 #s(literal 4 binary64) (.f64 p p))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.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)))))
(fma.f64 (fma.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) p) #s(literal -1/32 binary64)) x (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/32 binary64) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 x (pow.f64 p #s(literal 3 binary64)))) #s(literal -3/128 binary64))) x (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(fma.f64 #s(literal -1/16 binary64) (pow.f64 (/.f64 x p) #s(literal 3 binary64)) (fma.f64 (/.f64 x p) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
(fma.f64 (fma.f64 #s(literal 3/256 binary64) (*.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 p #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 x p) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 (.f64 x (/.f64 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 x (/.f64 x (pow.f64 p #s(literal 3 binary64)))) #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 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (pow.f64 p #s(literal 3 binary64)))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x) (.f64 #s(literal 2 binary64) p))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal -12 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/4 binary64) (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(fma.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal -12 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1/4 binary64) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) 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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (neg.f64 x)) (/.f64 (.f64 p p) (sqrt.f64 #s(literal 2 binary64))) (.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 (sqrt.f64 #s(literal 1/2 binary64)) x) (neg.f64 x)) (/.f64 (.f64 p p) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #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 #s(literal 1/2 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) #s(literal 2 binary64)) (.f64 p p) (fma.f64 #s(literal -32 binary64) (pow.f64 p #s(literal 6 binary64)) (neg.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)))) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (neg.f64 x)) (/.f64 (.f64 p p) (sqrt.f64 #s(literal 2 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 (/.f64 #s(literal -2 binary64) x) (/.f64 (*.f64 p p) 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 (/.f64 #s(literal -2 binary64) x) (/.f64 (.f64 p p) 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 (+ (* -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 (/.f64 #s(literal -2 binary64) x) (/.f64 (.f64 p p) 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)) (/.f64 (fma.f64 #s(literal -32 binary64) (pow.f64 p #s(literal 6 binary64)) (neg.f64 (.f64 (.f64 (*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (pow.f64 x #s(literal 6 binary64))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) 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 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) 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 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x)
(/ (pow p 2) (pow x 2))
(*.f64 (/.f64 p x) (/.f64 p x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (.f64 p p)) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p)) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 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))) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))) (.f64 p p)) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) 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 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (sqrt.f64 #s(literal 1/2 binary64)) p) (fma.f64 (/.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) p) p) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))) (.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 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (+.f64 (/.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) p) p) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) p) p) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) (/.f64 #s(literal -12 binary64) p))) (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) #s(literal 1/4 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -128 binary64) (pow.f64 p #s(literal 8 binary64))))) (.f64 (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 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) 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 #s(literal 2 binary64) x) (/.f64 (.f64 p p) 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 #s(literal 1/2 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (.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 #s(literal 1/2 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (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 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)) (pow.f64 x #s(literal 4 binary64))))) (.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 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x) (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 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)))) (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 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)) (pow.f64 x #s(literal 4 binary64))))) (*.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 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) 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 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x))

rewrite174.0ms (2.4%)

Memory

6.6MiB live, 168.3MiB 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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(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 3 binary64)))) (fma.f64 x (+.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (neg.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(fma.f64 (/.f64 #s(literal 1 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 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (neg.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64))
(fma.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64))
(fma.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))
(fma.f64 x (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(fma.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (fma.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64))))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #s(literal -1 binary64)) (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (-.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 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) 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))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -4 binary64) (.f64 p p) (.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -4 binary64) (.f64 p p) (.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (.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))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 #s(literal -4 binary64) (*.f64 p p)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 #s(literal -4 binary64) (.f64 p p) (*.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (*.f64 p #s(literal 4 binary64)) p))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 p #s(literal 4 binary64)) p))) (sqrt.f64 (-.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (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 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(exp.f64 (.f64 (log.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/2 binary64)))

eval136.0ms (1.9%)

Memory: -17.2MiB live, 103.3MiB allocated
Compiler: Compiled 12 478 to 2 045 computations (83.6% saved)

prune11.0ms (0.2%)

Memory

29.9MiB live, 29.9MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	387	7	394
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	388	7	395

Accuracy

99.9%

Counts

395 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.6%	(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)))
▶	7.6%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (neg.f64 x))))))
▶	54.5%	(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))))
	20.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
▶	35.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	58.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	25.2%	#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 118 to 112 computations (5.1% saved)

simplify50.0ms (0.7%)

Memory

-27.9MiB live, 11.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

96×	`lower-+.f32`
94×	`lower-+.f64`
88×	`lower-fma.f32`
82×	`lower-fma.f64`
60×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	292
0	55	281
1	90	275
2	107	275
3	112	275
4	115	275
5	119	275
6	152	275
7	194	275
8	213	275
9	217	275
0	217	273

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize136.0ms (1.9%)

Memory

-9.5MiB live, 134.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(/.f64 x #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x)))
accuracy	4.1408506181828635	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (neg.f64 x))))))
accuracy	7.143118033037141	(+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))))
accuracy	47.81243894196698	#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))
accuracy	0	(/.f64 x p)
accuracy	0.00390625	(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
accuracy	4.1408506181828635	(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))))
accuracy	29.029154062954994	#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)))
accuracy	4.1408506181828635	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
accuracy	42.180333805527184	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64))
accuracy	4.1408506181828635	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	27.11544366558412	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.00390625	(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))
accuracy	4.1408506181828635	(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	13.469552762971226	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
accuracy	14.227977766887406	(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))

