Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze510.0ms (5.1%)

Memory

30.8MiB live, 659.5MiB 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)

sample2.1s (21.6%)

Memory

56.0MiB live, 3 012.3MiB allocated

Samples

952.0ms	6 251×	0	valid
357.0ms	978×	2	valid
134.0ms	660×	1	valid
122.0ms	367×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

const: 323.0ms (25.4% of total)

ival-mult: 251.0ms (19.8% of total)

ival-sqrt: 234.0ms (18.4% of total)

ival-add: 138.0ms (10.9% of total)

ival-div: 101.0ms (8% of total)

adjust: 98.0ms (7.7% of total)

ival-fabs: 63.0ms (5% of total)

ival-<: 38.0ms (3% of total)

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

exact: 9.0ms (0.7% of total)

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

Bogosity

explain338.0ms (3.4%)

Memory

-1.5MiB live, 318.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
70	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
25	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
25	-	2	(-2.883856766100166e-170 -3.9415681502461e-10)	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
0	-	0	-	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`p`
0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	-	0	-	`#s(literal 1/2 binary64)`
0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	oflow-rescue	70	0
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	70
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	70
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	25	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	uflow-rescue	23	0
↳	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	underflow	10
↳	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`	underflow	33
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	33
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	12
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	53

Confusion

	Predicted +	Predicted -
+	48	0
-	70	138

Precision

0.4067796610169492

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	48	0	0
-	70	0	138

Precision?

0.4067796610169492

Recall?

1.0

Freqs

test

number	freq
0	138
1	118

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms	396×	0	valid
24.0ms	30×	3	valid
13.0ms	54×	2	valid
5.0ms	32×	1	valid

Compiler

Compiled 211 to 46 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-sqrt: 25.0ms (40.8% of total)

ival-mult: 19.0ms (31% of total)

ival-add: 7.0ms (11.4% of total)

ival-div: 5.0ms (8.2% of total)

adjust: 4.0ms (6.5% of total)

exact: 1.0ms (1.6% of total)

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

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

preprocess67.0ms (0.7%)

Memory

-13.2MiB live, 23.3MiB 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	82.7%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB 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)

localize110.0ms (1.1%)

Memory

2.2MiB live, 71.5MiB 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	5.40712221032969	(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	5.5314704139523565	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	16.26125716354799	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

44.0ms	27×	2	valid
17.0ms	198×	0	valid
5.0ms	15×	3	valid
2.0ms	16×	1	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-add: 40.0ms (70.7% of total)

ival-mult: 7.0ms (12.4% of total)

ival-sqrt: 5.0ms (8.8% of total)

ival-div: 2.0ms (3.5% of total)

adjust: 2.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

series48.0ms (0.5%)

Memory

1.8MiB live, 44.8MiB 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>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
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#s(alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -2 p) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))) (taylor -inf p) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 p) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#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
25.0ms	x	@	inf	(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
3.0ms	x	@	-inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
2.0ms	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))))))

simplify622.0ms (6.3%)

Memory

-180.7MiB live, 425.5MiB 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))

rewrite222.0ms (2.2%)

Memory

19.1MiB live, 412.5MiB 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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eval78.0ms (0.8%)

Memory: -14.5MiB live, 151.6MiB allocated
Compiler: Compiled 16 971 to 2 158 computations (87.3% saved)

prune67.0ms (0.7%)

Memory

11.4MiB live, 168.2MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	435	9	444
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	436	9	445

Accuracy

99.7%

Counts

445 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	82.7%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	55.8%	(sqrt.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
▶	7.6%	(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)))))
	23.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
	55.9%	(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))))
▶	15.4%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
	34.6%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	58.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	24.6%	#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 232 to 150 computations (35.3% saved)

simplify38.0ms (0.4%)

Memory

20.2MiB live, 56.8MiB 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	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
cost-diff	0	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Rules

464×	`lower-fma.f32`
460×	`lower-fma.f64`
450×	`lower-*.f32`
436×	`lower-*.f64`
220×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	300
0	63	286
1	108	286
2	162	286
3	304	286
4	489	286
5	579	286
6	714	286
7	853	286
8	935	286
9	1113	286
10	1122	286
11	1123	286
12	1123	286
0	1123	284

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize129.0ms (1.3%)

