Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze572.0ms (6.9%)

Memory

-40.3MiB live, 870.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.5s (29.7%)

Memory

-46.7MiB live, 3 269.8MiB allocated

Samples

951.0ms	6 190×	0	valid
615.0ms	1 025×	2	valid
187.0ms	414×	3	valid
154.0ms	627×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-mult: 559.0ms (34.7% of total)

const: 303.0ms (18.8% of total)

ival-sqrt: 198.0ms (12.3% of total)

ival-div: 165.0ms (10.2% of total)

ival-add: 146.0ms (9.1% of total)

ival-fabs: 97.0ms (6% of total)

adjust: 78.0ms (4.8% of total)

ival-<: 41.0ms (2.5% of total)

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

exact: 11.0ms (0.7% of total)

ival-assert: 4.0ms (0.2% of total)

Bogosity

explain328.0ms (4%)

Memory

-10.3MiB live, 352.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
58	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
39	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
26	-	2	(8.336292274827288e-130 -3.1274853232528147e+28)	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
0	-	0	-	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`p`
0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	-	0	-	`#s(literal 1/2 binary64)`
0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	oflow-rescue	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	39	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	24	0
↳	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	underflow	9
↳	`(.f64 #s(literal 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	33
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	33
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	13
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	69

Confusion

	Predicted +	Predicted -
+	63	0
-	58	135

Precision

0.5206611570247934

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	63	0	0
-	58	1	134

Precision?

0.5163934426229508

Recall?

1.0

Freqs

test

number	freq
0	135
1	121

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms	370×	0	valid
46.0ms	66×	2	valid
42.0ms	28×	3	valid
10.0ms	48×	1	valid

Compiler

Compiled 209 to 46 computations (78% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-div: 32.0ms (29.6% of total)

ival-sqrt: 32.0ms (29.6% of total)

adjust: 17.0ms (15.8% of total)

ival-mult: 16.0ms (14.8% of total)

ival-add: 10.0ms (9.3% of total)

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

exact: 1.0ms (0.9% of total)

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

preprocess71.0ms (0.9%)

Memory

-15.6MiB live, 22.1MiB allocated

Algorithm

1×	egg-herbie

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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.1%	(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%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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)

localize54.0ms (0.7%)

Memory

10.2MiB live, 49.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 #s(literal 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	5.650184305514433	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
accuracy	8.798644286665853	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	13.496552057002047	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

27.0ms	185×	0	valid
8.0ms	33×	2	valid
5.0ms	14×	3	valid
4.0ms	24×	1	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-sqrt: 15.0ms (47.4% of total)

ival-mult: 7.0ms (22.1% of total)

ival-add: 4.0ms (12.7% of total)

ival-div: 3.0ms (9.5% of total)

adjust: 2.0ms (6.3% 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

-14.6MiB live, 23.5MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -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
20.0ms	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))))
2.0ms	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))))

simplify227.0ms (2.8%)

Memory

5.2MiB live, 130.1MiB allocated

Algorithm

1×	egg-herbie

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)))))
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x
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#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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x
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(pow x 2)
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(/ (+ (* 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))
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(/ (+ (* 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))
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(* -1 x)
(neg.f64 x)
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(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
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rewrite160.0ms (1.9%)

Memory

15.0MiB live, 211.3MiB allocated

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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eval67.0ms (0.8%)

Memory: 6.3MiB live, 129.9MiB allocated
Compiler: Compiled 12 478 to 2 045 computations (83.6% saved)

prune20.0ms (0.2%)

Memory

-32.6MiB live, 51.1MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	381	13	394
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	382	13	395

Accuracy

99.9%

Counts

395 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.1%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	72.8%	(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)))
	45.3%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
▶	7.2%	(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))))))
	45.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
	29.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
▶	16.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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))))
	14.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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))))
	22.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
	38.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	50.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	29.8%	#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)))
	28.0%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x 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)))

Compiler

Compiled 406 to 308 computations (24.1% saved)

simplify34.0ms (0.4%)

Memory

9.6MiB live, 48.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	385
0	76	370
1	128	366
2	196	366
3	376	366
4	608	366
5	710	366
6	830	366
7	955	366
8	1056	366
9	1178	366
10	1185	366
11	1189	366
0	1189	360

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize139.0ms (1.7%)

Memory

-11.2MiB live, 216.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	5.22347689713908	(/.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))
accuracy	5.650184305514433	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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))))
accuracy	15.654009654016829	(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))
accuracy	44.968556291588534	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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)))
accuracy	0	(neg.f64 x)
accuracy	0.44140625	(*.f64 p (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.47265625	(.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	44.72255219206247	#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)))
accuracy	0.00390625	(.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	5.650184305514433	(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	8.798644286665853	(+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))))
accuracy	44.870614610384656	#s(approx (sqrt (+ (* (* 4 p) p) (* x x))) (neg.f64 x))
accuracy	5.650184305514433	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	32.437567657795405	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.00390625	(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
accuracy	5.650184305514433	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	8.789957863545217	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	13.496552057002047	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))

