Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze471.0ms (5.3%)

Memory

15.6MiB live, 662.7MiB 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)

sample2.3s (25.9%)

Memory

-86.5MiB live, 3 190.4MiB allocated

Samples

1.2s	6 192×	0	valid
335.0ms	1 039×	2	valid
150.0ms	430×	3	valid
123.0ms	595×	1	valid

Precisions

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

ival-mult: 563.0ms (37% of total)

const: 275.0ms (18.1% of total)

ival-sqrt: 184.0ms (12.1% of total)

ival-div: 147.0ms (9.7% of total)

ival-add: 131.0ms (8.6% of total)

adjust: 81.0ms (5.3% of total)

ival-fabs: 70.0ms (4.6% of total)

ival-<: 48.0ms (3.2% of total)

ival-and: 10.0ms (0.7% of total)

exact: 9.0ms (0.6% of total)

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

Bogosity

explain252.0ms (2.8%)

Memory

-32.9MiB live, 357.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
57	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
40	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
27	-	2	(-1.5520753876095634e-86 -1.910327219528795e+73)	`(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	57	0
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	57
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	57
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	40	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	25	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	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))))))`	underflow	28
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	28
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	15
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	59

Confusion

	Predicted +	Predicted -
+	65	0
-	57	134

Precision

0.5327868852459017

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	65	0	0
-	57	0	134

Precision?

0.5327868852459017

Recall?

1.0

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms	378×	0	valid
24.0ms	54×	1	valid
20.0ms	60×	2	valid
6.0ms	20×	3	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 (40.9% of total)

ival-add: 13.0ms (21.2% of total)

ival-mult: 13.0ms (21.2% 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)

preprocess65.0ms (0.7%)

Memory

1.5MiB live, 39.7MiB 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
▶	76.1%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize58.0ms (0.7%)

Memory

7.5MiB live, 43.3MiB 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	6.014883735639362	(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	9.122104135743406	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	13.209135952898679	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

29.0ms	189×	0	valid
7.0ms	30×	2	valid
4.0ms	27×	1	valid
3.0ms	10×	3	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

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

ival-sqrt: 18.0ms (55.4% of total)

ival-mult: 6.0ms (18.5% of total)

ival-add: 3.0ms (9.2% of total)

ival-div: 2.0ms (6.2% of total)

adjust: 2.0ms (6.2% of total)

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.3%)

Memory

-12.1MiB live, 24.3MiB allocated

Counts

6 → 144

Calls

Call 1

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

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/4 (/ x p))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6)))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#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
3.0ms	x	@	-inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
2.0ms	x	@	-inf	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1.0ms	x	@	inf	(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
1.0ms	p	@	0	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))
1.0ms	x	@	inf	(* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))

simplify270.0ms (3%)

Memory

25.4MiB live, 411.9MiB 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))

rewrite257.0ms (2.9%)

Memory

-35.6MiB live, 466.5MiB 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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eval118.0ms (1.3%)

Memory: 11.9MiB live, 128.2MiB allocated
Compiler: Compiled 16 971 to 2 158 computations (87.3% saved)

prune64.0ms (0.7%)

Memory

24.5MiB live, 140.0MiB 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
▶	76.1%	(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)))
▶	4.8%	(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)))))
▶	17.0%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x)))))
	26.1%	(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))))
	50.4%	(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))))
▶	17.0%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
	35.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	54.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
	28.2%	#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 196 to 136 computations (30.6% saved)

simplify23.0ms (0.3%)

Memory

-41.4MiB live, 19.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

126×	`lower-*.f32`
110×	`lower-*.f64`
42×	`*-commutative`
36×	`lower-/.f32`
30×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	342
0	60	327
1	106	327
2	140	327
3	165	327
4	166	327
0	166	325

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

localize105.0ms (1.2%)

