Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze463.0ms (4.1%)

Memory

-3.0MiB live, 795.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.0s (18.1%)

Memory

29.9MiB live, 2 559.4MiB allocated

Samples

956.0ms	6 257×	0	valid
323.0ms	944×	2	valid
143.0ms	431×	3	valid
119.0ms	624×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

const: 267.0ms (22.3% of total)

ival-mult: 234.0ms (19.5% of total)

ival-sqrt: 199.0ms (16.6% of total)

ival-add: 156.0ms (13% of total)

ival-div: 107.0ms (8.9% of total)

ival-fabs: 88.0ms (7.3% of total)

adjust: 77.0ms (6.4% of total)

ival-<: 47.0ms (3.9% of total)

ival-and: 11.0ms (0.9% of total)

exact: 9.0ms (0.8% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain277.0ms (2.5%)

Memory

-15.9MiB live, 300.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
57	0	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
52	1	(4.2777612965795035e-175 -2.0460886654065334e-13)	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
19	0	-	3	(4.2777612965795035e-175 -2.0460886654065334e-13)	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
0	0	-	0	-	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	0	-	0	-	`#s(literal 4 binary64)`
0	0	-	0	-	`(*.f64 x x)`
0	0	-	0	-	`p`
0	0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	0	-	0	-	`#s(literal 1/2 binary64)`
0	0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	oflow-rescue	57	0
↳	`(*.f64 #s(literal 4 binary64) p)`	overflow	1
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	57
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	57
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	53	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	uflow-rescue	16	0
↳	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	underflow	8
↳	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`	underflow	24
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	24
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	10
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	60

Confusion

	Predicted +	Predicted -
+	69	0
-	57	130

Precision

0.5476190476190477

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	69	0	0
-	57	0	130

Precision?

0.5476190476190477

Recall?

1.0

Freqs

test

number	freq
0	130
1	126

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms	360×	0	valid
23.0ms	60×	2	valid
18.0ms	60×	1	valid
10.0ms	32×	3	valid

Compiler

Compiled 211 to 46 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-add: 16.0ms (26.9% of total)

ival-mult: 13.0ms (21.8% of total)

adjust: 12.0ms (20.2% of total)

ival-sqrt: 11.0ms (18.5% of total)

ival-div: 6.0ms (10.1% of total)

exact: 1.0ms (1.7% of total)

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

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

preprocess65.0ms (0.6%)

Memory

17.4MiB live, 55.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs p)

Compiler

Compiled 19 to 14 computations (26.3% saved)

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.3%	(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)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0%)

Memory

9.8MiB live, 9.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize63.0ms (0.6%)

Memory

-36.0MiB live, 91.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
accuracy	3.7277915408953737	(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	11.802965704543722	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	13.213635482933146	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

25.0ms	180×	0	valid
9.0ms	16×	3	valid
7.0ms	30×	2	valid
5.0ms	30×	1	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 10.0ms (40.3% of total)

ival-sqrt: 5.0ms (20.2% of total)

ival-add: 4.0ms (16.1% of total)

ival-div: 3.0ms (12.1% of total)

adjust: 2.0ms (8.1% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

10.5MiB live, 49.3MiB allocated

Counts

6 → 144

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

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/4 (/ x p))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
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#s(alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -2 p) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ x p)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow p 2) (pow x 2)))) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))))) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.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))) 1) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.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 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.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 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) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) 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 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) 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 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.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) (+ (* -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 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ x p)) (taylor inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p) (taylor inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p) (taylor inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p) (taylor inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ x p)) (taylor -inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)) (taylor -inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)) (taylor -inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)) (taylor -inf p) (#s(alt (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) (patch (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #<representation binary64>) () ())) ())

Calls

36 calls:

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

simplify327.0ms (2.9%)

Memory

-7.3MiB live, 392.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10 048×	`lower-fma.f64`
10 048×	`lower-fma.f32`
7 228×	`lower-*.f64`
7 228×	`lower-*.f32`
4 784×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	472	2993
1	1444	2876
2	4985	2834
0	8534	2634