Samples

61.0ms	197×	0	valid
14.0ms	30×	2	valid
8.0ms	12×	3	valid
6.0ms	17×	1	valid

Compiler

Compiled 265 to 29 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-sqrt: 14.0ms (29.9% of total)

ival-mult: 12.0ms (25.6% of total)

ival-add: 8.0ms (17.1% of total)

ival-div: 7.0ms (14.9% of total)

adjust: 4.0ms (8.5% of total)

ival-neg: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series37.0ms (0.5%)

Memory

11.5MiB live, 50.4MiB allocated

Counts

18 → 432

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	((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))) (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)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ x p) 1/4) 1/2) (/ x p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (+ (* (* p 4) p) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))))
3.0ms	x	@	-inf	((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))) (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)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ x p) 1/4) 1/2) (/ x p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (+ (* (* p 4) p) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))))
3.0ms	p	@	0	((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))) (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)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ x p) 1/4) 1/2) (/ x p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (+ (* (* p 4) p) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))))
2.0ms	p	@	inf	((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))) (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)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ x p) 1/4) 1/2) (/ x p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (+ (* (* p 4) p) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))))
2.0ms	x	@	inf	((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))) (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)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ x p) 1/4) 1/2) (/ x p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (+ (* (* p 4) p) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))))

simplify246.0ms (3.4%)

Memory

-9.8MiB live, 229.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 978×	`lower-fma.f64`
7 978×	`lower-fma.f32`
6 838×	`lower-*.f64`
6 838×	`lower-*.f32`
2 908×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	664	9334
1	2017	8844
2	6920	8718
0	8136	8138

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 428

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)))))
(/ 1/2 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)))))
(* (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)))))
(* (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)))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
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))))))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (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)))))
(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)))))
(/ 1/4 p)
(/ (+ 1/4 (* -1/32 (/ (pow x 2) (pow p 2)))) p)
(/ (+ 1/4 (+ (* -1/2 (/ (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))) (pow p 4))) (* -1/32 (/ (pow x 2) (pow p 2))))) p)
(/ (+ 1/4 (+ (* -1/2 (/ (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))) (pow p 4))) (+ (* -1/2 (/ (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))))) (pow p 6))) (* -1/32 (/ (pow x 2) (pow p 2)))))) 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)))))))
(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))))))
1/2
(+ 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))))))
1/2
(+ 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))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
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)
(/ (+ (* -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)
(* 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))))
(* 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)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(/ -1/4 p)
(* -1 (/ (+ 1/4 (* -1/32 (/ (pow x 2) (pow p 2)))) p))
(* -1 (/ (+ 1/4 (+ (* -1/2 (/ (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))) (pow p 4))) (* -1/32 (/ (pow x 2) (pow p 2))))) p))
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1/2
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(/ x p)
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1
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(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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(* 4 (pow p 2))
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1
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1
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(/ 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)
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)))))))
(* (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))))
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1
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(* (sqrt 1/2) (sqrt 2))
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(+ (* -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))))
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1
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(* (sqrt 1/2) (sqrt 2))
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1
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(/ x p)
(/ x p)
(/ x p)
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1
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(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
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2
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(+ 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))))))
1
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(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)))))
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 (/ 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))
(* -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 (* (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))
(* -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))
(* -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))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ (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 (/ (* 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
(- (* 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)
(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 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 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.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 p (/.f64 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))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.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 p (/.f64 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)))
(fma.f64 (neg.f64 p) (/.f64 p (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) 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 #s(literal 3 binary64) (pow.f64 x #s(literal 5 binary64))) p) p (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.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 p (/.f64 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) (pow.f64 x #s(literal 3 binary64)))) (*.f64 p p) (/.f64 #s(literal 1/2 binary64) x))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 #s(literal -2 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 3 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 (pow.f64 p #s(literal 4 binary64)) (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 5 binary64)))) #s(literal 4 binary64) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) 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))))
(+ (* (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 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 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 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.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 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x)) (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 p p) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 p p) (/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 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))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.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 p (/.f64 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))
(* (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)))
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1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
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(* (sqrt 1/2) (sqrt 2))
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1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
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(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
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(* 1/4 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
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(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
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(* (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)))
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2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 2 binary64))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
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(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
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1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
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(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
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(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
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(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
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(+ (* 4 (pow p 2)) (pow x 2))
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(+ (* 4 (pow p 2)) (pow x 2))
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x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
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(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
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(/ 1/4 p)
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(/ (+ 1/4 (* -1/32 (/ (pow x 2) (pow p 2)))) p)
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(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x (/.f64 x p)) #s(literal 2 binary64)) p)
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
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(* 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)))))))
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(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
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(fma.f64 (fma.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) p) #s(literal -1/32 binary64)) x (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/4 binary64))) x (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal -3/64 binary64) (pow.f64 p #s(literal 3 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
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1
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1/2
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1/2
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(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) p)) (/.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1/2 binary64) (.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) (.f64 (.f64 x x) p)) (/.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) (/.f64 #s(literal -12 binary64) p))) (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) #s(literal 1/4 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -128 binary64) (pow.f64 p #s(literal 8 binary64))))) (.f64 (pow.f64 x #s(literal 6 binary64)) p)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (/.f64 (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))
(/ (pow p 2) (pow x 2))
(*.f64 (/.f64 p x) (/.f64 p x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (.f64 p p)) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (fma.f64 p p (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #s(literal 1/2 binary64) (.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x))) (fma.f64 p p (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #s(literal 1/2 binary64) (.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
(* 1/4 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ (pow p 2) (pow x 2))
(*.f64 (/.f64 p x) (/.f64 p x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (.f64 p p)) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (fma.f64 p p (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #s(literal 1/2 binary64) (.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x))) (fma.f64 p p (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #s(literal 1/2 binary64) (.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (neg.f64 p) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) p)) (/.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (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 (/ (+ (* 1/4 (/ (* (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 1/4 binary64) (.f64 (.f64 x x) p)) (/.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1/2 binary64) (.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) (.f64 (.f64 x x) p)) (/.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) (/.f64 #s(literal -12 binary64) p))) (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) #s(literal 1/4 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -128 binary64) (pow.f64 p #s(literal 8 binary64))))) (.f64 (pow.f64 x #s(literal 6 binary64)) p)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 p p)) (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p))) (/.f64 (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))
(* 2 (/ (pow p 2) (pow x 2)))
(.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) 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 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) 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 #s(literal 1/2 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (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 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)) (pow.f64 x #s(literal 4 binary64))))) (.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) (+.f64 (/.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 binary64))) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x))) (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 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal -12 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal -1 binary64)))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
(fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal -12 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 x x))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 x x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) 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 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x))