Memory

28.9MiB live, 140.9MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x))))
accuracy	6.014883735639362	(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x)))))
accuracy	8.247598717713482	(/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x))
accuracy	45.11466552710011	#s(approx (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x)))
accuracy	0	(*.f64 p p)
accuracy	6.014883735639362	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x))))
accuracy	8.248779978192168	(/.f64 (.f64 p p) (.f64 x x))
accuracy	45.114802874101194	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (/.f64 (.f64 p p) (.f64 x x)))
accuracy	0	(.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	6.014883735639362	(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	9.122104135743406	(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64)))
accuracy	45.64997970263664	#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64))
accuracy	6.014883735639362	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	29.541805054460973	#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	6.014883735639362	(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	9.11373722242291	(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	13.209135952898679	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))

Samples

36.0ms	189×	0	valid
15.0ms	32×	2	valid
8.0ms	25×	1	valid
6.0ms	10×	3	valid

Compiler

Compiled 293 to 30 computations (89.8% saved)

Precisions

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

ival-mult: 16.0ms (36.4% of total)

ival-sqrt: 9.0ms (20.5% of total)

ival-div: 8.0ms (18.2% of total)

ival-add: 7.0ms (15.9% of total)

adjust: 3.0ms (6.8% of total)

exact: 1.0ms (2.3% of total)

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

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

series34.0ms (0.4%)

Memory

-41.1MiB live, 45.0MiB allocated

Counts

18 → 420

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

Calls

105 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
2.0ms	x	@	0	(/ (* p p) (* x x))
1.0ms	x	@	inf	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
1.0ms	x	@	0	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
1.0ms	p	@	0	(/ (* p p) (* x x))

simplify375.0ms (4.2%)

Memory

15.1MiB live, 291.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 612×	`lower-fma.f64`
7 612×	`lower-fma.f32`
6 514×	`lower-*.f64`
6 514×	`lower-*.f32`
2 804×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	597	9337
1	1835	8860
2	6385	8715
0	8027	8163

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 418

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

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

rewrite340.0ms (3.8%)

Memory

23.8MiB live, 255.2MiB allocated

Rules

6 454×	`lower-fma.f32`
6 450×	`lower-fma.f64`
4 532×	`lower-*.f32`
4 516×	`lower-*.f64`
3 418×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	298
0	60	283
1	209	277
2	1135	269
0	8561	267

Stop Event

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

Counts

18 → 408

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

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

eval160.0ms (1.8%)

Memory: -0.8MiB live, 237.1MiB allocated
Compiler: Compiled 20 834 to 2 046 computations (90.2% saved)

prune114.0ms (1.3%)

Memory

14.3MiB live, 212.4MiB allocated

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	821	5	826
Fresh	4	0	4
Picked	3	2	5
Done	0	0	0
Total	828	7	835

Accuracy

99.9%

Counts

835 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.1%	(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)))
▶	50.4%	(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))))
✓	54.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	19.7%	(exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64)))
▶	26.5%	#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)))
▶	28.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
▶	35.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 118 to 77 computations (34.7% saved)

simplify19.0ms (0.2%)

Memory

-14.4MiB live, 22.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

192×	`lower-fma.f32`
188×	`lower-fma.f64`
146×	`lower-*.f32`
144×	`lower-+.f64`
144×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	287
0	58	285
1	102	284
2	148	284
3	191	284
4	210	284
5	223	284
6	256	284
7	318	284
8	384	284
9	398	284
10	399	284
0	399	266

Stop Event

1×	iter limit
1×	saturated
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)
(exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64)))
(.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64))
(log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))))
#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))
(.f64 p (/.f64 p (.f64 x x)))
p
(/.f64 p (*.f64 x x))
(*.f64 x x)
x
#s(literal 1/2 binary64)

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

localize181.0ms (2%)

Memory

15.4MiB live, 300.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.20703125	(/.f64 p (*.f64 x x))
accuracy	1.3782186244783372	(exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64)))
accuracy	14.269523441349278	(log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))))
accuracy	45.114802874101194	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 p p)
accuracy	8.248779978192168	(/.f64 (.f64 p p) (.f64 x x))
accuracy	47.03496640611928	#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	45.710299840807494	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
accuracy	41.10813024045848	#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	0.13671875	(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
accuracy	6.014883735639362	(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	31.67067348131318	#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