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

Calls

Call 1

Inputs
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
1
(+ 1 (* -1/2 (/ x p)))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* -1/2 (/ x p))
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 3/512 binary64) (.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(fma.f64 #s(literal -1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p)) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64))))) (.f64 #s(literal -256 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p)))))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 p p))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 p (.f64 p (fma.f64 #s(literal -10 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 5 binary64)))) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 (.f64 #s(literal -1/32 binary64) (.f64 x (.f64 x x))) (.f64 p p))) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) x (fma.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (.f64 #s(literal -1/32 binary64) (.f64 x (.f64 x x))) (.f64 p p)))) p))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(.f64 p (.f64 p (fma.f64 x (/.f64 x (*.f64 p p)) #s(literal 4 binary64))))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(fma.f64 x x (.f64 (.f64 p p) #s(literal 4 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1 binary64)))
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(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 6 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -2 binary64) (.f64 x x))) #s(literal 2 binary64))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -20 binary64) (/.f64 #s(literal 6 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ x p)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(fma.f64 x (fma.f64 (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
(fma.f64 x (fma.f64 (/.f64 (.f64 x x) (.f64 p (.f64 p p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)) (fma.f64 (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)) (neg.f64 (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) p))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) x (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) #s(literal 3/256 binary64)) (.f64 (.f64 p p) (*.f64 p p))))) p))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 p (.f64 p (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x))) x)
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 2 binary64) x)) x)
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (*.f64 p p))) #s(literal 2 binary64))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 p (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(neg.f64 (.f64 p (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (*.f64 p p))) #s(literal 2 binary64))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 p (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (*.f64 p p))) #s(literal 2 binary64)))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(neg.f64 (.f64 p (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x (/.f64 x (.f64 p p))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 p #s(literal 6 binary64))))))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) p) (.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (.f64 p (.f64 p p))) #s(literal -1/64 binary64) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 p #s(literal 2 binary64)))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) #s(literal 1/512 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) (.f64 p #s(literal 2 binary64)))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) (*.f64 #s(literal 2 binary64) x) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (*.f64 x x)))) x)
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal -2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (*.f64 x x)))) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))))) x))
(* 1/2 (/ x p))
(*.f64 #s(literal 1/2 binary64) (/.f64 x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(.f64 x (fma.f64 (/.f64 (.f64 x x) (.f64 p (.f64 p p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 #s(literal 3/256 binary64) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (.f64 p (*.f64 p p)))) (/.f64 #s(literal 1/2 binary64) p)))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -5/2048 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 7 binary64))) (/.f64 #s(literal 3/256 binary64) (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/2 binary64) p)))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 6 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64)))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 (+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 6 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64))) (/.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64) (neg.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (*.f64 p p))))) (pow.f64 x #s(literal 6 binary64))))
-1
#s(literal -1 binary64)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (/.f64 (fma.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal -12 binary64) (.f64 p p)) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 6 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -2 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -20 binary64) (/.f64 #s(literal 6 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(* 1/2 (/ x p))
(*.f64 #s(literal 1/2 binary64) (/.f64 x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) #s(literal 3/256 binary64)) (.f64 (.f64 p p) (*.f64 p p))))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 x (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 p #s(literal 6 binary64))))) p)
(* -1/2 (/ x p))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) p)
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) #s(literal 3/256 binary64)) (.f64 (.f64 p p) (*.f64 p p))))) (neg.f64 p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 p p)) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 x (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 p #s(literal 6 binary64))))) (neg.f64 p))

rewrite233.0ms (2.1%)

Memory

-2.1MiB live, 341.5MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
0	23	78
1	77	78
2	501	78
3	6967	78
0	8492	70

Stop Event

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

Counts

6 → 302

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

Outputs
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (/.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
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eval88.0ms (0.8%)

Memory: -3.8MiB live, 109.1MiB allocated
Compiler: Compiled 16 971 to 2 158 computations (87.3% saved)

prune85.0ms (0.8%)

Memory

-11.8MiB live, 149.0MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	433	11	444
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	434	11	445

Accuracy

99.8%

Counts

445 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.9%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
	71.0%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64)))
	52.4%	(sqrt.f64 (/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
	8.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))))))
▶	7.3%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
	24.7%	(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))))
	47.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
▶	23.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
	34.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	52.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	31.5%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x)))

Compiler

Compiled 306 to 204 computations (33.3% saved)

simplify41.0ms (0.4%)

Memory

12.8MiB live, 55.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

468×	`lower-fma.f32`
466×	`lower-fma.f64`
454×	`lower-*.f32`
438×	`lower-*.f64`
224×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	318
0	64	309
1	106	309
2	162	309
3	305	309
4	491	309
5	586	309
6	721	309
7	859	309
8	941	309
9	1123	309
10	1134	309
11	1135	309
12	1135	309
0	1135	302

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize381.0ms (3.4%)

Memory

-8.0MiB live, 199.2MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.41796875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
accuracy	0.4375	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p))
accuracy	43.602598255849394	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x)))
accuracy	0	(*.f64 p p)
accuracy	3.7277915408953737	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
accuracy	8.492396844122032	(/.f64 (.f64 p p) (.f64 x x))
accuracy	43.05838147303608	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x)))
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64))))
accuracy	3.7277915408953737	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64)))))
accuracy	11.802965704543722	(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64)))
accuracy	43.538196050482014	#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64))
accuracy	3.7277915408953737	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	30.99986827871954	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.37109375	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	3.7221096708193744	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))
accuracy	11.802965704543722	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
accuracy	13.213635482933146	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))

Samples

127.0ms	180×	0	valid
95.0ms	16×	3	valid
15.0ms	30×	2	valid
15.0ms	30×	1	valid

Compiler

Compiled 287 to 33 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-add: 81.0ms (59.5% of total)

ival-sqrt: 25.0ms (18.4% of total)

ival-mult: 15.0ms (11% of total)

ival-div: 9.0ms (6.6% of total)

adjust: 4.0ms (2.9% of total)

exact: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

series104.0ms (0.9%)

Memory

20.3MiB live, 57.6MiB allocated

Counts

21 → 432

Calls

Call 1

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

Outputs
#s(alt (sqrt 1/2) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p))))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3)))))))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #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 inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x)) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x)) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x)) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<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 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #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 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #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 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #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 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt 1/2) (taylor inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p))) (taylor inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p)))) (taylor inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3)))))) (taylor inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt 1/2) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p))) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p))) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p))) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (/ x p))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 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 (/ (- (* -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))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (* p (sqrt 2)) x)) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #<representation binary64>) () ())) ())
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#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* p (* (sqrt 1/2) (sqrt 2))) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (patch (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p)) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 2 (/ (pow p 2) x))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (+ 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 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))) (taylor inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -2 p) (taylor -inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor -inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor -inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))) (taylor -inf p) (#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor 0 p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* p (sqrt 2)) (taylor -inf p) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) p) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) p) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())