rewrite140.0ms (1.9%)

Memory

-5.9MiB live, 263.9MiB allocated

Rules

3 944×	`lower-/.f32`
3 938×	`lower-/.f64`
3 916×	`lower-fma.f32`
3 910×	`lower-fma.f64`
3 622×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	271
0	55	260
1	202	254
2	1188	254
0	8608	252

Stop Event

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

Counts

18 → 408

Calls

Call 1

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

Outputs
(.f64 (sqrt.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (pow.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)) #s(literal 1/4 binary64)) (pow.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)) #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))) (/.f64 #s(literal 1 binary64) (sqrt.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)))))
(.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 (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 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 (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 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (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 (/.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 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (sqrt.f64 (pow.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 (/.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 binary64))))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (pow.f64 (pow.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 (/.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 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.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)))) #s(literal 1/2 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 #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 1/4 binary64))
(pow.f64 (pow.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)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.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)) #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 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 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #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 (/.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 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #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 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -3/2 binary64)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))) (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) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -3/2 binary64)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal 1 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 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
(/.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 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 (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #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 (/.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 (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 (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))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (.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))))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (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 (/.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 #s(literal 1 binary64) (/.f64 (sqrt.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))) (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)))))
(/.f64 #s(literal 1 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) (-.f64 #s(literal 1/4 binary64) (.f64 (.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))))) (sqrt.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 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)))))
(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)))
(exp.f64 (.f64 (log.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))) #s(literal 1/2 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (pow.f64 (-.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)))
(.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -3/2 binary64)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))) (pow.f64 (-.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)))
(.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -3/2 binary64)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.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))) (/.f64 #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 1/2 binary64)))))
(.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))) (/.f64 #s(literal 1 binary64) (neg.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)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (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 (/.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 (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 (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 binary64)))
(.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (.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))))))
(.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (pow.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 (/.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 binary64)))
(.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal 1/2 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)))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 (neg.f64 x) x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)))) (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) p) p))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 (neg.f64 x) x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) p) p)))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 (neg.f64 x) x))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))
(/.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64))))))
(/.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) p) p)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (/.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 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (.f64 (.f64 #s(literal 4 binary64) p) p))
(fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))
(fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 (neg.f64 x) x)))))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (.f64 #s(literal 4 binary64) p) p))
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(fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(fma.f64 p (.f64 #s(literal 4 binary64) p) (.f64 x x))
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(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 4 binary64) p) p))) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (-.f64 (.f64 x x) (.f64 (*.f64 #s(literal 4 binary64) p) p))))
(-.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 (neg.f64 x) x))))
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(+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 (neg.f64 x) x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 p p) #s(literal 4 binary64) (*.f64 (neg.f64 x) x)))))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 4 binary64) p) p))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (neg.f64 x))))
(.f64 #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (neg.f64 x)) #s(literal 1 binary64))
#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))
(/.f64 (neg.f64 #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))) #s(literal -1 binary64))
(/.f64 #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x)) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))))

eval127.0ms (1.8%)

Memory: 16.0MiB live, 293.1MiB allocated
Compiler: Compiled 19 562 to 2 626 computations (86.6% saved)

prune21.0ms (0.3%)

Memory

-15.2MiB live, 70.7MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	833	3	836
Fresh	2	0	2
Picked	2	3	5
Done	0	0	0
Total	837	6	843

Accuracy

100.0%

Counts

843 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.6%	(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)))
▶	59.0%	(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x)))))))
✓	54.5%	(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))))
✓	58.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	25.4%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x))
▶	35.0%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 64 to 49 computations (23.4% saved)

simplify257.0ms (3.6%)

Memory

27.2MiB live, 186.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

7 656×	`lower-fma.f32`
7 654×	`lower-fma.f64`
3 144×	`lower-*.f32`
3 138×	`lower-*.f64`
1 792×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	205
0	43	203
1	70	203
2	109	203
3	184	203
4	379	203
5	872	203
6	2028	203
7	4167	203
8	5419	203
9	6135	203
10	6342	203
11	6394	203
12	6415	203
13	6418	203
14	6541	203
15	6587	203
16	6587	203
17	7336	203
0	8410	198

Stop Event

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

Calls

Call 1

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

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

localize101.0ms (1.4%)

Memory

-15.4MiB live, 227.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	5.408936598885739	(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))
accuracy	8.23837478572806	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x))))))
accuracy	12.564069571191498	(-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
accuracy	13.469552762971226	(sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))
accuracy	0	(/.f64 (neg.f64 p) x)
accuracy	0	(neg.f64 p)
accuracy	47.71580431600188	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x))
accuracy	41.60077985514111	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