78.0ms	75×	2	valid
40.0ms	127×	0	valid
20.0ms	44×	1	valid
8.0ms	10×	3	valid

Compiler

Compiled 227 to 38 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-log: 29.0ms (24.1% of total)

adjust: 26.0ms (21.6% of total)

ival-mult: 21.0ms (17.4% of total)

ival-div: 18.0ms (14.9% of total)

ival-add: 13.0ms (10.8% of total)

ival-sqrt: 9.0ms (7.5% of total)

ival-exp: 4.0ms (3.3% of total)

exact: 1.0ms (0.8% of total)

ival-neg: 1.0ms (0.8% of total)

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

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

series38.0ms (0.4%)

Memory

-39.2MiB live, 83.5MiB allocated

Counts

18 → 384

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 (exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64)) (patch (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) (patch (log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<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>) () ())) ())
#s(alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))))) (taylor inf x) (#s(alt (sqrt.f64 #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))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6)))))) (taylor inf x) (#s(alt (sqrt.f64 #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 (/ p x)) (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 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x)) (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 (+ (log 1/2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) p)) (* 1/2 x)) p))) (taylor -inf p) (#s(alt (log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) (patch (log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) p)) (* -1/8 (pow x 2))) p)) (* 1/2 x)) p))) (taylor -inf p) (#s(alt (log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) (patch (log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/4 (/ x p))) (taylor 0 x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 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 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 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 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 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 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 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 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/4 (/ x p))) (taylor inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))) (taylor inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 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))))) (taylor inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor -inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/4 (/ x p))) (taylor -inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))) (taylor -inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ 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))) (taylor -inf p) (#s(alt #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) (patch #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf p) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor 0 x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ p (pow x 2)) (taylor -inf x) (#s(alt (/.f64 p (.f64 x x)) (patch (/.f64 p (.f64 x x)) #<representation binary64>) () ())) ())

Calls

96 calls:

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

simplify279.0ms (3.1%)

Memory

-4.2MiB live, 439.3MiB allocated

Algorithm

1×	egg-herbie

Rules

10 320×	`lower-fma.f64`
10 320×	`lower-fma.f32`
7 826×	`lower-*.f64`
7 826×	`lower-*.f32`
5 018×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	520	6881
1	1441	6627
2	4683	6495
0	8767	6042