Calls

108 calls:

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

simplify953.0ms (8.5%)

Memory

1.8MiB live, 467.3MiB allocated

Algorithm

1×	egg-herbie

Rules

9 552×	`lower-fma.f64`
9 552×	`lower-fma.f32`
7 202×	`lower-*.f64`
7 202×	`lower-*.f32`
4 124×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	553	9519
1	1691	8955
2	5878	8804
0	8796	8266

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 430

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))
(+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2))))))
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(* -1 (/ (* p (sqrt 2)) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 2)))) x))
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(sqrt 2)
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1
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1
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1
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2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
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(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
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1
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(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
1
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(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
1
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-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
1
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(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* -1/2 (/ x p))
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(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(sqrt 1/2)
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(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
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(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
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1
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(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

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

rewrite324.0ms (2.9%)

Memory

-8.4MiB live, 285.7MiB allocated

Rules

4 138×	`lower-*.f32`
4 122×	`lower-*.f64`
3 790×	`lower-/.f32`
3 784×	`lower-/.f64`
3 660×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	280
0	64	270
1	211	250
2	1094	246
0	8581	238

Stop Event

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

Counts

21 → 434

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (*.f64 x x)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 (log1p.f64 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x))))) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (log1p.f64 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (*.f64 x x))))) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)))) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)) (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x))))) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x (/.f64 x (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)))) #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (/.f64 x (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)))) #s(literal 1/4 binary64)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)) (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)))))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 x (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x))))))))
(/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 x (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)))))))
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(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x (neg.f64 x))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 #s(literal -16 binary64) (.f64 (.f64 p p) (.f64 p p))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (*.f64 p p) #s(literal -4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 #s(literal -16 binary64) (.f64 (.f64 p p) (.f64 p p))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (*.f64 p p) #s(literal -4 binary64))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 #s(literal -16 binary64) (.f64 (.f64 p p) (.f64 p p))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 (*.f64 p p) #s(literal -4 binary64))))))
(.f64 (pow.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 p (.f64 p #s(literal 4 binary64)) (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 p (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
(+.f64 #s(literal 0 binary64) (neg.f64 x))
(-.f64 #s(literal 0 binary64) x)
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x #s(literal 0 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 x x) x))
(neg.f64 x)
(neg.f64 (/.f64 x #s(literal 1 binary64)))
(neg.f64 (/.f64 (*.f64 x x) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (neg.f64 (.f64 x (.f64 x x)))))
(/.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 x x) (neg.f64 x))
(/.f64 (neg.f64 x) #s(literal 1 binary64))
(/.f64 (*.f64 x (neg.f64 x)) x)
(/.f64 (.f64 x (.f64 x x)) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (.f64 x (.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (.f64 x (.f64 x x))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 0 binary64) (neg.f64 x)))))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 x #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(.f64 (.f64 x (neg.f64 x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (neg.f64 (.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))

eval390.0ms (3.5%)

Memory: 15.3MiB live, 246.8MiB allocated
Compiler: Compiled 21 713 to 2 252 computations (89.6% saved)

prune482.0ms (4.3%)

Memory

-16.1MiB live, 190.0MiB allocated

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	869	2	871
Fresh	0	6	6
Picked	3	2	5
Done	0	0	0
Total	872	10	882

Accuracy

99.9%

Counts

882 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.9%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
▶	47.9%	(.f64 (sqrt.f64 #s(approx (+ 1 (/ x (sqrt (+ ( x x) (* p (* 4 p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
▶	71.0%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64)))
▶	52.4%	(sqrt.f64 (/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
	8.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))))))
	24.7%	(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))))
▶	47.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
▶	34.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
✓	52.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	31.9%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (neg.f64 p) x))

Compiler

Compiled 256 to 164 computations (35.9% saved)

simplify696.0ms (6.2%)

Memory

12.0MiB live, 437.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

33 408×	`lower-fma.f32`
33 400×	`lower-fma.f64`
3 824×	`lower-*.f32`
3 814×	`lower-*.f64`
3 016×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	407
0	73	403
1	112	399
2	135	399
3	158	399
4	182	399
5	212	399
6	267	399
7	410	399
8	777	399
9	1421	399
10	2879	399
11	4955	399
12	5714	399
13	6044	399
14	6236	399
15	6298	399
16	6328	399
17	6924	399
18	7351	399
19	7556	399
20	7556	399
21	7556	399
0	8625	395

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

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

localize273.0ms (2.4%)

Memory

-18.3MiB live, 422.8MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	6.886209610803904	(+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
accuracy	7.035236030473934	(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))
accuracy	13.213635482933144	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
accuracy	18.68932199213143	(+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.37109375	(.f64 (sqrt.f64 #s(approx (+ 1 (/ x (sqrt (+ ( x x) (* p (* 4 p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	3.7221096708193744	(sqrt.f64 #s(approx (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64))))
accuracy	33.23146033129243	#s(approx (+ 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))
accuracy	0	(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
accuracy	0	(/.f64 x p)
accuracy	3.7277915408953737	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
accuracy	33.23113594370439	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
accuracy	3.7277915408953737	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
accuracy	42.8179450298199	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64))
accuracy	0.00390625	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
accuracy	3.7277915408953737	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64)))
accuracy	13.213635482933144	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
accuracy	18.339636256028026	(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))