Samples

64.0ms	185×	0	valid
20.0ms	33×	2	valid
12.0ms	14×	3	valid
11.0ms	24×	1	valid

Compiler

Compiled 328 to 41 computations (87.5% saved)

Precisions

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

ival-div: 23.0ms (29.5% of total)

ival-mult: 21.0ms (26.9% of total)

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

ival-add: 9.0ms (11.5% of total)

adjust: 6.0ms (7.7% of total)

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

exact: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

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

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

series48.0ms (0.6%)

Memory

-0.9MiB live, 80.8MiB allocated

Counts

20 → 444

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	p	@	0	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (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)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))) (neg x))
6.0ms	p	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (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)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))) (neg x))
3.0ms	x	@	-inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (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)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))) (neg x))
3.0ms	x	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (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)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))) (neg x))
3.0ms	x	@	0	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (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)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (sqrt (+ (* (* 4 p) p) (* x x))) (neg x))

simplify196.0ms (2.4%)

Memory

-6.9MiB live, 265.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	622	9482
1	1903	9015
2	6570	8890
0	8099	8347

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 440

Calls

Call 1

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

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

rewrite218.0ms (2.6%)

Memory

-1.4MiB live, 118.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	324
0	76	309
1	268	291
2	1592	291
0	8377	285

Stop Event

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

Counts

20 → 445

Calls

Call 1

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

Outputs
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eval271.0ms (3.3%)

Memory: -1.1MiB live, 156.0MiB allocated
Compiler: Compiled 21 108 to 2 837 computations (86.6% saved)

prune68.0ms (0.8%)

Memory

19.6MiB live, 59.2MiB allocated

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	901	8	909
Fresh	4	4	8
Picked	3	2	5
Done	0	0	0
Total	908	14	922

Accuracy

100.0%

Counts

922 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.1%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	77.1%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)))
	72.8%	(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)))
▶	8.2%	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	45.3%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
▶	45.2%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
	14.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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))))
▶	17.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
✓	50.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	30.0%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))
	28.3%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
	30.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
▶	38.2%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
	28.0%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x 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)))

Compiler

Compiled 438 to 322 computations (26.5% saved)

simplify137.0ms (1.7%)

Memory

-26.5MiB live, 22.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 p p)))
cost-diff	0	(/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
cost-diff	0	(fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))
cost-diff	0	#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64)))
cost-diff	0	(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 x p)
cost-diff	0	(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
cost-diff	0	(/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))
cost-diff	0	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	474
0	88	466
1	155	458
2	236	449
3	391	449
4	914	444
5	1390	444
6	1897	444
7	2132	444
8	2170	444
9	2185	444
10	2185	444
11	2185	444
12	2505	444
13	3008	444
14	3178	444
15	3218	444
16	3227	444
17	3233	444
18	3237	444
19	3237	444
20	3237	444
21	3237	444
22	3684	444
23	4469	444
0	4469	435

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize202.0ms (2.4%)

Memory

16.4MiB live, 134.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	3.1733559561478235	(/.f64 (*.f64 p p) x)
accuracy	5.22347689713908	(/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))
accuracy	5.650184305514433	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
accuracy	44.968556291588534	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)))
accuracy	3.1733559561478235	(/.f64 (*.f64 p p) x)
accuracy	5.650184305514433	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	8.789957863545217	(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	45.09093243463248	#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64)))
accuracy	0	(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
accuracy	0	(/.f64 x p)
accuracy	5.650184305514433	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
accuracy	34.99471217760045	#s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
accuracy	39.560710184548455	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
accuracy	0.14232073018988264	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x))
accuracy	5.650184305514433	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)))
accuracy	8.789957863545217	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))
accuracy	13.496552057002047	(sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))

Samples

63.0ms	185×	0	valid
45.0ms	33×	2	valid
31.0ms	14×	3	valid
30.0ms	24×	1	valid

Compiler

Compiled 343 to 53 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 125.0ms

ival-div: 43.0ms (34.4% of total)

ival-mult: 43.0ms (34.4% of total)

ival-add: 14.0ms (11.2% of total)

ival-sqrt: 13.0ms (10.4% of total)

adjust: 8.0ms (6.4% of total)

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

exact: 1.0ms (0.8% of total)

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

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

series77.0ms (0.9%)