Memory

25.0MiB live, 289.4MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.3828125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) p)
accuracy	0.46875	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p))
accuracy	48.09204133195089	#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	5.40712221032969	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
accuracy	7.658985764401478	(/.f64 (.f64 p p) (.f64 x x))
accuracy	47.41210924343697	#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	5.40712221032969	(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	5.5314704139523565	(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64)))
accuracy	47.94033507415952	#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64))
accuracy	5.40712221032969	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	26.635394675469314	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.0078125	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))
accuracy	5.40712221032969	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	5.522903072577995	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	16.26125716354799	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))

Samples

43.0ms	198×	0	valid
19.0ms	15×	3	valid
18.0ms	27×	2	valid
6.0ms	16×	1	valid

Compiler

Compiled 270 to 33 computations (87.8% saved)

Precisions

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

ival-sqrt: 19.0ms (31.7% of total)

ival-mult: 16.0ms (26.7% of total)

ival-div: 12.0ms (20% of total)

ival-add: 8.0ms (13.4% of total)

adjust: 4.0ms (6.7% of total)

exact: 1.0ms (1.7% of total)

ival-neg: 1.0ms (1.7% of total)

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

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

series59.0ms (0.6%)

Memory

-27.5MiB live, 94.6MiB allocated

Counts

20 → 408

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (patch (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (patch (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.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 (.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 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#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

102 calls:

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

simplify254.0ms (2.6%)

Memory

14.5MiB live, 400.8MiB allocated

Algorithm

1×	egg-herbie

Rules

7 582×	`lower-fma.f64`
7 582×	`lower-fma.f32`
6 492×	`lower-*.f64`
6 492×	`lower-*.f32`
2 804×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	598	8579
1	1837	8132
2	6390	8008
0	8025	7523

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 406

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)))
(* 1/2 (/ 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))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
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)))))
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1
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1/2
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1
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(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
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1/2
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1/2
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(+ (* -1 (/ (* (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 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (* (sqrt 1/2) (sqrt 2)))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* p (sqrt 2))
(* 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) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 p p) (.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/128 binary64) (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64))) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 p p)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
(* -1 (/ p x))
(/.f64 p (neg.f64 x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) p) (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 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) #s(literal -1/64 binary64)) (.f64 p p)))) (.f64 p (.f64 (.f64 x x) (.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 p (.f64 x x))) p)) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) #s(literal -1/64 binary64)) (.f64 p p)))) (.f64 p (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) #s(literal -1/64 binary64)) (.f64 p p)))) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 p p))) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal 144 binary64)) (.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 (.f64 (.f64 (.f64 p p) (.f64 p p)) (.f64 (.f64 p p) (.f64 p p))) #s(literal -64 binary64)))) (.f64 p (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 p (*.f64 x x))) p)) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p p) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 #s(literal -69/16 binary64) (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/512 binary64) (/.f64 (.f64 x (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64)))) (.f64 p (.f64 p (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/128 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/512 binary64) (/.f64 (.f64 x (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(fma.f64 x (fma.f64 #s(literal -1/32 binary64) (.f64 x (/.f64 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 x (.f64 x (fma.f64 #s(literal 3/512 binary64) (.f64 x (/.f64 x (pow.f64 p #s(literal 5 binary64)))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p))))) (/.f64 #s(literal 1/4 binary64) p)) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 (+.f64 (fma.f64 (neg.f64 p) (/.f64 p (.f64 x x)) #s(literal 1 binary64)) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64)) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 p p (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) #s(literal 1/4 binary64)) (.f64 x x))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 p p (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (.f64 x x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x x))
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(* 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)

rewrite240.0ms (2.4%)

Memory

8.2MiB live, 342.8MiB allocated

Rules

5 100×	`lower-/.f32`
5 094×	`lower-/.f64`
4 660×	`lower-*.f32`
4 646×	`lower-*.f64`
3 208×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	265
0	63	251
1	213	231
2	1194	229
0	8211	227

Stop Event

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

Counts

20 → 427

Calls

Call 1

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

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

eval111.0ms (1.1%)

Memory: -23.0MiB live, 213.7MiB allocated
Compiler: Compiled 20 471 to 2 055 computations (90% saved)

prune91.0ms (0.9%)