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

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)))))
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(+ (* 1/2 (log 1/2)) (* x (+ (* x (- (* -1/96 (/ x (pow p 3))) (* 1/16 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (* 1/48 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2)))) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (+ (* 1/1440 (/ (+ (* -240 (pow p 6)) (+ (* -180 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -180 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (pow x 4))) (* 1/48 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2))))) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (+ (* 1/80640 (/ (+ (* -10080 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -10080 (* (pow p 4) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -10080 (+ (* -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)))))))) (+ (* -10080 (pow p 8)) (* -1260 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)))))) (pow x 6))) (+ (* 1/1440 (/ (+ (* -240 (pow p 6)) (+ (* -180 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -180 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (pow x 4))) (* 1/48 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2)))))) (pow x 2))
(* 1/2 (+ (log (pow p 2)) (* 2 (log (/ -1 x)))))
(+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 1/2 (+ (log (pow p 2)) (* 2 (log (/ -1 x))))))
(+ (* 1/48 (/ (+ (* -3/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 4))) (* 6 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))) (pow x 4))) (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 1/2 (+ (log (pow p 2)) (* 2 (log (/ -1 x)))))))
(+ (* 1/1440 (/ (+ (* -45 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 4))) (+ (* 15/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 3) (pow p 6))) (* 180 (/ (+ (* -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))) (+ (* 1/48 (/ (+ (* -3/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 4))) (* 6 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))) (pow x 4))) (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 1/2 (+ (log (pow p 2)) (* 2 (log (/ -1 x))))))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 5/4 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* -11/3 (/ (pow p 2) (pow x 6))) (* 5/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 93/8 (/ (pow p 2) (pow x 8))) (* 11/3 (/ 1 (pow x 6))))) (* 5/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/2 (log 1/2))
(+ (* 1/4 (/ x p)) (* 1/2 (log 1/2)))
(+ (* -1/16 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ x p)) (* 1/2 (log 1/2))))
(+ (* -1/16 (/ (pow x 2) (pow p 2))) (+ (* 1/12 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3))) (+ (* 1/4 (/ x p)) (* 1/2 (log 1/2)))))
(* 1/2 (log 1/2))
(+ (* -1/4 (/ x p)) (* 1/2 (log 1/2)))
(+ (* -1 (/ (+ (* 1/16 (/ (pow x 2) p)) (* 1/4 x)) p)) (* 1/2 (log 1/2)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/12 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) p)) (* -1/16 (pow x 2))) p)) (* 1/4 x)) p)) (* 1/2 (log 1/2)))
(log 1/2)
(+ (log 1/2) (* 1/2 (/ x p)))
(+ (log 1/2) (* x (+ (* -1/8 (/ x (pow p 2))) (* 1/2 (/ 1 p)))))
(+ (log 1/2) (* x (+ (* x (- (* -1/48 (/ x (pow p 3))) (* 1/8 (/ 1 (pow p 2))))) (* 1/2 (/ 1 p)))))
(* -1 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1 (pow p 2)) (* 1/24 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2)))) (pow x 2))
(/ (+ (* -1 (pow p 2)) (+ (* 1/720 (/ (+ (* -240 (pow p 6)) (+ (* -180 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -180 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (pow x 4))) (* 1/24 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2))))) (pow x 2))
(/ (+ (* -1 (pow p 2)) (+ (* 1/40320 (/ (+ (* -10080 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -10080 (* (pow p 4) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -10080 (+ (* -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)))))))) (+ (* -10080 (pow p 8)) (* -1260 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)))))) (pow x 6))) (+ (* 1/720 (/ (+ (* -240 (pow p 6)) (+ (* -180 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -180 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (pow x 4))) (* 1/24 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2)))))) (pow x 2))
(+ (log (pow p 2)) (* 2 (log (/ -1 x))))
(+ (log (pow p 2)) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 2 (log (/ -1 x)))))
(+ (log (pow p 2)) (+ (* 1/24 (/ (+ (* -3/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 4))) (* 6 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))) (pow x 4))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 2 (log (/ -1 x))))))
(+ (log (pow p 2)) (+ (* 1/720 (/ (+ (* -45 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 4))) (+ (* 15/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 3) (pow p 6))) (* 180 (/ (+ (* -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))) (+ (* 1/24 (/ (+ (* -3/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 4))) (* 6 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))) (pow x 4))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 2 (log (/ -1 x)))))))
(* -1 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 5/2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (- (* (pow p 2) (+ (* -22/3 (/ (pow p 2) (pow x 6))) (* 5/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 93/4 (/ (pow p 2) (pow x 8))) (* 22/3 (/ 1 (pow x 6))))) (* 5/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(log 1/2)
(+ (log 1/2) (* 1/2 (/ x p)))
(+ (log 1/2) (+ (* -1/8 (/ (pow x 2) (pow p 2))) (* 1/2 (/ x p))))
(+ (log 1/2) (+ (* -1/8 (/ (pow x 2) (pow p 2))) (+ (* 1/6 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3))) (* 1/2 (/ x p)))))
(log 1/2)
(+ (log 1/2) (* -1/2 (/ x p)))
(+ (log 1/2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) p)) (* 1/2 x)) p)))
(+ (log 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) p)) (* -1/8 (pow x 2))) p)) (* 1/2 x)) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))

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

rewrite207.0ms (2.3%)

Memory

1.8MiB live, 364.6MiB allocated

Rules

4 606×	`lower-fma.f32`
4 602×	`lower-fma.f64`
4 086×	`lower-/.f32`
4 078×	`lower-/.f64`
3 812×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	263
0	58	261
1	219	246
2	1314	246
0	8379	228