Samples

30.0ms	61×	2	valid
23.0ms	138×	0	valid
19.0ms	25×	3	valid
10.0ms	32×	1	valid

Compiler

Compiled 211 to 29 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-div: 14.0ms (22.6% of total)

ival-sqrt: 12.0ms (19.4% of total)

ival-mult: 12.0ms (19.4% of total)

ival-add: 10.0ms (16.1% of total)

adjust: 8.0ms (12.9% of total)

ival-sub: 4.0ms (6.5% of total)

ival-neg: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.5%)

Memory

-0.3MiB live, 80.6MiB allocated

Counts

10 → 228

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 p) (#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 (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#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 (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#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 (+ 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 #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 1 (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) #<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 #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) #<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 #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* -1 p) (taylor 0 p) (#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow p 2) (pow x 2))) (taylor 0 p) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow p 2) (+ (* (pow p 2) (- (* 32 (/ (pow p 2) (pow x 6))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -128 (/ (pow p 2) (pow x 8))) (* 32 (/ 1 (pow x 6))))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x))))))) (patch (sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #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 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x))))))) (patch (sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #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 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x))))))) (patch (sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x))))))) #<representation binary64>) () ())) ())
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#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 #s(literal 4 binary64) p) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) 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 #s(literal 4 binary64) p) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) 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 #s(literal 4 binary64) p) p (.f64 x x))))) (patch (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg p) x) (neg p) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
5.0ms	p	@	inf	((sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg p) x) (neg p) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
4.0ms	x	@	-inf	((sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg p) x) (neg p) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
3.0ms	p	@	0	((sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg p) x) (neg p) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
2.0ms	x	@	0	((sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg p) x) (neg p) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (sqrt (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

simplify155.0ms (2.2%)

Memory

-5.4MiB live, 313.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 330×	`lower-fma.f64`
8 330×	`lower-fma.f32`
6 904×	`lower-*.f64`
6 904×	`lower-*.f32`
3 134×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	745	5554
1	2296	5399
0	8017	5046

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 226

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

rewrite162.0ms (2.3%)

Memory

-2.5MiB live, 314.9MiB allocated

Rules

4 814×	`lower-fma.f32`
4 812×	`lower-fma.f64`
4 662×	`lower-/.f32`
4 654×	`lower-/.f64`
4 354×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	160
0	43	158
1	179	158
2	1136	128
0	8441	126

Stop Event

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

Counts

10 → 282

Calls

Call 1

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

Outputs
#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)) (/.f64 (neg.f64 p) x))
(.f64 (.f64 (neg.f64 p) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (neg.f64 x) p))))
(*.f64 #s(literal -1 binary64) (/.f64 p x))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) p) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 p))
(*.f64 (neg.f64 p) (pow.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 p) x))
(*.f64 p (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (neg.f64 x) p) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 0 binary64) x) #s(literal 3 binary64)) (pow.f64 (/.f64 p x) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 0 binary64) x) (fma.f64 (/.f64 p x) (/.f64 p x) (*.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 p x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 p x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (/.f64 p x) (/.f64 p x) (*.f64 #s(literal 0 binary64) (/.f64 p x)))))
(/.f64 (neg.f64 (*.f64 (neg.f64 p) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 x)) (.f64 x (neg.f64 p))) (*.f64 (neg.f64 x) x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x p)) (.f64 x #s(literal 1 binary64))) (*.f64 x (/.f64 x p)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 x p)) (*.f64 x x))
(/.f64 (*.f64 (neg.f64 p) #s(literal 1 binary64)) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (neg.f64 x) p)))
(/.f64 (neg.f64 p) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 p) x)
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (neg.f64 p) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (neg.f64 x) p))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p))
(/.f64 p (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 p (neg.f64 x))
(neg.f64 (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 x))) (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 p p)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) p)))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 p #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 p p (.f64 #s(literal 0 binary64) p)))))
(*.f64 #s(literal -1 binary64) p)
(*.f64 p #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 p) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 p p) (.f64 #s(literal 0 binary64) (neg.f64 p)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 p p))) (neg.f64 (+.f64 #s(literal 0 binary64) p)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 p #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 p p (*.f64 #s(literal 0 binary64) p)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 p p)) (+.f64 #s(literal 0 binary64) p))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 p #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 p p (*.f64 #s(literal 0 binary64) p))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) (*.f64 p p))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (fma.f64 p p (*.f64 #s(literal 0 binary64) p))) (-.f64 #s(literal 0 binary64) (pow.f64 p #s(literal 3 binary64)))))
(neg.f64 p)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) p)) (/.f64 (*.f64 p p) (+.f64 #s(literal 0 binary64) p)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 p p (.f64 #s(literal 0 binary64) p)))) (/.f64 (pow.f64 p #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 p p (.f64 #s(literal 0 binary64) p)))))
(-.f64 #s(literal 0 binary64) p)
(+.f64 #s(literal 0 binary64) (neg.f64 p))
(.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 4 binary64)))) (pow.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64)))) (pow.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 (neg.f64 x) (/.f64 x (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) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 4 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 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64))))) (neg.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 4 binary64))) #s(literal 1/2 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 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 4 binary64)))) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64)))) (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 4 binary64))) #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 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64))) #s(literal 1/2 binary64)) (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #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 #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 4 binary64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 6 binary64))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))))
(.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (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 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #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 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (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 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))))
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(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))))
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(/.f64 #s(literal 1 binary64) (pow.f64 (-.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 (/.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 (neg.f64 (neg.f64 x)) (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal -1 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) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1 binary64))
(fma.f64 x (neg.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 x (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (+.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) (/.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 (/.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) (+.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) (/.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 #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 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(-.f64 (pow.f64 (+.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))) #s(literal -1 binary64)) (/.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 3 binary64)) (+.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #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 (/.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)))))

eval76.0ms (1.1%)