Memory

2.7MiB live, 200.4MiB allocated

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	828	5	833
Fresh	3	1	4
Picked	3	2	5
Done	0	0	0
Total	834	8	842

Accuracy

99.9%

Counts

842 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	82.7%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	55.8%	(sqrt.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))))
▶	55.9%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
	14.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))))
✓	58.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	24.2%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
▶	24.9%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
▶	34.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 186 to 113 computations (39.2% saved)

simplify155.0ms (1.6%)

Memory

-1.4MiB live, 172.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

5 040×	`lower-fma.f32`
5 032×	`lower-fma.f64`
2 460×	`lower-*.f32`
2 450×	`lower-*.f64`
1 492×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	316
0	63	316
1	104	316
2	177	316
3	299	316
4	563	316
5	1069	316
6	2653	316
7	4767	316
8	5583	316
9	6680	316
0	8058	309

Stop Event

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

Calls

Call 1

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

localize137.0ms (1.4%)

Memory

0.6MiB live, 236.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	5.617248023118156	(.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))))
accuracy	8.326452081453004	(-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
accuracy	16.26125716354799	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
accuracy	27.706249089003144	(fma.f64 (neg.f64 x) (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
accuracy	0	(*.f64 p p)
accuracy	0.20273112915303823	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
accuracy	7.658985764401478	(/.f64 (.f64 p p) (.f64 x x))
accuracy	48.49066370041653	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 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	48.09204133195089	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
accuracy	41.866936059043894	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal 1/4 binary64) p)
accuracy	0.10546875	(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
accuracy	5.40712221032969	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
accuracy	28.16321105582179	#s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))

Samples

31.0ms	54×	2	valid
29.0ms	141×	0	valid
17.0ms	24×	3	valid
14.0ms	37×	1	valid

Compiler

Compiled 307 to 34 computations (88.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 19.0ms (29.3% of total)

ival-div: 15.0ms (23.1% of total)

adjust: 9.0ms (13.9% of total)

ival-sqrt: 9.0ms (13.9% of total)

ival-add: 9.0ms (13.9% of total)

ival-sub: 2.0ms (3.1% of total)

exact: 1.0ms (1.5% of total)

ival-neg: 1.0ms (1.5% of total)

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

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

series64.0ms (0.6%)

Memory

-17.8MiB live, 61.5MiB allocated

Counts

17 → 372

Calls

Call 1

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

93 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(sqrt (* (+ (* (neg x) (/ x (+ (* x x) (* p (* 4 p))))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))
5.0ms	x	@	-inf	(+ (* (neg x) (/ x (+ (* x x) (* p (* 4 p))))) 1)
2.0ms	p	@	0	(+ (* (neg x) (/ x (+ (* x x) (* p (* 4 p))))) 1)
2.0ms	x	@	-inf	(sqrt (* (+ (* (neg x) (/ x (+ (* x x) (* p (* 4 p))))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))))))
2.0ms	x	@	inf	(* (+ (* (neg x) (/ x (+ (* x x) (* p (* 4 p))))) 1) (/ 1/2 (- 1 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))

simplify513.0ms (5.2%)

Memory

49.2MiB live, 358.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 954×	`lower-fma.f64`
7 954×	`lower-fma.f32`
6 588×	`lower-*.f64`
6 588×	`lower-*.f32`
3 222×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	724	7546
1	2203	7345
2	7731	7325
0	8270	6857