Memory

1.1MiB live, 42.2MiB allocated

Counts

19 → 456

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (patch (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (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 (sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ ( (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 #s(approx (/ x (sqrt (+ ( (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal -1 binary64))) (patch #s(approx (/ x (sqrt (+ ( (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) (patch (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (patch #s(approx (+ ( (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 p p))) #<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 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 p) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))) #<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 binary64) (/.f64 (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))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))) #<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 binary64) (/.f64 (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))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))) #<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 binary64) (/.f64 (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))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) #<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 binary64) (/.f64 (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)) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) #<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 binary64) (/.f64 (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)) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (patch (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (patch (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (patch (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) (patch (/.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 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 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) (patch (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) (patch (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) (patch (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) (patch (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow p 2) (taylor -inf x) (#s(alt #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (patch #s(approx (+ ( (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 p p))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (taylor -inf x) (#s(alt #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (patch #s(approx (+ ( (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 p p))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (taylor -inf x) (#s(alt #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (patch #s(approx (+ ( (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 p p))) #<representation binary64>) () ())) ())
#s(alt (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (taylor -inf x) (#s(alt #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (patch #s(approx (+ ( (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (*.f64 p p))) #<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 (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
37.0ms	x	@	0	((/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2)) (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2) (/ (sqrt (+ (* (* 4 p) p) (* x x))) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 x) (/ (* p p) x)) -1) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (+ (* (* 4 p) p) (* x x))) (/ (* p p) x))
7.0ms	x	@	inf	((/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2)) (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2) (/ (sqrt (+ (* (* 4 p) p) (* x x))) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 x) (/ (* p p) x)) -1) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (+ (* (* 4 p) p) (* x x))) (/ (* p p) x))
3.0ms	x	@	-inf	((/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2)) (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2) (/ (sqrt (+ (* (* 4 p) p) (* x x))) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 x) (/ (* p p) x)) -1) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (+ (* (* 4 p) p) (* x x))) (/ (* p p) x))
3.0ms	p	@	inf	((/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2)) (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2) (/ (sqrt (+ (* (* 4 p) p) (* x x))) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 x) (/ (* p p) x)) -1) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (+ (* (* 4 p) p) (* x x))) (/ (* p p) x))
3.0ms	p	@	0	((/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) (sqrt (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2)) (+ (* (/ 1 (/ (sqrt (+ (* (* 4 p) p) (* x x))) x)) 1/2) 1/2) (/ (sqrt (+ (* (* 4 p) p) (* x x))) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 x) (/ (* p p) x)) -1) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/ (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (* x x)) (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (sqrt (+ (* (* 4 p) p) (* x x))) (/ (* p p) x))

simplify233.0ms (2.8%)

Memory

13.4MiB live, 127.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	645	8608
1	1989	8332
2	6894	8243
0	8157	7692

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 454

Calls

Call 1

Inputs
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1
(+ 1 (* 2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
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x
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(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(pow p 2)
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(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)

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

rewrite236.0ms (2.9%)

Memory

-3.1MiB live, 116.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	397
0	88	380
1	355	372
2	2262	372
0	8254	368

Stop Event

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

Counts

19 → 303

Calls

Call 1

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

Outputs
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eval157.0ms (1.9%)

Memory: 1.2MiB live, 121.8MiB allocated
Compiler: Compiled 17 806 to 2 359 computations (86.8% saved)

prune73.0ms (0.9%)

Memory

-23.4MiB live, 52.9MiB allocated

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	798	2	800
Fresh	1	6	7
Picked	1	4	5
Done	0	2	2
Total	800	14	814

Accuracy

100.0%

Counts

814 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.1%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	77.1%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)))
▶	72.8%	(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)))
▶	8.2%	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	45.3%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
✓	45.2%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
▶	14.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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))))
✓	17.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
✓	50.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	30.0%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))
▶	28.3%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
▶	30.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
✓	38.2%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
	28.0%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x 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)))

Compiler

Compiled 390 to 283 computations (27.4% saved)

simplify213.0ms (2.6%)

Memory

-1.0MiB live, 122.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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))))
cost-diff	320	(.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))))
cost-diff	320	(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))
cost-diff	7488	(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))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
cost-diff	0	(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x))
cost-diff	0	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))
cost-diff	0	#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64)))
cost-diff	0	(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(neg.f64 p)
cost-diff	0	(/.f64 (neg.f64 p) x)
cost-diff	0	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
cost-diff	0	(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	586
0	106	568
1	191	561
2	328	554
3	593	538
4	1094	496
5	2654	496
6	4840	496
7	7170	496
0	8040	487