Memory: 10.3MiB live, 204.5MiB allocated
Compiler: Compiled 18 924 to 2 090 computations (89% saved)

prune15.0ms (0.2%)

Memory

16.1MiB live, 55.5MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	505	3	508
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	505	9	514

Accuracy

100.0%

Counts

514 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.6%	(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)))
▶	59.8%	(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (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))))))))
✓	59.0%	(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x)))))))
▶	59.8%	(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.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)))))))))
✓	54.5%	(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))))
✓	58.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	25.4%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x))
▶	25.4%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p)))
✓	35.0%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 167 to 97 computations (41.9% saved)

simplify204.0ms (2.8%)

Memory

-13.0MiB live, 351.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	128	(-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))
cost-diff	128	(/.f64 (fma.f64 (neg.f64 x) (/.f64 x (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))))))
cost-diff	128	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64))
cost-diff	5760	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (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)))))))
cost-diff	128	(-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))
cost-diff	128	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64))
cost-diff	448	(.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.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)))))))
cost-diff	5760	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.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))))))))
cost-diff	0	(neg.f64 x)
cost-diff	0	(/.f64 (neg.f64 x) p)
cost-diff	0	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p))

Rules

23 152×	`lower-fma.f32`
23 148×	`lower-fma.f64`
4 150×	`lower-*.f32`
4 142×	`lower-*.f64`
2 714×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	549
0	59	554
1	111	411
2	223	409
3	583	409
4	2335	409
5	5519	409
0	8626	400

Stop Event

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

Calls

Call 1

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

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

localize155.0ms (2.2%)

Memory

-13.5MiB live, 464.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	8.23837478572806	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (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)))))))
accuracy	12.564069571191498	(-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
accuracy	13.469552762971226	(sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))
accuracy	28.528485459922965	(fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64))
accuracy	8.23837478572806	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.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))))))))
accuracy	12.564069571191498	(-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))))
accuracy	13.469552762971226	(sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))
accuracy	28.528485459922965	(fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64))
accuracy	0	(/.f64 (neg.f64 x) p)
accuracy	0	(neg.f64 x)
accuracy	0.4686071220384187	(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p))
accuracy	47.71580431600188	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p)))

Samples

44.0ms	62×	2	valid
36.0ms	138×	0	valid
23.0ms	24×	3	valid
15.0ms	32×	1	valid

Compiler

Compiled 587 to 38 computations (93.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-div: 25.0ms (29.1% of total)

ival-mult: 19.0ms (22.1% of total)

ival-sqrt: 17.0ms (19.8% of total)

adjust: 10.0ms (11.6% of total)

ival-add: 9.0ms (10.5% of total)

ival-sub: 4.0ms (4.7% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series59.0ms (0.8%)

Memory

13.1MiB live, 138.8MiB allocated

Counts

13 → 300

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	p	@	-inf	((/ 1 (/ (neg x) p)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg x) p) (neg x) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))))) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))
6.0ms	p	@	inf	((/ 1 (/ (neg x) p)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg x) p) (neg x) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))))) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))
3.0ms	p	@	0	((/ 1 (/ (neg x) p)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg x) p) (neg x) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))))) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))
3.0ms	x	@	-inf	((/ 1 (/ (neg x) p)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg x) p) (neg x) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))))) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))
2.0ms	x	@	inf	((/ 1 (/ (neg x) p)) (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/ (neg x) p) (neg x) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))))) (* (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (/ 1 (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))) (/ (* (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))) 1/2) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (- 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg x) (/ x (+ (* (* 4 p) p) (* x x)))) 1) (sqrt (+ (* (* 4 p) p) (* x x))) (- 1 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))

simplify179.0ms (2.5%)

Memory

18.6MiB live, 370.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 328×	`lower-fma.f64`
9 328×	`lower-fma.f32`
6 728×	`lower-*.f64`
6 728×	`lower-*.f32`
3 356×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	665	6022
1	2059	5933
2	6829	5874
0	8451	5455