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 370

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)))))))
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(+ 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) (* 1/4 (/ (* 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
(+ 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))))))
(* 4 (/ (pow p 2) (pow x 2)))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4))))) (pow x 2))
(/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* 4 (/ (pow p 2) (pow x 2)))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4))))) (pow x 2))
(/ (+ (* -256 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 4) (pow x 2))) (+ (* 4 (pow p 2)) (* 64 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* 4 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* -16 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* 64 (/ (pow p 2) (pow x 6))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -256 (/ (pow p 2) (pow x 8))) (* 64 (/ 1 (pow x 6))))) (* 16 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/4 (/ (pow x 2) (pow p 2))))
(+ 1 (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/16 (/ (pow x 4) (pow p 4)))))
(+ 1 (+ (* -1/4 (/ (pow x 2) (pow p 2))) (+ (* -1/64 (/ (pow x 6) (pow p 6))) (* 1/16 (/ (pow x 4) (pow p 4))))))
1
(+ 1 (* -1/4 (/ (pow x 2) (pow p 2))))
(+ 1 (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/16 (/ (pow x 4) (pow p 4)))))
(+ 1 (+ (* -1/4 (/ (pow x 2) (pow p 2))) (+ (* -1/64 (/ (pow x 6) (pow p 6))) (* 1/16 (/ (pow x 4) (pow p 4))))))
(* 2 p)
(+ (* 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 (* -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 (/ (pow p 2) (pow x 2)))
(/ (- (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -2 (pow p 2))) (pow x 2))
(/ (- (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (+ (* -2 (pow p 2)) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))))) (pow x 2))
(/ (- (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* -2 (pow p 2)) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4)))))) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
(* 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 (* -1/2 (/ x p)))
(- (+ 1 (* 1/16 (/ (pow x 3) (pow p 3)))) (* 1/2 (/ x p)))
(- (+ 1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* -1 (/ (- (* 1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)))
(+ 1 (* -1 (/ (- (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4)) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)))

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

rewrite339.0ms (3.4%)

Memory

-1.0MiB live, 280.7MiB allocated

Rules

4 562×	`lower-*.f32`
4 552×	`lower-*.f64`
4 320×	`lower-/.f32`
4 308×	`lower-/.f64`
3 924×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	243
0	63	213
1	222	207
2	1546	207
0	8343	200

Stop Event

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

Counts

17 → 480

Calls

Call 1

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

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

eval179.0ms (1.8%)

Memory: -2.8MiB live, 221.0MiB allocated
Compiler: Compiled 29 357 to 2 474 computations (91.6% saved)

prune168.0ms (1.7%)

Memory

-24.5MiB live, 230.9MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	873	1	874
Fresh	0	1	1
Picked	1	4	5
Done	0	2	2
Total	874	8	882

Accuracy

99.9%

Counts

882 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	82.7%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	55.9%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
▶	55.6%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 (+.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))))
▶	14.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))))
✓	58.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	24.2%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
✓	24.9%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
✓	34.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 97 to 63 computations (35.1% saved)

simplify292.0ms (2.9%)

Memory

23.6MiB live, 182.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 (+.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))))
cost-diff	128	(+.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p)) #s(literal -1/4 binary64))
cost-diff	320	(.f64 (.f64 x #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/4 binary64)))
cost-diff	320	(.f64 (+.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))))
cost-diff	192	(.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64))
cost-diff	12928	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))

Rules

6 480×	`lower-*.f32`
6 468×	`lower-*.f64`
2 384×	`cube-prod`
1 840×	`lower-/.f32`
1 832×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	263
0	58	245
1	111	238
2	190	238
3	391	238
4	985	232
5	1376	232
6	2177	232
7	2397	232
8	2468	232
9	2491	232
10	2507	232
11	2507	232
12	2546	232
13	2621	232
14	2698	232
15	3593	232
16	3719	232
17	3888	232
18	4080	232
19	4389	232
20	4895	232
21	6029	232
22	6431	232
23	6907	232
24	7173	232
25	7369	232
26	7437	232
27	7507	232
28	7577	232
0	8007	220

Stop Event

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

Calls

Call 1

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

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

localize133.0ms (1.3%)

Memory

-17.8MiB live, 212.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	5.40712221032969	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 (+.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))))
accuracy	7.871187954359864	(/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p))
accuracy	13.41841292813332	(.f64 (+.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))
accuracy	28.16321105582179	#s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 (+.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (*.f64 p p)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))))
accuracy	5.40712221032969	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))))
accuracy	7.919713801418313	(/.f64 (.f64 x x) (.f64 p p))
accuracy	30.11806971670658	(log.f64 (/.f64 (.f64 x x) (.f64 p p)))
accuracy	47.41210924343697	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64))))

Samples

51.0ms	198×	0	valid
18.0ms	27×	2	valid
12.0ms	15×	3	valid
8.0ms	16×	1	valid

Compiler

Compiled 198 to 41 computations (79.3% saved)

Precisions

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

ival-mult: 19.0ms (27.2% of total)

ival-div: 17.0ms (24.3% of total)

ival-sqrt: 11.0ms (15.8% of total)

ival-add: 9.0ms (12.9% of total)

adjust: 5.0ms (7.2% of total)

ival-log: 4.0ms (5.7% of total)

ival-exp: 3.0ms (4.3% of total)

exact: 1.0ms (1.4% of total)