Samples

81.0ms	122×	0	valid
62.0ms	62×	2	valid
41.0ms	28×	3	valid
27.0ms	44×	1	valid

Compiler

Compiled 393 to 41 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

ival-div: 66.0ms (41.1% of total)

ival-mult: 39.0ms (24.3% of total)

ival-sqrt: 21.0ms (13.1% of total)

ival-add: 19.0ms (11.8% of total)

adjust: 14.0ms (8.7% of total)

exact: 1.0ms (0.6% of total)

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

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

series61.0ms (0.5%)

Memory

35.8MiB live, 112.9MiB allocated

Counts

20 → 456

Calls

Call 1

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

Outputs
#s(alt (sqrt 1/2) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6)))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt 1/2) (taylor inf p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2) (taylor -inf p) (#s(alt (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2) (taylor -inf p) (#s(alt (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (/ x p)) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<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 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))))) (pow x 2)) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2)) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ (pow p 2) (pow x 2))) 2) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ (pow p 2) (pow x 2))) (taylor 0 p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (/ x p)) 1) (taylor inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))) 1) (taylor inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))) 1) (taylor inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (/ x p)) 1) (taylor -inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)) 1) (taylor -inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)) 1) (taylor -inf p) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #<representation binary64>) () ())) ())

Calls

114 calls:

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

simplify359.0ms (3.2%)

Memory

4.2MiB live, 629.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 436×	`lower-fma.f64`
11 436×	`lower-fma.f32`
8 112×	`lower-*.f64`
8 112×	`lower-*.f32`
5 130×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1016	10877
1	3106	10312
0	8810	9662

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 454

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(/ 1/4 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)))
(/ 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)
(/ -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))
(/ 1/2 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)))
(/ 1/4 p)
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x
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x
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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
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1
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1/2
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1/2
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(/ (+ (* 1/4 x) (* 1/2 p)) p)
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1/2
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(sqrt 1/2)
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(* (sqrt 1/2) (sqrt 2))
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(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))
(+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 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 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 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 (/ (- (* -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)))))))
(* -1 (/ (* p (sqrt 2)) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 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 (/ (- (* 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 2))))) x))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 2))))))
(+ (sqrt 2) (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6))))) (sqrt 2))) (* 1/2 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (sqrt 2))))) (/ 1 (* (pow x 2) (sqrt 2))))))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (* 1/4 (/ x p))))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ x p)) (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (pow p 3))))))
1
(+ 1 (* -1/4 (/ x p)))
(+ 1 (* -1 (/ (+ (* 1/32 (/ (pow x 2) p)) (* 1/4 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) p)) (* -1/32 (pow x 2))) p)) (* 1/4 x)) p)))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
(+ 1 (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))))
1
(+ 1 (* -1/2 (/ x p)))
(+ 1 (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* 1/2 (/ x p)))
(* 1/2 (/ x p))
(* x (+ (* 1/2 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/2 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/2 (/ 1 p)) (/ 1 x)))
(* 1/2 (/ x p))
(* x (+ (* 1/2 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/2 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/2 (/ 1 p)) (/ 1 x)))
(* 1/2 (/ x p))
(/ (+ p (* 1/2 x)) p)
(/ (+ p (* 1/2 x)) p)
(/ (+ p (* 1/2 x)) p)
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* 1/2 (/ x p)))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* 1/2 (/ x p)))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow p 6))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))) 1)
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 6)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))))) (pow p 2))) (+ (* 1/4 (/ (* (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/2 (/ (* (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 2)))))))) (* (pow x 6) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* 1/2 (/ (* (- (* -8 (pow p 4)) (* -2 (pow p 4))) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* (pow p 2) (pow (sqrt 2) 2))))))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/64 (pow x 3)) (* 1/16 (pow x 3)))) (pow p 3))) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/32 (* (pow x 2) (sqrt 1/2))) (* 1/2 (/ (* (sqrt 1/2) (+ (* -1/64 (pow x 3)) (* 1/16 (pow x 3)))) p))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))))
(+ 1 (+ (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))) (* 1/2 (/ (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))) (pow x 4)))))
(+ 1 (+ (* 1/2 (/ (- (* -128 (pow p 6)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))))) (pow p 2))) (+ (* 1/4 (/ (* (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 2)))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))) (* 1/2 (/ (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))) (pow x 4))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4)))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
-1/2
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(- (* (pow x 2) (+ (* -1/32 (/ (pow x 2) (pow p 4))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/128 (/ (pow x 2) (pow p 6))) (* 1/32 (/ 1 (pow p 4))))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(* -2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 8 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -32 (/ (pow p 2) (pow x 6))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 8))) (* 32 (/ 1 (pow x 6))))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
-1/2
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)
-1/2
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)
-1
(- (* 1/2 (/ x p)) 1)
(- (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))) 1)
(- (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) 1)
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
-2
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
(* -2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
-1
(- (* 1/2 (/ x p)) 1)
(- (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))) 1)
(- (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))) 1)
-1
(- (* -1/2 (/ x p)) 1)
(- (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)) 1)
(- (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)) 1)

Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 p p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 x (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 p p) (.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/128 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 p p))))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (.f64 p p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (fma.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 p p)) (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64) (.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64))))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1 binary64)))
(* -1 (/ p x))
(/.f64 p (neg.f64 x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (*.f64 x x))) p) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (fma.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)) #s(literal -1/64 binary64)))) (.f64 p (pow.f64 x #s(literal 4 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) p)) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (fma.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 8 binary64))))) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (fma.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)) #s(literal -1/64 binary64)))) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 6 binary64)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (fma.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)) #s(literal -1/64 binary64)))) (.f64 p (pow.f64 x #s(literal 4 binary64))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 p (*.f64 x x))) p)) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 #s(literal -69/16 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) #s(literal 1 binary64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(fma.f64 #s(literal -1/128 binary64) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 p p)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64)) (.f64 #s(literal 1/512 binary64) (/.f64 (.f64 x (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (.f64 p p)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (/.f64 (.f64 #s(literal -1/128 binary64) (.f64 x x)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 p 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 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/128 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64)) (.f64 #s(literal 1/512 binary64) (/.f64 (.f64 x (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 3/512 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
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1/2
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(* (sqrt 1/2) (sqrt 2))
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1/2
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1
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1
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1/2
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(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 #s(literal 3 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -10 binary64) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 p (.f64 p p))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/256 binary64)) (pow.f64 p #s(literal 5 binary64))) (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 p (.f64 p p))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) (.f64 x #s(literal 1/4 binary64))) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/256 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) (.f64 x #s(literal 1/4 binary64)))) p))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ (* -1/32 (/ (pow x 2) (pow p 4))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 p p))) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/128 (/ (pow x 2) (pow p 6))) (* 1/32 (/ 1 (pow p 4))))) (* 1/8 (/ 1 (pow p 2))))) 1/2)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/128 binary64) (/.f64 (.f64 x x) (pow.f64 p #s(literal 6 binary64))) (/.f64 #s(literal -1/32 binary64) (pow.f64 p #s(literal 4 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 p p))) #s(literal -1/2 binary64))
(* -2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (*.f64 x x))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 8 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/.f64 (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) (.f64 x x)) (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -32 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -32 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) (.f64 x x)) (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 128 binary64) (pow.f64 p #s(literal 8 binary64))) (pow.f64 x #s(literal 6 binary64)))))) (.f64 x x))
(* -2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (*.f64 x x))
(/ (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 8 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (* 8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/.f64 (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) (.f64 x x)) (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal -32 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
(/ (+ (* -32 (/ (pow p 6) (pow x 4))) (+ (* -2 (pow p 2)) (+ (* 8 (/ (pow p 4) (pow x 2))) (* 128 (/ (pow p 8) (pow x 6)))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -32 binary64) (fma.f64 #s(literal 8 binary64) (/.f64 (pow.f64 p #s(literal 4 binary64)) (.f64 x x)) (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 128 binary64) (pow.f64 p #s(literal 8 binary64))) (pow.f64 x #s(literal 6 binary64)))))) (.f64 x x))
(* -2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (*.f64 x x))
(* (pow p 2) (- (* 8 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (fma.f64 #s(literal 8 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* (pow p 2) (- (* (pow p 2) (+ (* -32 (/ (pow p 2) (pow x 6))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -32 binary64) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 8))) (* 32 (/ 1 (pow x 6))))) (* 8 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 8 binary64))) #s(literal 128 binary64) (/.f64 #s(literal -32 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -2 binary64) (.f64 x x))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/2 binary64))
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 p p)) (fma.f64 #s(literal -1/32 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)
(fma.f64 #s(literal -1/32 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 #s(literal 1/128 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/2 binary64))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ (pow x 2) (pow p 2))) 1/2)
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/2 binary64))
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/8 (/ (pow x 2) (pow p 2)))) 1/2)
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 p p)) (fma.f64 #s(literal -1/32 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(- (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/128 (/ (pow x 6) (pow p 6))) (* 1/8 (/ (pow x 2) (pow p 2))))) 1/2)
(fma.f64 #s(literal -1/32 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 #s(literal 1/128 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 p #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1/2 binary64))))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ x p)) 1)
(fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal -1 binary64))
(- (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))) 1)
(fma.f64 x (fma.f64 (/.f64 (.f64 x x) (.f64 p (*.f64 p p))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) p)) #s(literal -1 binary64))
(- (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) 1)
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (pow.f64 p #s(literal 5 binary64))) #s(literal 3/256 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1/2 binary64) p)) #s(literal -1 binary64))
(* -2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (*.f64 x x))
(/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 x x))) (.f64 x x))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 x x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64))) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (fma.f64 (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 8 binary64))))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 p (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (.f64 x x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 p p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64))) (pow.f64 x #s(literal 4 binary64))))) (.f64 x x))
-2
#s(literal -2 binary64)
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal -2 binary64))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -2 binary64)))
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
(+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 32 binary64))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal -2 binary64)))
(* -2 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (*.f64 x x))
(* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (fma.f64 #s(literal 6 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -20 binary64) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -2 binary64) (*.f64 x x))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 8 binary64))) #s(literal 70 binary64) (/.f64 #s(literal -20 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -2 binary64) (.f64 x x))))
-1
#s(literal -1 binary64)
(- (* 1/2 (/ x p)) 1)
(fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal -1 binary64))
(- (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))) 1)
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p (.f64 p p))) #s(literal -1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal -1 binary64)))
(- (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))) 1)
(fma.f64 (neg.f64 x) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/256 binary64)) (pow.f64 p #s(literal 5 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p (*.f64 p p))) #s(literal -1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal -1 binary64))))
-1
#s(literal -1 binary64)
(- (* -1/2 (/ x p)) 1)
(fma.f64 #s(literal -1/2 binary64) (/.f64 x p) #s(literal -1 binary64))
(- (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)) 1)
(+.f64 (/.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) #s(literal -1/16 binary64) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 p)) #s(literal -1 binary64))
(- (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)) 1)
(+.f64 (/.f64 (-.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 p p)) #s(literal -1/16 binary64) (.f64 #s(literal 1/2 binary64) x)) (/.f64 (.f64 x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/256 binary64))) (pow.f64 p #s(literal 4 binary64)))) (neg.f64 p)) #s(literal -1 binary64))