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 298

Calls

Call 1

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

Outputs
(* -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
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 p (/.f64 p x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.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 p (/.f64 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 (/ x p))
(/.f64 (neg.f64 x) p)
(* -1 (/ x p))
(/.f64 (neg.f64 x) p)
(* -1 (/ x p))
(/.f64 (neg.f64 x) p)
(* -1 (/ x p))
(/.f64 (neg.f64 x) p)
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.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 p (/.f64 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))
(* 2 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) p) p)
(* (pow p 2) (+ (* -6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal -6 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* 20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64))) p) p (/.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))
(* (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)))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 8 binary64)))) #s(literal -70 binary64) (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.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))
(* 2 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) p) p)
(* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal -8 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* 32 (/ (pow p 2) (pow x 6))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 6 binary64))) p) p (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -128 (/ (pow p 2) (pow x 8))) (* 32 (/ 1 (pow x 6))))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -128 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 8 binary64)))) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 p p))
2
#s(literal 2 binary64)
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 p (/.f64 p 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 (.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.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 p (/.f64 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 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.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 p (/.f64 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))
(* 2 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) p) p)
(* (pow p 2) (+ (* -6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal -6 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* 20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64))) p) p (/.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))
(* (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)))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 8 binary64)))) #s(literal -70 binary64) (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.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))
(* 4 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) p) p)
(* (pow p 2) (+ (* -16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal -16 binary64) (.f64 p (/.f64 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 (.f64 (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) 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))
(* (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 #s(literal -256 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 8 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))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 3 binary64)))) #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 (pow.f64 p #s(literal 4 binary64)) (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 5 binary64)))) #s(literal 4 binary64) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))
(* 4 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) p) p)
(* (pow p 2) (+ (* -16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal -16 binary64) (.f64 p (/.f64 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 (.f64 (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))) 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))
(* (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 #s(literal -256 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 8 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 (/ 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)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/128 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (/.f64 (/.f64 x p) p) (/.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) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/128 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (/.f64 (/.f64 x p) p) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) x (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 p #s(literal 3 binary64))) (/.f64 (fma.f64 #s(literal 1/512 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (*.f64 #s(literal -1/32 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (/ x p))
(/.f64 (neg.f64 x) p)
(* -1 (/ x p))
(/.f64 (neg.f64 x) p)
(* -1 (/ x p))
(/.f64 (neg.f64 x) p)
(* -1 (/ x p))
(/.f64 (neg.f64 x) p)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal -1/32 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(fma.f64 (.f64 (.f64 #s(literal -3/256 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal -1/2 binary64) (fma.f64 (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal -1/32 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ x p)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) p) x #s(literal 1 binary64))
(- (+ 1 (* 1/16 (/ (pow x 3) (pow p 3)))) (* 1/2 (/ x p)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) p) x (fma.f64 #s(literal 1/16 binary64) (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal 1 binary64)))
(- (+ 1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(fma.f64 (*.f64 #s(literal -3/256 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 x (pow.f64 p #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal -1/2 binary64) p) x (fma.f64 #s(literal 1/16 binary64) (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal 1 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 (/ (pow x 2) (pow p 2))))
(fma.f64 (/.f64 #s(literal -1/8 binary64) p) (*.f64 x (/.f64 x p)) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/8 (/ (pow x 2) (pow p 2))) (* 1/32 (/ (pow x 4) (pow p 4)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal 1/32 binary64) (fma.f64 (/.f64 #s(literal -1/8 binary64) p) (*.f64 x (/.f64 x p)) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/8 (/ (pow x 2) (pow p 2))) (+ (* -1/128 (/ (pow x 6) (pow p 6))) (* 1/32 (/ (pow x 4) (pow p 4))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) #s(literal -1/128 binary64) (/.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 p #s(literal 4 binary64)))) (fma.f64 (/.f64 #s(literal -1/8 binary64) p) (.f64 x (/.f64 x p)) #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ x p)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) p) x #s(literal 1 binary64))
(- (+ 1 (* -1/16 (/ (pow x 3) (pow p 3)))) (* -1/2 (/ x p)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) p) x (fma.f64 #s(literal -1/16 binary64) (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal 1 binary64)))
(- (+ 1 (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5)))) (+ (* -1/2 (/ x p)) (* 1/16 (/ (pow x 3) (pow p 3)))))
(fma.f64 (neg.f64 (*.f64 #s(literal -3/256 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 x (pow.f64 p #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) p) x (fma.f64 #s(literal -1/16 binary64) (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal 1 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 (pow.f64 (/.f64 x p) #s(literal 3 binary64)) #s(literal -1/32 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
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(/.f64 (fma.f64 (/.f64 #s(literal -8 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (.f64 (.f64 #s(literal 2 binary64) p) p))) (*.f64 x x))
(/ (+ (* -128 (/ (pow p 8) (pow x 6))) (+ (* -8 (/ (pow p 4) (pow x 2))) (+ (* 2 (pow p 2)) (* 32 (/ (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 -128 binary64) (fma.f64 (/.f64 #s(literal -8 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 32 binary64) (.f64 (.f64 #s(literal 2 binary64) p) p)))) (*.f64 x x))
(* 2 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) p) p)
(/ (- (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -2 (pow p 2))) (pow x 2))
(fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) p) p (/.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 4 binary64))))
(/ (- (* 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))
(/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 2 binary64) p) p)) (*.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))) (+ (* -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))
(/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 p p)) #s(literal 2 binary64) (fma.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 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))) #s(literal 1/2 binary64) (fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal -12 binary64) x) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 2 binary64) p) p))) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(*.f64 (/.f64 p x) (/.f64 p x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (.f64 p p)) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) x) (fma.f64 p p (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 p p)) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 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 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 p p)) #s(literal 2 binary64) (fma.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 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)) x) (/.f64 #s(literal -12 binary64) x))) (fma.f64 p p (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 p p)) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
2
#s(literal 2 binary64)
(- (+ 2 (* -8 (/ (pow p 2) (pow x 2)))) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) (/.f64 #s(literal -12 binary64) p)) (fma.f64 (/.f64 #s(literal -8 binary64) x) (*.f64 p (/.f64 p x)) #s(literal 2 binary64)))
(- (+ 2 (+ (* -8 (/ (pow p 2) (pow x 2))) (* 32 (/ (pow p 4) (pow x 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) (pow x 4)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (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 p 2) (pow x 4)))))))
(-.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal -8 binary64) x) (.f64 p (/.f64 p x)) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) p) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 #s(literal -8 binary64) (.f64 p p))) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p)) (.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) (/.f64 #s(literal -12 binary64) (.f64 p p)) (/.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 p p))) #s(literal 1/2 binary64))))
(- (+ 2 (+ (* -128 (/ (pow p 6) (pow x 6))) (+ (* -8 (/ (pow p 2) (pow x 2))) (* 32 (/ (pow p 4) (pow x 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) (pow x 4)))) (+ (* 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) (pow x 6)))) (+ (* 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) (pow x 6)))) (+ (* 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 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (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 p 2) (pow x 4))))))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -128 binary64) (fma.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal 32 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal -8 binary64) x) (.f64 p (/.f64 p x)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) p) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 #s(literal -8 binary64) (.f64 p p))) (.f64 p p)) (.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal -12 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 32 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) p) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) p) (.f64 (/.f64 (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) p) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 #s(literal -8 binary64) (.f64 p p))) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p)) #s(literal -1/4 binary64)))) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) p) p)))) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 p p)) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (/.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) p) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 #s(literal -8 binary64) (.f64 p p))) (pow.f64 x #s(literal 6 binary64))) (.f64 p p)) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (/.f64 (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (.f64 p p)) #s(literal 2 binary64) (fma.f64 (.f64 #s(literal 144 binary64) (pow.f64 p #s(literal 8 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 p p)) (fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) (/.f64 #s(literal -12 binary64) (.f64 p p)) (/.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))) (pow.f64 x #s(literal 4 binary64))) (*.f64 p p))))))))
(* 4 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) p) p)
(/ (+ (* -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 #s(literal -16 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) 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 #s(literal -16 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64)))))) (*.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 (pow.f64 p #s(literal 8 binary64)) (/.f64 #s(literal -256 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal -16 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64))))))) (*.f64 x x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p (/.f64 p x)) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(.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 #s(literal 2 binary64) x) (.f64 p (/.f64 p x)) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(neg.f64 (fma.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) p) p (/.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))))) x x))
(* 4 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) p) p)
(/ (+ (* -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 #s(literal -16 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) 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 #s(literal -16 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64)))))) (*.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 (pow.f64 p #s(literal 8 binary64)) (/.f64 #s(literal -256 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal -16 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 4 binary64))))))) (*.f64 x x))