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

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

series86.0ms (0.9%)

Memory

20.7MiB live, 149.2MiB allocated

Counts

12 → 276

Calls

Call 1

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

Outputs
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor 0 p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf p) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* 2 (log x)))) (taylor 0 x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* 2 (log x)))) (taylor 0 x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* 2 (log x)))) (taylor 0 x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* 2 (log x)))) (taylor 0 x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ 1 x))))) (taylor inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ 1 x))))) (taylor inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ 1 x))))) (taylor inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ 1 x))))) (taylor inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ 1 (pow p 2))) (* -2 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* -2 (log p)))) (taylor 0 p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* -2 (log p)))) (taylor 0 p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* -2 (log p)))) (taylor 0 p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* -2 (log p)))) (taylor 0 p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ 1 p))))) (taylor inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ 1 p))))) (taylor inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ 1 p))))) (taylor inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ 1 p))))) (taylor inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ -1 p))))) (taylor -inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ -1 p))))) (taylor -inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ -1 p))))) (taylor -inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (pow x 2)) (* 2 (log (/ -1 p))))) (taylor -inf p) (#s(alt (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 p p))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 1/16 (/ (pow x 2) (pow p 2))) (taylor -inf p) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p)) (patch (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (* 1/16 (/ (pow x 2) (pow p 2))) (taylor -inf p) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p)) (patch (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (* 1/16 (/ (pow x 2) (pow p 2))) (taylor -inf p) (#s(alt (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p)) (patch (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 p p)) #<representation binary64>) () ())) ())

Calls

69 calls:

Time	Variable		Point	Expression
35.0ms	x	@	0	(* (log (/ (* x x) (* p p))) -1)
19.0ms	p	@	0	(* (log (/ (* x x) (* p p))) -1)
6.0ms	x	@	inf	(* (log (/ (* x x) (* p p))) -1)
6.0ms	p	@	inf	(* (log (/ (* x x) (* p p))) -1)
2.0ms	x	@	0	(* (+ (/ (* (* x 1/4) (* x 1/4)) (* p p)) -1/4) (/ 1 (+ (* x (/ 1/4 p)) -1/2)))

simplify303.0ms (3.1%)

Memory

-11.0MiB live, 375.5MiB allocated

Algorithm

1×	egg-herbie

Rules

7 796×	`lower-fma.f64`
7 796×	`lower-fma.f32`
7 398×	`lower-*.f64`
7 398×	`lower-*.f32`
3 916×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	469	4029
1	1413	3871
2	4938	3808
0	8591	3599

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

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

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

rewrite937.0ms (9.5%)

Memory

-4.1MiB live, 384.6MiB allocated

Rules

6 508×	`lower-fma.f32`
6 506×	`lower-fma.f64`
5 324×	`lower-*.f32`
5 312×	`lower-*.f64`
4 738×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	225
0	58	201
1	242	151
2	1543	144
0	8644	132