Stop Event

1×	iter limit
1×	node limit
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
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(/.f64 (neg.f64 p) x)
(neg.f64 p)
p
x
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x
(*.f64 p p)
p
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(/.f64 (*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p)
(*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))
#s(literal -12 binary64)
(pow.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
(neg.f64 x)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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)))
(/.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))
(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))
#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 (pow.f64 p #s(literal 4 binary64)) x)
(pow.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
x
(/.f64 #s(literal -12 binary64) x)
#s(literal -12 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 4 binary64)))
(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 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))))
#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)))
#s(literal 64 binary64)
(pow.f64 p #s(literal 6 binary64))
#s(literal 6 binary64)
(pow.f64 x #s(literal 4 binary64))
(*.f64 x 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
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(/.f64 (neg.f64 p) x)
(neg.f64 p)
p
x
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64)))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))
(fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x
(*.f64 p p)
p
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) (/.f64 #s(literal -3/2 binary64) p) p) (neg.f64 x)))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x))
(/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) (/.f64 #s(literal -3/2 binary64) p) p) (neg.f64 x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)
(fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) (/.f64 #s(literal -3/2 binary64) p) p)
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(/.f64 (*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p)
(/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) p)
(*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))
(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))
#s(literal -12 binary64)
(pow.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
(neg.f64 x)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) #s(literal -3 binary64) (fma.f64 p p (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 10 binary64)) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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)))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) #s(literal -3 binary64) (fma.f64 p p (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 10 binary64)) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x)))
(/.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))
(/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) #s(literal -3 binary64) (fma.f64 p p (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 10 binary64)) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
(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))
(fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) #s(literal -3 binary64) (fma.f64 p p (/.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 10 binary64)) (pow.f64 x #s(literal 4 binary64)))))
#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))))
(fma.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) x) #s(literal -12 binary64) (/.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 40 binary64)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (pow.f64 p #s(literal 4 binary64)) x)
(pow.f64 p #s(literal 4 binary64))
p
#s(literal 4 binary64)
x
(/.f64 #s(literal -12 binary64) x)
#s(literal -12 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 4 binary64)))
(/.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 40 binary64)) (pow.f64 x #s(literal 4 binary64)))
(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 (pow.f64 p #s(literal 6 binary64)) #s(literal 40 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))))
(*.f64 #s(literal -24 binary64) (pow.f64 p #s(literal 4 binary64)))
#s(literal 2 binary64)
(*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))
(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))
(*.f64 p p)
(*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))
(*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64))
#s(literal 64 binary64)
(pow.f64 p #s(literal 6 binary64))
#s(literal 6 binary64)
(pow.f64 x #s(literal 4 binary64))
(*.f64 x x)

localize351.0ms (4.3%)

Memory

7.9MiB live, 444.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	15.748356945191393	(/.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)))
accuracy	17.408757625342524	(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))))
accuracy	18.410156250000004	(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))))
accuracy	44.178964733026845	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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)))
accuracy	0.9354382665659818	(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x))
accuracy	3.974358731008464	(/.f64 (*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p)
accuracy	4.034159058462728	(fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)
accuracy	44.91937156286616	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
accuracy	3.08310366540457	(fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))
accuracy	5.650184305514433	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	8.789957863545217	(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	45.09093243463248	#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64)))
accuracy	0	(/.f64 (neg.f64 p) x)
accuracy	0	(neg.f64 p)
accuracy	44.72255219206247	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
accuracy	0.00390625	(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))
accuracy	5.650184305514433	(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	13.496552057002047	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
accuracy	17.244409107040894	(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

122.0ms	33×	2	valid
93.0ms	185×	0	valid
68.0ms	14×	3	valid
19.0ms	24×	1	valid

Compiler

Compiled 481 to 63 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 170.0ms

ival-div: 74.0ms (43.5% of total)

ival-mult: 33.0ms (19.4% of total)

ival-add: 17.0ms (10% of total)

ival-pow: 17.0ms (10% of total)

ival-sqrt: 14.0ms (8.2% of total)

adjust: 11.0ms (6.5% of total)

ival-neg: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series70.0ms (0.8%)

Memory

18.0MiB live, 174.2MiB allocated

Counts

25 → 528

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 #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())
#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())
#s(alt (neg.f64 p) (patch (neg.f64 p) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) (patch #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x))) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)) (patch (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (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)))) (patch (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)))) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (patch (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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)))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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)))) #<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 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) (patch (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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))) #<representation binary64>) () ())
#s(alt (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)))) (patch (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)))) #<representation binary64>) () ())
#s(alt (/.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))) (patch (/.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))) #<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>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 (* x x)) (* p p)) -1) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (/ 1/8 (* x x)) (* x x) (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (+ (* 1/4 (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))) (* p p)) (* 2 (* -12 (pow p 4))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ (* (* p 4) p) (* x x)) (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (/ (* -12 (pow p 4)) p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4))) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))
7.0ms	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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 (* x x)) (* p p)) -1) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (/ 1/8 (* x x)) (* x x) (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (+ (* 1/4 (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))) (* p p)) (* 2 (* -12 (pow p 4))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ (* (* p 4) p) (* x x)) (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (/ (* -12 (pow p 4)) p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4))) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))
6.0ms	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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 (* x x)) (* p p)) -1) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (/ 1/8 (* x x)) (* x x) (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (+ (* 1/4 (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))) (* p p)) (* 2 (* -12 (pow p 4))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ (* (* p 4) p) (* x x)) (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (/ (* -12 (pow p 4)) p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4))) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))
5.0ms	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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 (* x x)) (* p p)) -1) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (/ 1/8 (* x x)) (* x x) (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (+ (* 1/4 (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))) (* p p)) (* 2 (* -12 (pow p 4))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ (* (* p 4) p) (* x x)) (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (/ (* -12 (pow p 4)) p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4))) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))
4.0ms	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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (+ (* (/ 2 (* x x)) (* p p)) -1) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (/ 1/8 (* x x)) (* x x) (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (+ (* 1/4 (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))) (* p p)) (* 2 (* -12 (pow p 4))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ (* (* p 4) p) (* x x)) (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (/ (* -12 (pow p 4)) p) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4))) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))

simplify193.0ms (2.3%)