Stop Event

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

Counts

18 → 299

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

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

eval102.0ms (1.1%)

Memory: 7.2MiB live, 202.9MiB allocated
Compiler: Compiled 14 324 to 1 452 computations (89.9% saved)

prune82.0ms (0.9%)

Memory

-2.5MiB live, 200.2MiB allocated

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	706	5	711
Fresh	0	0	0
Picked	1	4	5
Done	0	2	2
Total	707	11	718

Accuracy

99.9%

Counts

718 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	19.5%	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x))))))
✓	76.1%	(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)))
✓	50.4%	(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))))
▶	50.4%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))))
✓	54.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	19.6%	(exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (exp.f64 (.f64 (log.f64 (/.f64 (*.f64 x x) p)) #s(literal -1 binary64)))))) #s(literal 1/2 binary64)))
✓	26.5%	#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)))
▶	13.0%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.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))))))
✓	28.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
▶	25.7%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64))))
✓	35.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 220 to 143 computations (35% saved)

simplify154.0ms (1.7%)

Memory

18.5MiB live, 174.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (exp.f64 (.f64 (log.f64 (/.f64 (*.f64 x x) p)) #s(literal -1 binary64)))))) #s(literal 1/2 binary64))
cost-diff	320	(.f64 (log.f64 (/.f64 (.f64 x x) p)) #s(literal -1 binary64))
cost-diff	12480	(exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (exp.f64 (.f64 (log.f64 (/.f64 (*.f64 x x) p)) #s(literal -1 binary64)))))) #s(literal 1/2 binary64)))
cost-diff	12800	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) p)) #s(literal -1 binary64)))
cost-diff	0	#s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x))))
cost-diff	0	(log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
cost-diff	0	(exp.f64 #s(literal 1/2 binary64))
cost-diff	18624	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x))))))
cost-diff	0	(log.f64 (/.f64 (neg.f64 x) p))
cost-diff	0	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64))))
cost-diff	320	(*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64))
cost-diff	12800	(exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64)))
cost-diff	192	(+.f64 #s(literal 0 binary64) (fma.f64 p (/.f64 p (.f64 x x)) (.f64 #s(literal 0 binary64) (/.f64 p x))))
cost-diff	1024	(*.f64 #s(literal 0 binary64) (/.f64 p x))
cost-diff	3328	(/.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)))))
cost-diff	5184	(pow.f64 (/.f64 p x) #s(literal 3 binary64))
cost-diff	0	(/.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 (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (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) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))

Rules

5 534×	`lower-*.f32`
5 524×	`lower-*.f64`
2 874×	`lower-fma.f32`
2 870×	`lower-fma.f64`
2 076×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	525
0	93	478
1	167	468
2	256	432
3	592	420
4	2432	420
5	3988	418
6	6398	418
0	8167	396

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

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

localize294.0ms (3.3%)

Memory

7.7MiB live, 291.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	2.211054116753972	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) p)) #s(literal -1 binary64)))
accuracy	6.053331963338844	(log.f64 (/.f64 (*.f64 x x) p))
accuracy	6.91609969136635	(log.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (exp.f64 (.f64 (log.f64 (/.f64 (*.f64 x x) p)) #s(literal -1 binary64))))))
accuracy	15.177612944136126	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (exp.f64 (.f64 (log.f64 (/.f64 (*.f64 x x) p)) #s(literal -1 binary64)))))
accuracy	0.08984375	(/.f64 p (*.f64 x x))
accuracy	1.5296317634815553	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x))))))
accuracy	6.91609969136635	(log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x)))))
accuracy	15.177612944136126	#s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x))))
accuracy	0	(neg.f64 x)
accuracy	2.576592750094466	(log.f64 (/.f64 (neg.f64 x) p))
accuracy	2.6483864624686455	(exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64)))
accuracy	14.990789029017213	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64))))
accuracy	0.14490131837909412	(pow.f64 (/.f64 p x) #s(literal 3 binary64))
accuracy	1.9687389917665112	(*.f64 #s(literal 0 binary64) (/.f64 p x))
accuracy	14.990789029017213	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.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))))))
accuracy	19.33822656846789	(/.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)))))
accuracy	0.06640625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
accuracy	0.08203125	(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
accuracy	6.014883735639362	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))))
accuracy	16.700890298628256	#s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))))