Stop Event

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

Counts

12 → 428

Calls

Call 1

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

Outputs
(exp.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p)))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 x x))) (/.f64 (.f64 p p) (neg.f64 (*.f64 x x))))
(/.f64 (.f64 p p) (.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 p p))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 p p)))
(/.f64 (neg.f64 (.f64 p p)) (neg.f64 (.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (.f64 p p))) (neg.f64 (neg.f64 (.f64 x x))))
(/.f64 (/.f64 (*.f64 p p) x) x)
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (.f64 #s(literal 2 binary64) (log.f64 x))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (.f64 p p))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (.f64 x x)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (.f64 p p)))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (*.f64 x x) p))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 p)))
(/.f64 (neg.f64 (/.f64 (*.f64 p p) x)) (neg.f64 x))
(pow.f64 (/.f64 (.f64 x x) (.f64 p p)) #s(literal -1 binary64))
(pow.f64 (/.f64 x p) #s(literal -2 binary64))
(pow.f64 (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p))))
(pow.f64 (/.f64 p x) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 x p)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 (.f64 x x) (.f64 p p)) (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1/2 binary64))
(.f64 p (/.f64 p (.f64 x x)))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 p p)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 p p) x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 p p)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p x) (/.f64 p x))
(.f64 (/.f64 p #s(literal 1 binary64)) (/.f64 p (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 p p))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x p)) (/.f64 #s(literal 1 binary64) (/.f64 x p)))
(.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (.f64 #s(literal 2 binary64) (log.f64 x))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal -2 binary64) (log.f64 p))))
(.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 x)) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x (.f64 p p)))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x p))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x p))))
(.f64 (pow.f64 (neg.f64 (.f64 x x)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 p p))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x x) p) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) p) #s(literal -1 binary64)))
(.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 (neg.f64 p) (.f64 x x)))
(*.f64 (/.f64 p (neg.f64 x)) (/.f64 (neg.f64 p) x))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 p p) (neg.f64 x)))
(*.f64 (/.f64 (neg.f64 p) x) (/.f64 p (neg.f64 x)))
(log.f64 (/.f64 (.f64 p p) (.f64 x x)))
(+.f64 (log.f64 (.f64 p p)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))))
(+.f64 (log.f64 p) (log.f64 (/.f64 p (*.f64 x x))))
(+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (log.f64 (.f64 p p)))
(+.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) (log.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 p p))))
(+.f64 (log.f64 (/.f64 p x)) (log.f64 (/.f64 p x)))
(+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 x p))) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 x p))))
(-.f64 (log.f64 (.f64 p p)) (.f64 #s(literal 2 binary64) (log.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p))))
(-.f64 (log.f64 (neg.f64 (.f64 p p))) (log.f64 (neg.f64 (.f64 x x))))
(-.f64 (log.f64 (/.f64 (*.f64 p p) x)) (log.f64 x))
(fma.f64 #s(literal 2 binary64) (log.f64 p) (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(fma.f64 (log.f64 p) #s(literal 2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(neg.f64 (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p))))
(.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p))) #s(literal -1 binary64))
(.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p))) (log.f64 (exp.f64 #s(literal -1 binary64))))
(.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (log.f64 (/.f64 x p))))
(exp.f64 (.f64 (log.f64 #s(approx (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x)))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x))))
(pow.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 #s(approx (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x))) #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x))))) #s(literal 1/2 binary64))
(.f64 (pow.f64 #s(approx (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x))) #s(literal 1/4 binary64)))
#s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 (.f64 p p) (.f64 x x)))
(+.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) #s(literal -1/4 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) #s(literal -1/4 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (*.f64 p p)))))
(+.f64 (.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))) (*.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))))
(+.f64 (.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))) (.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (*.f64 p p))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal -1/2 binary64))
(-.f64 (/.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (*.f64 p p))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/16 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) x))) (.f64 (.f64 p p) (.f64 p p))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)) #s(literal 1/4 binary64))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)) #s(literal 1/4 binary64))) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/16 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) x))) (.f64 (.f64 p p) (.f64 p p))) (.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 p (.f64 p p)) #s(literal 64 binary64))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) p)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) p)))))
(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 #s(literal 1/4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) p) x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p) #s(literal 1/2 binary64))
(fma.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64)))))
(fma.f64 (/.f64 #s(literal 1/4 binary64) p) x #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) #s(literal -1/4 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) #s(literal -1/4 binary64) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal 1/16 binary64) (.f64 p p)))))
(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
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eval123.0ms (1.2%)

Memory: -11.9MiB live, 143.7MiB allocated
Compiler: Compiled 17 193 to 2 164 computations (87.4% saved)

prune105.0ms (1.1%)

Memory

26.8MiB live, 144.0MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	703	1	704
Fresh	0	0	0
Picked	1	1	2
Done	0	6	6
Total	704	8	712

Accuracy

99.9%

Counts

712 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	82.7%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	55.9%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
	55.6%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) x) (*.f64 p p)) x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal -1/2 binary64))))))
✓	14.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 p p))) #s(literal -1 binary64)))))
✓	58.9%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	24.2%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64)))
✓	24.9%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
✓	34.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 295 to 138 computations (53.2% saved)

regimes50.0ms (0.5%)

Memory

-8.4MiB live, 36.4MiB allocated

Counts

17 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

19.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
6.0ms	p
5.0ms	x
5.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
82.7%	1	`p`
85.5%	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))))`
82.7%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes25.0ms (0.2%)