rewrite313.0ms (2.8%)

Memory

-2.2MiB live, 490.7MiB allocated

Rules

5 128×	`lower-fma.f32`
5 120×	`lower-fma.f64`
4 630×	`lower-/.f32`
4 620×	`lower-/.f64`
4 410×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	319
0	73	314
1	271	310
2	1687	310
0	8653	306

Stop Event

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

Counts

20 → 447

Calls

Call 1

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

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

eval196.0ms (1.7%)

Memory: -11.8MiB live, 252.0MiB allocated
Compiler: Compiled 32 095 to 2 967 computations (90.8% saved)

prune150.0ms (1.3%)

Memory

-4.9MiB live, 317.9MiB allocated

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	995	5	1 000
Fresh	2	1	3
Picked	2	3	5
Done	0	2	2
Total	999	11	1 010

Accuracy

99.9%

Counts

1 010 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.9%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	47.9%	(.f64 (sqrt.f64 #s(approx (+ 1 (/ x (sqrt (+ ( x x) (* p (* 4 p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	71.0%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64)))
	52.4%	(sqrt.f64 (/.f64 (fma.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))))
▶	53.1%	(sqrt.f64 (/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))))))
▶	8.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))))))
✓	47.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
✓	52.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	25.1%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
▶	31.9%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (/.f64 p (neg.f64 x)))
▶	34.0%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 284 to 185 computations (34.9% saved)

simplify299.0ms (2.7%)

Memory

28.3MiB live, 295.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)))
cost-diff	0	(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))))))
cost-diff	128	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)))))
cost-diff	0	(*.f64 p p)
cost-diff	0	(/.f64 (.f64 p p) (.f64 x x))
cost-diff	0	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
cost-diff	0	(neg.f64 x)
cost-diff	0	(/.f64 p (neg.f64 x))
cost-diff	0	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (/.f64 p (neg.f64 x)))
cost-diff	0	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) #s(literal 1 binary64))
cost-diff	0	(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64))))))
cost-diff	0	(sqrt.f64 (/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))))))
cost-diff	128	(+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))
cost-diff	12480	(exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))

Rules

8 446×	`lower-fma.f32`
8 440×	`lower-fma.f64`
3 984×	`lower-*.f32`
3 968×	`lower-*.f64`
1 718×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	443
0	80	429
1	135	424
2	208	424
3	288	424
4	345	424
5	396	424
6	503	424
7	787	424
8	1375	424
9	2223	424
10	3681	424
11	5566	424
12	6793	424
13	7473	424
14	7573	424
15	7607	424
16	7941	424
0	8270	415

Stop Event

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

Calls

Call 1

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

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

localize271.0ms (2.4%)

Memory

-12.0MiB live, 474.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	3.7277915408953737	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))))))
accuracy	4.312817205343117	(fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
accuracy	11.802965704543722	(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))))
accuracy	43.948339573402635	#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64)))
accuracy	0	(*.f64 p p)
accuracy	0.19116556047758315	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
accuracy	8.492396844122032	(/.f64 (.f64 p p) (.f64 x x))
accuracy	47.90800042814436	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
accuracy	0	(/.f64 p (neg.f64 x))
accuracy	0	(neg.f64 x)
accuracy	43.602598255849394	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (/.f64 p (neg.f64 x)))
accuracy	42.22766016727139	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) #s(literal 1 binary64))
accuracy	6.886209610803904	(+.f64 #s(literal -1 binary64) (/.f64 x (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))))
accuracy	7.035236030473934	(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64))))))
accuracy	13.801527351785666	(log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p))))
accuracy	18.68932199213143	(+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))

Samples

86.0ms	62×	2	valid
47.0ms	122×	0	valid
34.0ms	28×	3	valid
30.0ms	44×	1	valid

Compiler

Compiled 402 to 47 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 156.0ms

ival-add: 34.0ms (21.8% of total)

ival-mult: 32.0ms (20.5% of total)

ival-sqrt: 28.0ms (17.9% of total)

ival-div: 22.0ms (14.1% of total)

adjust: 16.0ms (10.2% of total)

ival-exp: 11.0ms (7% of total)

ival-log: 11.0ms (7% of total)

exact: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

series35.0ms (0.3%)

Memory

-8.1MiB live, 69.8MiB allocated

Counts

19 → 432

Calls

Call 1

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

Outputs
#s(alt (* 2 p) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p)) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))) (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))) (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))) (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<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 (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<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 (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 2 (/ (pow p 2) x))) (taylor 0 p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<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 (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -2 p) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ (pow x 2) (pow p 2))) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (patch (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #<representation binary64>) () ())) ())
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Calls