Memory

14.8MiB live, 366.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	750	9083
1	2254	8706
2	7536	8664
0	8080	8175

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 523

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)))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
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))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 40 (pow p 6))
(pow p 2)
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(* (pow p 2) (+ 1 (* (pow p 2) (- (* 10 (/ (pow p 2) (pow x 4))) (* 3 (/ 1 (pow x 2)))))))
(* (pow p 2) (+ 1 (* (pow p 2) (- (* 10 (/ (pow p 2) (pow x 4))) (* 3 (/ 1 (pow x 2)))))))
(* -24 (pow p 4))
(* -24 (pow p 4))
(* -24 (pow p 4))
(* -24 (pow p 4))
(* (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))))))))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
p
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* -12 (pow p 3))
(* -12 (pow p 3))
(* -12 (pow p 3))
(* -12 (pow p 3))
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)))))
(* -12 (/ (pow p 4) (pow x 2)))
(* (pow p 4) (- (* 40 (/ (pow p 2) (pow x 4))) (* 12 (/ 1 (pow x 2)))))
(* (pow p 4) (- (* 40 (/ (pow p 2) (pow x 4))) (* 12 (/ 1 (pow x 2)))))
(* (pow p 4) (- (* 40 (/ (pow p 2) (pow x 4))) (* 12 (/ 1 (pow x 2)))))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(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) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* 2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 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)))))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 10 (/ (pow p 6) (pow x 4)))
(* (pow p 6) (- (* 10 (/ 1 (pow x 4))) (* 3 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 6) (- (+ (/ 1 (pow p 4)) (* 10 (/ 1 (pow x 4)))) (/ 3 (* (pow p 2) (pow x 2)))))
(* (pow p 6) (- (+ (/ 1 (pow p 4)) (* 10 (/ 1 (pow x 4)))) (/ 3 (* (pow p 2) (pow x 2)))))
(* -24 (pow p 4))
(* -24 (pow p 4))
(* -24 (pow p 4))
(* -24 (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) (+ (* -1/32 (/ (* (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))))))
(* 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))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* -12 (pow p 3))
(* -12 (pow p 3))
(* -12 (pow p 3))
(* -12 (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)))))
(* 40 (/ (pow p 6) (pow x 4)))
(* (pow p 6) (- (* 40 (/ 1 (pow x 4))) (* 12 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 6) (- (* 40 (/ 1 (pow x 4))) (* 12 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 6) (- (* 40 (/ 1 (pow x 4))) (* 12 (/ 1 (* (pow p 2) (pow x 2))))))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(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))
(* -1 (/ (+ 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)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ 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)
(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)))
(* -1/2 (/ x p))
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(* 2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 2) (- (* 2 (/ 1 (pow x 2))) (/ 1 (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)))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 40 (pow p 6))
(* 10 (/ (pow p 6) (pow x 4)))
(* (pow p 6) (- (* 10 (/ 1 (pow x 4))) (* 3 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 6) (- (+ (/ 1 (pow p 4)) (* 10 (/ 1 (pow x 4)))) (/ 3 (* (pow p 2) (pow x 2)))))
(* (pow p 6) (- (+ (/ 1 (pow p 4)) (* 10 (/ 1 (pow x 4)))) (/ 3 (* (pow p 2) (pow x 2)))))
(* -24 (pow p 4))
(* -24 (pow p 4))
(* -24 (pow p 4))
(* -24 (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 (/ (+ (* -1/2 (/ (* (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)))
(* 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))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -12 (pow p 3))
(* -12 (pow p 3))
(* -12 (pow p 3))
(* -12 (pow p 3))
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)))
(* 40 (/ (pow p 6) (pow x 4)))
(* (pow p 6) (- (* 40 (/ 1 (pow x 4))) (* 12 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 6) (- (* 40 (/ 1 (pow x 4))) (* 12 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 6) (- (* 40 (/ 1 (pow x 4))) (* 12 (/ 1 (* (pow p 2) (pow x 2))))))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(* 40 (/ (pow p 6) (pow x 4)))
(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)))))))
1/2
(+ 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)))))
(/ 1/4 p)
(+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))
(+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))
(* 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)))))
(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))
(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)))))))
1/2
(+ 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)))))
(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* -1 (pow x 2)) (* 2 (pow p 2))) (pow x 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)))))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/4 (/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4)))
(/ (+ (* -3 (* (pow p 4) (pow x 2))) (* 1/4 (+ (* -24 (pow p 6)) (* 64 (pow p 6))))) (pow x 4))
(/ (+ (* 1/4 (+ (* -24 (pow p 6)) (* 64 (pow p 6)))) (* (pow x 2) (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))))) (pow x 4))
(/ (+ (* 1/4 (+ (* -24 (pow p 6)) (* 64 (pow p 6)))) (* (pow x 2) (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))))) (pow x 4))
(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))))))))
(* 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))
(* -3/2 (/ (pow p 3) (pow x 2)))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 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)))))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (+ (* -12 (* (pow p 4) (pow x 2))) (* 64 (pow p 6)))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (+ (* -12 (* (pow p 4) (pow x 2))) (* 64 (pow p 6)))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (+ (* -12 (* (pow p 4) (pow x 2))) (* 64 (pow p 6)))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
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 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ 1/2 x)
(/ (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))) x)
(/ (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))) x)
(/ (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))))) x)
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 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))
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 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
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) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow p 2)
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(+ (* -3 (/ (pow p 4) (pow x 2))) (+ (* 1/4 (/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))
(+ (* -3 (/ (pow p 4) (pow x 2))) (+ (* 1/4 (/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(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)))))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(* -12 (/ (pow p 4) (pow x 2)))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(* -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 x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(* -1 (/ p x))
(* -1 (/ p 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))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow p 2)
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(+ (* -3 (/ (pow p 4) (pow x 2))) (+ (* 1/4 (/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))
(+ (* -3 (/ (pow p 4) (pow x 2))) (+ (* 1/4 (/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(pow 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)))))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (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))
(* -12 (/ (pow p 4) (pow x 2)))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))