Samples

91.0ms	125×	0	invalid
52.0ms	43×	1	valid
40.0ms	64×	0	valid
34.0ms	24×	2	valid

Compiler

Compiled 407 to 56 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 174.0ms

ival-log: 54.0ms (31.1% of total)

ival-div: 38.0ms (21.9% of total)

ival-mult: 21.0ms (12.1% of total)

ival-pow: 18.0ms (10.4% of total)

ival-exp: 14.0ms (8.1% of total)

ival-add: 10.0ms (5.8% of total)

adjust: 7.0ms (4% of total)

ival-sqrt: 7.0ms (4% of total)

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

exact: 1.0ms (0.6% of total)

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

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

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

series537.0ms (6%)

Memory

-17.4MiB live, 370.1MiB allocated

Counts

27 → 612

Calls

Call 1

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

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

Calls

153 calls:

Time	Variable		Point	Expression
118.0ms	p	@	0	(* (log (/ (neg x) p)) -1)
60.0ms	p	@	-inf	(* (log (/ (* x x) p)) -1)
52.0ms	x	@	inf	(* (log (/ (* x x) p)) -1)
47.0ms	x	@	0	(* (log (/ (neg x) p)) -1)
21.0ms	x	@	inf	(* (log (/ (neg x) p)) -1)

simplify326.0ms (3.6%)

Memory

19.1MiB live, 332.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 248×	`lower-fma.f64`
8 248×	`lower-fma.f32`
6 386×	`lower-*.f64`
6 386×	`lower-*.f32`
3 440×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	762	9807
1	2241	9382
2	7081	9138
0	8177	8580