108 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log (+ (* x x) (* 4 (* p p))))
1.0ms	p	@	0	(/ p (neg x))
1.0ms	x	@	inf	(log (+ (* x x) (* 4 (* p p))))
1.0ms	p	@	inf	(log (+ (* x x) (* 4 (* p p))))
1.0ms	p	@	0	(log (+ (* x x) (* 4 (* p p))))

simplify546.0ms (4.9%)

Memory

-156.9MiB live, 506.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 830×	`lower-fma.f64`
10 830×	`lower-fma.f32`
7 526×	`lower-*.f64`
7 526×	`lower-*.f32`
4 860×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	919	9315
1	2810	8957
0	8314	8402

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 430

Calls

Call 1

Inputs
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))) 1)
(- (* (pow x 2) (+ (* (pow x 2) (- (* 1/64 (/ (pow x 2) (pow p 6))) (* 1/16 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))) 1)
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(/ (- (* 16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (* -64 (/ (pow p 6) (pow x 4))) (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2)))) (pow x 2))
(/ (- (* 256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* -4 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
-1
(- (* 1/4 (/ (pow x 2) (pow p 2))) 1)
(- (+ (* -1/16 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))) 1)
(- (+ (* 1/64 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))) (+ 1 (* 1/16 (/ (pow x 4) (pow p 4)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
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(+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 6)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))))) (pow p 2))) (+ (* 1/4 (/ (* (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/2 (/ (* (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 2)))))))) (* (pow x 6) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (+ (* 1/4 (/ (pow (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) 2) (pow (sqrt 2) 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* 1/2 (/ (* (- (* -8 (pow p 4)) (* -2 (pow p 4))) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* (pow p 2) (pow (sqrt 2) 2))))))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -8 (pow p 4)) (* -2 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (+ (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -8 (pow p 4)) (* -2 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/64 (pow x 3)) (* 1/16 (pow x 3)))) (pow p 3))) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/32 (* (pow x 2) (sqrt 1/2))) (* 1/2 (/ (* (sqrt 1/2) (+ (* -1/64 (pow x 3)) (* 1/16 (pow x 3)))) p))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))))
(+ 1 (+ (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))) (* 1/2 (/ (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))) (pow x 4)))))
(+ 1 (+ (* 1/2 (/ (- (* -128 (pow p 6)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))))) (pow p 2))) (+ (* 1/4 (/ (* (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 2)))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2)))) (pow x 2))) (* 1/2 (/ (- (* 32 (pow p 4)) (+ (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 2)) (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow p 2))))) (pow p 2))) (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2))))) (pow x 4))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (- (* -128 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -8 (pow p 4)) (* -2 (pow p 4)))))))) (pow x 6))) (+ (* 1/2 (/ (- (* -8 (pow p 4)) (* -2 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (- (* 32 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -8 (pow p 4)) (* -2 (pow p 4))))) (* -1/2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
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(sqrt 1/2)
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1
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2
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2
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1
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1
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1
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-1
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1
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(log (* 4 (pow p 2)))
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(+ (log 4) (* -2 (log (/ 1 p))))
(+ (log 4) (+ (* -2 (log (/ 1 p))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ (log 4) (+ (* -2 (log (/ 1 p))) (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(+ (log 4) (+ (* -2 (log (/ 1 p))) (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/192 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(+ (log 4) (* -2 (log (/ -1 p))))
(+ (log 4) (+ (* -2 (log (/ -1 p))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ (log 4) (+ (* -2 (log (/ -1 p))) (+ (* -1/32 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(+ (log 4) (+ (* -2 (log (/ -1 p))) (+ (* -1/32 (/ (pow x 4) (pow p 4))) (+ (* 1/192 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
-1
(- (* 1/2 (/ x p)) 1)
(- (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))) 1)
(- (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))) 1)
(* -2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2)))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))))) (pow x 2))
(/ (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
-2
(- (* 2 (/ (pow p 2) (pow x 2))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 2)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 2)
(* -2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 70 (/ (pow p 2) (pow x 8))) (* 20 (/ 1 (pow x 6))))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2)))))
-1
(- (* 1/2 (/ x p)) 1)
(- (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))) 1)
(- (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p)))) 1)
-1
(- (* -1/2 (/ x p)) 1)
(- (* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)) 1)
(- (* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)) 1)
-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)
(* 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))))
(* 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))))
(* 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))
-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
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (* 2 (/ (pow p 2) (pow x 2))) 1)

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

rewrite432.0ms (3.8%)

Memory

-18.3MiB live, 335.7MiB allocated

Rules

4 986×	`lower-fma.f32`
4 980×	`lower-fma.f64`
4 746×	`lower-/.f32`
4 734×	`lower-/.f64`
4 520×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	323
0	80	307
1	313	296
2	1939	296
0	9026	283

Stop Event

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

Counts

19 → 484

Calls

Call 1

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

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

eval238.0ms (2.1%)

Memory: 2.4MiB live, 242.6MiB allocated
Compiler: Compiled 31 607 to 3 142 computations (90.1% saved)

prune161.0ms (1.4%)

Memory

10.5MiB live, 288.5MiB allocated

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	949	1	950
Fresh	0	1	1
Picked	1	4	5
Done	0	5	5
Total	950	11	961