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))))
(-.f64 #s(literal 1 binary64) (*.f64 (/.f64 p x) (/.f64 p x)))
(+ 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)))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 p (/.f64 p (pow.f64 x #s(literal 3 binary64)))))
(+ (* (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 (fma.f64 (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)))) (.f64 p p) (/.f64 #s(literal 2 binary64) x)) (*.f64 p p) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 #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 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 p)
(neg.f64 p)
(* -1 p)
(neg.f64 p)
(* -1 p)
(neg.f64 p)
(* -1 p)
(neg.f64 p)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 #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))))
(-.f64 #s(literal 1 binary64) (*.f64 (/.f64 p x) (/.f64 p x)))
(+ 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
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.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 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -20 binary64) (.f64 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 1 binary64))
-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))
(- (* 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))
(- (* 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
#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))
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(/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) p) p) #s(literal -1/64 binary64) (fma.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) p)) #s(literal 1/2 binary64) (+.f64 (/.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 x x)) p)) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (-.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) #s(literal -12 binary64)) (pow.f64 p #s(literal 4 binary64)) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 1/4 binary64) (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -64 binary64))) (.f64 (.f64 #s(literal -3/2 binary64) (pow.f64 p #s(literal 4 binary64))) (/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) p) p) #s(literal -1/64 binary64) (fma.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 p p)))) (.f64 (pow.f64 x #s(literal 6 binary64)) p)) (/.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) p) p) #s(literal -1/64 binary64) (fma.f64 (.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) p))) (+.f64 (/.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (pow.f64 p #s(literal 4 binary64))) p) (.f64 x x)) p)) (neg.f64 x))
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -3/2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p) (neg.f64 x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -3/2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p) (neg.f64 x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -3/2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p) (neg.f64 x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow p 2)
(*.f64 p p)
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (*.f64 p p))
(+ (* -3 (/ (pow p 4) (pow x 2))) (+ (* 1/4 (/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))
(fma.f64 (/.f64 #s(literal -3 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 10 binary64) (*.f64 p p)))
(+ (* -3 (/ (pow p 4) (pow x 2))) (+ (* 1/4 (/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))
(fma.f64 (/.f64 #s(literal -3 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 10 binary64) (*.f64 p p)))
(* -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 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) p (/.f64 (/.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (*.f64 x x) p)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))) (.f64 #s(literal 1/32 binary64) (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) p) p))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) p (/.f64 (/.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 x x) p)) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 #s(literal 1/2 binary64) (fma.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))) (.f64 #s(literal 1/32 binary64) (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) p) p))) (.f64 (.f64 #s(literal 2 binary64) p) p)) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) #s(literal -12 binary64)) (pow.f64 p #s(literal 4 binary64)) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 p p)) #s(literal 2 binary64) (.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -128 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 6 binary64)))) (.f64 (-.f64 (fma.f64 (.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))) (.f64 #s(literal 1/32 binary64) (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 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)))))) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) p (/.f64 (/.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 x x) p)) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 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))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(fma.f64 (/.f64 #s(literal -3/2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p)
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(fma.f64 (/.f64 #s(literal -3/2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p)
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(fma.f64 (/.f64 #s(literal -3/2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) 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 -3 binary64) x) (/.f64 (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 -3 binary64) x) (/.f64 (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 (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 (/.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) #s(literal -12 binary64)) (pow.f64 p #s(literal 4 binary64)) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 p p)) #s(literal 2 binary64) (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -256 binary64) (.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64) (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (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 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64)))))) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(*.f64 (/.f64 #s(literal -12 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal -24 binary64) x) (/.f64 (pow.f64 p #s(literal 6 binary64)) x) (fma.f64 (/.f64 #s(literal 64 binary64) x) (/.f64 (pow.f64 p #s(literal 6 binary64)) x) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))))) (.f64 x x))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal -24 binary64) x) (/.f64 (pow.f64 p #s(literal 6 binary64)) x) (fma.f64 (/.f64 #s(literal 64 binary64) x) (/.f64 (pow.f64 p #s(literal 6 binary64)) x) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))))) (.f64 x x))
(/ (+ (* -24 (/ (pow p 6) (pow x 2))) (+ (* -12 (pow p 4)) (* 64 (/ (pow p 6) (pow x 2))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal -24 binary64) x) (/.f64 (pow.f64 p #s(literal 6 binary64)) x) (fma.f64 (/.f64 #s(literal 64 binary64) x) (/.f64 (pow.f64 p #s(literal 6 binary64)) x) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))))) (.f64 x x))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(*.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 40 binary64) (pow.f64 x #s(literal 4 binary64))))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(*.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 40 binary64) (pow.f64 x #s(literal 4 binary64))))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(*.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 40 binary64) (pow.f64 x #s(literal 4 binary64))))
(/ (+ (* -24 (pow p 6)) (* 64 (pow p 6))) (pow x 4))
(*.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 40 binary64) (pow.f64 x #s(literal 4 binary64))))