rewrite212.0ms (2.9%)

Memory

-26.0MiB live, 572.7MiB allocated

Rules

4 982×	`lower-/.f32`
4 966×	`lower-/.f64`
4 852×	`lower-*.f32`
4 844×	`lower-*.f64`
2 016×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	257
0	55	252
1	244	183
2	1732	153
0	8617	150

Stop Event

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

Counts

13 → 944

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (/.f64 (neg.f64 p) x) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (neg.f64 p) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 (neg.f64 p) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 p #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 p))
(*.f64 (pow.f64 p #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 (pow.f64 p #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 p #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(*.f64 (/.f64 (neg.f64 p) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 x p) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 p x))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 p) x))
(pow.f64 (exp.f64 (log.f64 (/.f64 (neg.f64 x) p))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (neg.f64 x) p) (/.f64 (neg.f64 x) p)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (neg.f64 p) x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (neg.f64 p) x) #s(literal 1 binary64))
(pow.f64 (/.f64 (neg.f64 x) p) #s(literal -1 binary64))
(/.f64 (neg.f64 (/.f64 p #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (pow.f64 p #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) p)) x)
(/.f64 (/.f64 p #s(literal -1 binary64)) x)
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(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 x x) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 (neg.f64 x) x)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (.f64 x x) (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64))))) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) (/.f64 x (pow.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 x) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 x (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64))))) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 x) (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 x (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 (neg.f64 x) x)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 x (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (neg.f64 x) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 (neg.f64 x) x)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 x (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (neg.f64 x) (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64))))) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 (neg.f64 x) x)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 (neg.f64 x) x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64))))) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64))))) #s(literal 1 binary64))
(fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64))
(fma.f64 (/.f64 (neg.f64 x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -1 binary64)) (/.f64 (neg.f64 x) (pow.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 (neg.f64 x) x) (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x) #s(literal 1 binary64))
(fma.f64 (.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))
(fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) (*.f64 (neg.f64 x) #s(literal 1 binary64)) #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))
(fma.f64 (.f64 x x) (neg.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64))
(fma.f64 x (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) #s(literal -1 binary64)) (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 x (neg.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.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 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) #s(literal -1 binary64)) (/.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) x) x)))) (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) #s(literal -1 binary64)) (/.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)) x) x)))))
(-.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)))))
(-.f64 (pow.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) (neg.f64 x) #s(literal -1 binary64))) (pow.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 (pow.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (fma.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x #s(literal 1 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) x))
(+.f64 (.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)))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))
(+.f64 #s(literal 1 binary64) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))) (neg.f64 x)))

eval283.0ms (3.9%)

Memory: 13.1MiB live, 756.8MiB allocated
Compiler: Compiled 93 404 to 4 971 computations (94.7% saved)

prune43.0ms (0.6%)

Memory

-0.1MiB live, 139.1MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	1 732	3	1 735
Fresh	0	0	0
Picked	3	0	3
Done	0	6	6
Total	1 735	9	1 744

Accuracy

100.0%

Counts

1 744 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.6%	(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)))
	59.8%	(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) 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)))))
	55.5%	(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #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 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))
✓	59.0%	(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x)))))))
✓	54.5%	(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))))
✓	58.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	25.4%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 (neg.f64 p) x))
	25.4%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal -1 binary64) (/.f64 x p)))
✓	35.0%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 479 to 181 computations (62.2% saved)

regimes36.0ms (0.5%)

Memory

9.9MiB live, 89.1MiB allocated

Counts

17 → 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 (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal -1 binary64) (/.f64 x p)))
#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p)))
(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 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (neg.f64 x))))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p 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) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (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 #s(literal 4 binary64) p) p (.f64 x x)))))))
(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) 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)))))
(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #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 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x))))))))
(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (neg.f64 x) (/.f64 x (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))))))))
(sqrt.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) #s(literal 1 binary64)) (/.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)))))))))

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

7 calls:

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

Results

Accuracy	Segments	Branch
82.1%	1	`p`
84.8%	2	`x`
100.0%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
100.0%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
100.0%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
82.1%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 66 to 56 computations (15.2% saved)

regimes13.0ms (0.2%)