Memory

-23.6MiB live, 16.1MiB allocated

Counts

11 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

14.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
3.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
3.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
99.6%	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)))))))`
99.6%	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))))))`
99.6%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.6%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes10.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

6 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

2.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
2.0ms	(+.f64 #s(literal 1 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
98.6%	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)))))))`
98.6%	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))))))`
98.6%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.6%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes10.0ms (0.1%)

Memory

-22.3MiB live, 16.4MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes12.0ms (0.1%)

Memory

23.5MiB live, 23.5MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
71.4%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
71.4%	2	`p`
62.0%	2	`x`
77.0%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
77.0%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
77.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
77.0%	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)

regimes22.0ms (0.2%)

Memory

-20.1MiB live, 18.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

15.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
1.0ms	p
1.0ms	x
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
34.6%	1	`x`
34.6%	1	`p`
34.6%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
34.6%	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)))))))`
34.6%	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))))))`
34.6%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
34.6%	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	-0.9999999999999161	-0.03252378223129951

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.3647243362531814e-5	0.9999999999780322
0.0ms	-0.9999999999999161	-0.03252378223129951

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	1.3647243362531814e-5	0.9999999999780322
0.0ms	-0.9999999999999161	-0.03252378223129951

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	1.3647243362531814e-5	0.9999999999780322
0.0ms	-0.9999999999999161	-0.03252378223129951

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch12.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	1.3647243362531814e-5	0.9999999999780322

Samples

6.0ms

144×

valid

Compiler

Compiled 121 to 100 computations (17.4% saved)

Precisions

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

ival-add: 1.0ms (36.6% of total)

ival-mult: 1.0ms (36.6% of total)

ival-sqrt: 1.0ms (36.6% of total)

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

exact: 0.0ms (0% of total)

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

simplify32.0ms (0.3%)

Memory

-11.4MiB live, 34.7MiB 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	61	417
1	72	417
2	78	417
3	83	417
4	86	417
5	87	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 -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (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 (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (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 (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (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 (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (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 (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (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 (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (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 (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x))) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 5902958103587057/295147905179352825856 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

soundness787.0ms (7.9%)

Memory

17.0MiB live, 487.6MiB allocated

Rules

10 048×	`lower-fma.f64`
10 048×	`lower-fma.f32`
7 582×	`lower-fma.f64`
7 582×	`lower-fma.f32`
7 228×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	598	8579
1	1837	8132
2	6390	8008
0	8025	7523
0	14	78
0	23	78
1	77	78
2	501	78
3	6967	78
0	8492	70
0	472	2993
1	1444	2876
2	4985	2834
0	8534	2634

Stop Event

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

Compiler

Compiled 930 to 370 computations (60.2% saved)

preprocess288.0ms (2.9%)

Memory: 13.8MiB live, 128.8MiB allocated
Compiler: Compiled 548 to 172 computations (68.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze510.0ms (5.1%)

sample2.1s (21.6%)

explain338.0ms (3.4%)

preprocess67.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize110.0ms (1.1%)

series48.0ms (0.5%)

simplify622.0ms (6.3%)

rewrite222.0ms (2.2%)

eval78.0ms (0.8%)

prune67.0ms (0.7%)

simplify38.0ms (0.4%)

localize129.0ms (1.3%)

series59.0ms (0.6%)

simplify254.0ms (2.6%)

rewrite240.0ms (2.4%)

eval111.0ms (1.1%)

prune91.0ms (0.9%)

simplify155.0ms (1.6%)

localize137.0ms (1.4%)

series64.0ms (0.6%)

simplify513.0ms (5.2%)

rewrite339.0ms (3.4%)

eval179.0ms (1.8%)

prune168.0ms (1.7%)

simplify292.0ms (2.9%)

localize133.0ms (1.3%)

series86.0ms (0.9%)

simplify303.0ms (3.1%)

rewrite937.0ms (9.5%)

eval123.0ms (1.2%)

prune105.0ms (1.1%)

regimes50.0ms (0.5%)

regimes25.0ms (0.2%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes12.0ms (0.1%)

regimes22.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch12.0ms (0.1%)

simplify32.0ms (0.3%)

soundness787.0ms (7.9%)

preprocess288.0ms (2.9%)

end0.0ms (0%)

Profiling