rewrite182.0ms (2.2%)

Memory

0.4MiB live, 362.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	464
0	106	448
1	422	423
2	3027	415
0	8422	406

Stop Event

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

Counts

25 → 586

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)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
(/.f64 (neg.f64 p) x)
(neg.f64 p)
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
#s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(*.f64 x x)
(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 #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 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (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))))
(fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)
(/.f64 (*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p)
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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)))
(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 (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)))

Outputs
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eval190.0ms (2.3%)

Memory: -30.4MiB live, 484.0MiB allocated
Compiler: Compiled 33 142 to 4 081 computations (87.7% saved)

prune39.0ms (0.5%)

Memory

28.4MiB live, 146.9MiB allocated

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	1 163	3	1 166
Fresh	1	2	3
Picked	2	3	5
Done	0	6	6
Total	1 166	14	1 180

Accuracy

100.0%

Counts

1 180 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.1%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	77.1%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)))
✓	72.8%	(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)))
✓	8.2%	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	45.3%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
✓	45.2%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
	15.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) #s(approx (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4))) (.f64 (fma.f64 #s(literal 40 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -12 binary64) (.f64 x x))) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p)) (*.f64 x x))))
✓	17.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
	17.7%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* 1/4 (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))) (* p p)) (.f64 (fma.f64 (fma.f64 #s(literal 10 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -3 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
✓	50.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	30.0%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))
✓	30.1%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
	29.7%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (-.f64 (*.f64 (pow.f64 (/.f64 p x) #s(literal 3 binary64)) #s(literal 3/2 binary64)) (/.f64 p x))))
✓	38.2%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 626 to 321 computations (48.7% saved)

regimes53.0ms (0.6%)

Memory

10.2MiB live, 130.4MiB allocated

Counts

27 → 2

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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))))
(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (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))))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.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 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 p p) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (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)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* (/ 1/4 x) (/ (* -12 (pow p 4)) x)) (* p p)) (.f64 (fma.f64 (/.f64 #s(literal -3 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
(sqrt.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (-.f64 (*.f64 (pow.f64 (/.f64 p x) #s(literal 3 binary64)) #s(literal 3/2 binary64)) (/.f64 p x))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p) (neg.f64 x)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.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))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 #s(approx (+ (* 1/4 (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4)))) (* p p)) (.f64 (fma.f64 (fma.f64 #s(literal 10 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -3 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64)) (.f64 p p))) (.f64 x x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x 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)))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #s(literal 1/4 binary64) #s(approx (+ (* (/ (pow p 4) x) (/ -12 x)) (/ (+ (* (* 2 (* -12 (pow p 4))) (* p p)) (* 64 (pow p 6))) (pow x 4))) (.f64 (fma.f64 #s(literal 40 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -12 binary64) (.f64 x x))) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p)) (*.f64 x x))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (fma.f64 #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))))

Outputs

#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (-.f64 (*.f64 (pow.f64 (/.f64 p x) #s(literal 3 binary64)) #s(literal 3/2 binary64)) (/.f64 p x))))

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

Calls

7 calls:

9.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
9.0ms	x
8.0ms	p
7.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
7.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Results

Accuracy	Segments	Branch
77.1%	1	`p`
83.1%	2	`x`
99.9%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.9%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.9%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
77.1%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 66 to 56 computations (15.2% saved)

regimes23.0ms (0.3%)

Memory

-20.4MiB live, 60.5MiB allocated

Counts

20 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

6.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
6.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
5.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
5.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
99.9%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.9%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.9%	2	`(/.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)

regimes18.0ms (0.2%)

Memory

1.5MiB live, 40.9MiB allocated

Counts

15 → 2

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.9%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.9%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.9%	2	`(/.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)

regimes17.0ms (0.2%)

Memory

6.0MiB live, 45.4MiB allocated

Counts

14 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.5%	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)))))))`
99.5%	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))))))`
99.5%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.5%	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 (0.1%)

Memory

-6.0MiB live, 33.6MiB allocated

Counts

8 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.3%	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)

regimes8.0ms (0.1%)