Memory

-6.7MiB live, 33.0MiB allocated

Counts

10 → 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 (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal -1 binary64) (/.f64 x p)))
#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p)))
(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 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (neg.f64 x))))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p 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)) #s(literal 1 binary64))

Calls

4 calls:

4.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
3.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

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

Compiler

Compiled 59 to 47 computations (20.3% saved)

regimes11.0ms (0.1%)

Memory

-19.1MiB live, 21.4MiB allocated

Counts

6 → 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 (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal -1 binary64) (/.f64 x p)))
#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* (* p 4) p) (* x x)))) x) 1/2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) p)))

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:

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))))))
2.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
2.0ms	(+.f64 #s(literal 1 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 59 to 47 computations (20.3% saved)

regimes12.0ms (0.2%)

Memory

29.3MiB live, 29.3MiB 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	p
2.0ms	x
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
72.2%	2	`p`
72.2%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
62.5%	2	`x`
76.6%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
76.6%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
76.6%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
76.6%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 66 to 56 computations (15.2% saved)

regimes11.0ms (0.1%)

Memory

-12.9MiB live, 25.2MiB 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 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
1.0ms	p
1.0ms	x
1.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
1.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)

Results

Accuracy	Segments	Branch
35.0%	1	`x`
35.0%	1	`p`
35.0%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
35.0%	1	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
35.0%	1	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
35.0%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
35.0%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 66 to 56 computations (15.2% saved)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.9756023968610845

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0009178352095605457	1.0
0.0ms	-0.9756023968610845	-0.14553608560620748

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.0009178352095605457	1.0
0.0ms	-0.9756023968610845	-0.14553608560620748

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch13.0ms (0.2%)

Memory

-17.6MiB live, 19.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.0009178352095605457	1.0

Samples

5.0ms

128×

valid

Compiler

Compiled 60 to 107 computations (-78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 1.0ms (41.2% of total)

ival-mult: 1.0ms (41.2% of total)

ival-sqrt: 1.0ms (41.2% of total)

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

exact: 0.0ms (0% of total)

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

simplify25.0ms (0.4%)

Memory

15.0MiB live, 53.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`-commutative-binary64-.f64`
8×	`+-commutative-binary64-+.f64`
6×	`neg-sub0-binary64--.f64-neg.f64`
6×	`neg-mul-1-binary64-*.f64-neg.f64`
6×	`sub-neg-binary64-neg.f64-+.f64--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	309
1	68	309
2	74	309
3	79	309
4	82	309
5	83	309

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ 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)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 1152921504606847/1152921504606846976 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)) #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 1152921504606847/1152921504606846976 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 -1 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 -1 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)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 1152921504606847/1152921504606846976 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)) #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 1152921504606847/1152921504606846976 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)) #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 1152921504606847/1152921504606846976 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 1152921504606847/1152921504606846976 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))

soundness407.0ms (5.7%)

Memory

6.4MiB live, 407.3MiB allocated

Rules

9 590×	`lower-fma.f64`
9 590×	`lower-fma.f32`
7 978×	`lower-fma.f64`
7 978×	`lower-fma.f32`
6 900×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	2486
1	1325	2377
2	4611	2304
0	8084	2141
0	14	66
0	23	66
1	77	66
2	501	66
3	6967	66
0	8492	59
0	664	9334
1	2017	8844
2	6920	8718
0	8136	8138

Stop Event

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

Compiler

Compiled 305 to 192 computations (37% saved)

preprocess74.0ms (1%)

Memory: -1.2MiB live, 112.8MiB allocated
Compiler: Compiled 416 to 176 computations (57.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	35	292
0	55	281
1	90	275
2	107	275
3	112	275
4	115	275
5	119	275
6	152	275
7	194	275
8	213	275
9	217	275
0	217	273

Iter	Nodes	Cost
0	35	292
0	55	281
1	90	275
2	107	275
3	112	275
4	115	275
5	119	275
6	152	275
7	194	275
8	213	275
9	217	275
0	217	273

start0.0ms (0%)

analyze466.0ms (6.5%)

sample2.4s (33.9%)

explain261.0ms (3.6%)

preprocess80.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize68.0ms (0.9%)

series26.0ms (0.4%)

simplify221.0ms (3.1%)

rewrite174.0ms (2.4%)

eval136.0ms (1.9%)

prune11.0ms (0.2%)

simplify50.0ms (0.7%)

localize136.0ms (1.9%)

series37.0ms (0.5%)

simplify246.0ms (3.4%)

rewrite140.0ms (1.9%)

eval127.0ms (1.8%)

prune21.0ms (0.3%)

simplify257.0ms (3.6%)

localize101.0ms (1.4%)

series35.0ms (0.5%)

simplify155.0ms (2.2%)

rewrite162.0ms (2.3%)

eval76.0ms (1.1%)

prune15.0ms (0.2%)

simplify204.0ms (2.8%)

localize155.0ms (2.2%)

series59.0ms (0.8%)

simplify179.0ms (2.5%)

rewrite212.0ms (2.9%)

eval283.0ms (3.9%)

prune43.0ms (0.6%)

regimes36.0ms (0.5%)

regimes13.0ms (0.2%)

regimes11.0ms (0.1%)

regimes12.0ms (0.2%)

regimes11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch13.0ms (0.2%)

simplify25.0ms (0.4%)

soundness407.0ms (5.7%)

preprocess74.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	35	292
0	55	281
1	90	275
2	107	275
3	112	275
4	115	275
5	119	275
6	152	275
7	194	275
8	213	275
9	217	275
0	217	273