Accuracy

99.9%

Counts

961 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.9%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	47.9%	(.f64 (sqrt.f64 #s(approx (+ 1 (/ x (sqrt (+ ( x x) (* p (* 4 p)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x p) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	71.0%	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64)))
	8.2%	(sqrt.f64 (fma.f64 #s(approx (/ x (sqrt (+ (* (* 4 p) 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)))
	52.4%	(sqrt.f64 (/.f64 (fma.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 #s(literal 4 binary64) (.f64 p p)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))))
✓	53.1%	(sqrt.f64 (/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 x (exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 #s(literal 4 binary64) (*.f64 p p)))) #s(literal 1/2 binary64)))))))
✓	47.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))))
✓	52.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	25.1%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
✓	31.9%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) (/.f64 p (neg.f64 x)))
✓	34.0%	#s(approx (sqrt (+ (* (/ 1/2 (sqrt (+ (* x x) (* p (* 4 p))))) x) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 436 to 193 computations (55.7% saved)

regimes44.0ms (0.4%)

Memory

6.5MiB live, 85.2MiB allocated

Counts

20 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

8.0ms	x
7.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
6.0ms	p
6.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
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
75.3%	1	`p`
82.5%	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))))`
75.3%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes19.0ms (0.2%)

Memory

2.7MiB live, 40.3MiB allocated

Counts

14 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

6.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
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
99.3%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.3%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.3%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.3%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes12.0ms (0.1%)

Memory

-17.0MiB live, 21.2MiB allocated

Counts

7 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
2.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
2.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
98.8%	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)))))))`
98.8%	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))))))`
98.8%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.8%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes9.0ms (0.1%)

Memory

23.2MiB live, 23.2MiB allocated

Counts

6 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.8%	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)))))))`
98.8%	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))))))`
98.8%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.8%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes13.0ms (0.1%)

Memory

-9.1MiB live, 30.1MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
65.9%	2	`p`
65.9%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
59.6%	2	`x`
70.6%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
70.6%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
70.6%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
70.6%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes9.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
34.0%	1	`x`
34.0%	1	`p`
34.0%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
34.0%	1	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
34.0%	1	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
34.0%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
34.0%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.9999852983335623

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.00414047160352341	0.9999999999975949
0.0ms	-0.9999852983335623	-0.12409355057561297

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.00414047160352341	0.9999999999975949
0.0ms	-0.9999852983335623	-0.12409355057561297

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.00414047160352341	0.9999999999975949
0.0ms	-0.9999852983335623	-0.12409355057561297

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch14.0ms (0.1%)

Memory

-46.5MiB live, 8.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.00414047160352341	0.9999999999975949

Samples

8.0ms

112×

valid

Compiler

Compiled 99 to 82 computations (17.2% saved)

Precisions

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

ival-add: 1.0ms (46.8% of total)

ival-mult: 1.0ms (46.8% of total)

ival-sqrt: 1.0ms (46.8% of total)

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

exact: 0.0ms (0% of total)

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

simplify10.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	417
1	74	417
2	80	417
3	85	417
4	88	417
5	89	417

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness627.0ms (5.6%)

Memory

36.6MiB live, 609.7MiB allocated

Rules

11 436×	`lower-fma.f64`
11 436×	`lower-fma.f32`
10 048×	`lower-fma.f64`
10 048×	`lower-fma.f32`
8 112×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	280
0	64	270
1	211	250
2	1094	246
0	8581	238
0	472	2993
1	1444	2876
2	4985	2834
0	8534	2634
0	1016	10877
1	3106	10312
0	8810	9662
0	14	78
0	23	78
1	77	78
2	501	78
3	6967	78
0	8492	70

Stop Event

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

Compiler

Compiled 470 to 250 computations (46.8% saved)

preprocess134.0ms (1.2%)

Memory: -15.3MiB live, 204.2MiB allocated
Compiler: Compiled 548 to 176 computations (67.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze463.0ms (4.1%)

sample2.0s (18.1%)

explain277.0ms (2.5%)

preprocess65.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

localize63.0ms (0.6%)

series24.0ms (0.2%)

simplify327.0ms (2.9%)

rewrite233.0ms (2.1%)

eval88.0ms (0.8%)

prune85.0ms (0.8%)

simplify41.0ms (0.4%)

localize381.0ms (3.4%)

series104.0ms (0.9%)

simplify953.0ms (8.5%)

rewrite324.0ms (2.9%)

eval390.0ms (3.5%)

prune482.0ms (4.3%)

simplify696.0ms (6.2%)

localize273.0ms (2.4%)

series61.0ms (0.5%)

simplify359.0ms (3.2%)

rewrite313.0ms (2.8%)

eval196.0ms (1.7%)

prune150.0ms (1.3%)

simplify299.0ms (2.7%)

localize271.0ms (2.4%)

series35.0ms (0.3%)

simplify546.0ms (4.9%)

rewrite432.0ms (3.8%)

eval238.0ms (2.1%)

prune161.0ms (1.4%)

regimes44.0ms (0.4%)

regimes19.0ms (0.2%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch14.0ms (0.1%)

simplify10.0ms (0.1%)

soundness627.0ms (5.6%)

preprocess134.0ms (1.2%)

end0.0ms (0%)

Profiling