Memory

20.0MiB live, 20.0MiB allocated

Counts

5 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.9%	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)))))))`
98.9%	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))))))`
98.9%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.9%	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)

regimes14.0ms (0.2%)

Memory

-15.4MiB live, 37.0MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

Outputs
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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))))
2.0ms	x
2.0ms	p
2.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
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
65.4%	2	`p`
65.4%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
60.9%	2	`x`
72.4%	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)))))))`
72.4%	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))))))`
72.4%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
72.4%	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)

regimes10.0ms (0.1%)

Memory

-11.5MiB live, 28.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
38.2%	1	`x`
38.2%	1	`p`
38.2%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
38.2%	1	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
38.2%	1	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
38.2%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
38.2%	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

1.7MiB live, 1.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.999999819856133	-0.9886596984103639

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.999999819856133

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.999999819856133

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	9.618242603971232e-5	0.9999999958510234
0.0ms	-0.9886596984103639	-4.468288573984065e-11

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	9.618242603971232e-5	0.9999999958510234
0.0ms	-0.9886596984103639	-4.468288573984065e-11

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	9.618242603971232e-5	0.9999999958510234
0.0ms	-0.9886596984103639	-4.468288573984065e-11

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch13.0ms (0.2%)

Memory

-14.0MiB live, 25.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	9.618242603971232e-5	0.9999999958510234

Samples

6.0ms

128×

valid

Compiler

Compiled 60 to 107 computations (-78.3% saved)

Precisions

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

ival-add: 1.0ms (36% of total)

ival-mult: 1.0ms (36% of total)

ival-sqrt: 1.0ms (36% of total)

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

exact: 0.0ms (0% of total)

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

simplify29.0ms (0.3%)

Memory

5.3MiB live, 85.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	543
1	102	543
2	109	543
3	114	543
4	117	543
5	118	543

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 -4458563631096791/4503599627370496 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (-.f64 (.f64 (pow.f64 (/.f64 p x) #s(literal 3 binary64)) #s(literal 3/2 binary64)) (/.f64 p x)))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (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))))
(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 (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/73786976294838206464 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/73786976294838206464 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -4458563631096791/4503599627370496 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (-.f64 (.f64 (pow.f64 (/.f64 p x) #s(literal 3 binary64)) #s(literal 3/2 binary64)) (/.f64 p x)))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -4458563631096791/4503599627370496 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (/ (+ (* (/ 1/8 (* x x)) (/ (* -12 (pow p 4)) p)) p) (neg x)) (-.f64 (.f64 #s(literal 3/2 binary64) (pow.f64 (/.f64 p x) #s(literal 3 binary64))) (/.f64 p x)))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(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 (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (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))))
(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 (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (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))))
(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 (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/73786976294838206464 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 7378697629483821/73786976294838206464 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/73786976294838206464 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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 (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 7378697629483821/73786976294838206464 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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 (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 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 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

soundness661.0ms (8%)

Memory

-4.7MiB live, 791.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	2486
1	1325	2377
2	4611	2304
0	8084	2141
0	750	9083
1	2254	8706
2	7536	8664
0	8080	8175
0	14	66
0	23	66
1	77	66
2	501	66
3	6967	66
0	8492	59
0	622	9482
1	1903	9015
2	6570	8890
0	8099	8347

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
1×	iter limit
1×	node limit

Compiler

Compiled 1 162 to 494 computations (57.5% saved)

preprocess67.0ms (0.8%)

Memory: 7.9MiB live, 165.7MiB allocated
Compiler: Compiled 696 to 230 computations (67% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze572.0ms (6.9%)

sample2.5s (29.7%)

explain328.0ms (4%)

preprocess71.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize54.0ms (0.7%)

series37.0ms (0.5%)

simplify227.0ms (2.8%)

rewrite160.0ms (1.9%)

eval67.0ms (0.8%)

prune20.0ms (0.2%)

simplify34.0ms (0.4%)

localize139.0ms (1.7%)

series48.0ms (0.6%)

simplify196.0ms (2.4%)

rewrite218.0ms (2.6%)

eval271.0ms (3.3%)

prune68.0ms (0.8%)

simplify137.0ms (1.7%)

localize202.0ms (2.4%)

series77.0ms (0.9%)

simplify233.0ms (2.8%)

rewrite236.0ms (2.9%)

eval157.0ms (1.9%)

prune73.0ms (0.9%)

simplify213.0ms (2.6%)

localize351.0ms (4.3%)

series70.0ms (0.8%)

simplify193.0ms (2.3%)

rewrite182.0ms (2.2%)

eval190.0ms (2.3%)

prune39.0ms (0.5%)

regimes53.0ms (0.6%)

regimes23.0ms (0.3%)

regimes18.0ms (0.2%)

regimes17.0ms (0.2%)

regimes12.0ms (0.1%)

regimes8.0ms (0.1%)

regimes14.0ms (0.2%)

regimes10.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch13.0ms (0.2%)

simplify29.0ms (0.3%)

soundness661.0ms (8%)

preprocess67.0ms (0.8%)

end0.0ms (0%)

Profiling