Stop Event

1×	iter limit
1×	node limit

Counts

612 → 612

Calls

Call 1

Inputs
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)))
(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)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))
(+ 2 (* x (- (* x (+ (* -1/4 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))
(* 4 (/ p x))
(/ (+ (* -8 (/ (pow p 2) x)) (* 4 p)) x)
(/ (- (+ (* 4 p) (* 16 (/ (pow p 3) (pow x 2)))) (* 8 (/ (pow p 2) x))) x)
(/ (- (+ (* -32 (/ (pow p 4) (pow x 3))) (* 4 p)) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 8 (/ (pow p 2) x)))) x)
(* 4 (/ p x))
(* -1 (/ (+ (* -4 p) (* 8 (/ (pow p 2) x))) x))
(* -1 (/ (+ (* -4 p) (* -1 (/ (- (* 16 (/ (pow p 3) x)) (* 8 (pow p 2))) x))) x))
(* -1 (/ (+ (* -4 p) (* -1 (/ (- (* -1 (/ (- (* 32 (/ (pow p 4) x)) (* 16 (pow p 3))) x)) (* 8 (pow p 2))) x))) x))
(* 4 (/ p x))
(* p (+ (* -8 (/ p (pow x 2))) (* 4 (/ 1 x))))
(* p (+ (* p (- (* 16 (/ p (pow x 3))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))
(* p (+ (* p (- (* p (+ (* -32 (/ p (pow x 4))) (* 16 (/ 1 (pow x 3))))) (* 8 (/ 1 (pow x 2))))) (* 4 (/ 1 x))))
2
(+ 2 (* -1 (/ x p)))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
(- (+ 2 (* -1/4 (/ (pow x 3) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) (* -1 x)) p)))
(+ 2 (* -1 (/ (- (* -1 (/ (- (* -1/4 (/ (pow x 3) p)) (* -1/2 (pow x 2))) p)) (* -1 x)) p)))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(/ (pow p 3) (pow x 3))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(/ (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 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (+ (log x) (log (/ -1 p))))
(* -1 (+ (log x) (log (/ -1 p))))
(* -1 (+ (log x) (log (/ -1 p))))
(* -1 (+ (log x) (log (/ -1 p))))
(* -1 (+ (log (/ -1 p)) (* -1 (log (/ 1 x)))))
(* -1 (+ (log (/ -1 p)) (* -1 (log (/ 1 x)))))
(* -1 (+ (log (/ -1 p)) (* -1 (log (/ 1 x)))))
(* -1 (+ (log (/ -1 p)) (* -1 (log (/ 1 x)))))
(* -1 (+ (log (/ 1 p)) (* -1 (log (/ -1 x)))))
(* -1 (+ (log (/ 1 p)) (* -1 (log (/ -1 x)))))
(* -1 (+ (log (/ 1 p)) (* -1 (log (/ -1 x)))))
(* -1 (+ (log (/ 1 p)) (* -1 (log (/ -1 x)))))
(* -1 (+ (log (* -1 x)) (* -1 (log p))))
(* -1 (+ (log (* -1 x)) (* -1 (log p))))
(* -1 (+ (log (* -1 x)) (* -1 (log p))))
(* -1 (+ (log (* -1 x)) (* -1 (log p))))
(* -1 (+ (log (* -1 x)) (log (/ 1 p))))
(* -1 (+ (log (* -1 x)) (log (/ 1 p))))
(* -1 (+ (log (* -1 x)) (log (/ 1 p))))
(* -1 (+ (log (* -1 x)) (log (/ 1 p))))
(* -1 (+ (log x) (log (/ -1 p))))
(* -1 (+ (log x) (log (/ -1 p))))
(* -1 (+ (log x) (log (/ -1 p))))
(* -1 (+ (log x) (log (/ -1 p))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 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 x) (log (/ -1 p)))
(+ (log x) (log (/ -1 p)))
(+ (log x) (log (/ -1 p)))
(+ (log x) (log (/ -1 p)))
(+ (log (/ -1 p)) (* -1 (log (/ 1 x))))
(+ (log (/ -1 p)) (* -1 (log (/ 1 x))))
(+ (log (/ -1 p)) (* -1 (log (/ 1 x))))
(+ (log (/ -1 p)) (* -1 (log (/ 1 x))))
(+ (log (/ 1 p)) (* -1 (log (/ -1 x))))
(+ (log (/ 1 p)) (* -1 (log (/ -1 x))))
(+ (log (/ 1 p)) (* -1 (log (/ -1 x))))
(+ (log (/ 1 p)) (* -1 (log (/ -1 x))))
(+ (log (* -1 x)) (* -1 (log p)))
(+ (log (* -1 x)) (* -1 (log p)))
(+ (log (* -1 x)) (* -1 (log p)))
(+ (log (* -1 x)) (* -1 (log p)))
(+ (log (* -1 x)) (log (/ 1 p)))
(+ (log (* -1 x)) (log (/ 1 p)))
(+ (log (* -1 x)) (log (/ 1 p)))
(+ (log (* -1 x)) (log (/ 1 p)))
(+ (log x) (log (/ -1 p)))
(+ (log x) (log (/ -1 p)))
(+ (log x) (log (/ -1 p)))
(+ (log x) (log (/ -1 p)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
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1
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(+ (* -1/4 (/ x p)) (* 1/2 (log 1/2)))
(+ (* -1 (/ (+ (* 1/16 (/ (pow x 2) p)) (* 1/4 x)) p)) (* 1/2 (log 1/2)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/12 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) p)) (* -1/16 (pow x 2))) p)) (* 1/4 x)) p)) (* 1/2 (log 1/2)))
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)))
(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 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
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)))
(log 1/2)
(+ (log 1/2) (* 1/2 (/ x p)))
(+ (log 1/2) (* x (+ (* -1/8 (/ x (pow p 2))) (* 1/2 (/ 1 p)))))
(+ (log 1/2) (* x (+ (* x (- (* -1/48 (/ x (pow p 3))) (* 1/8 (/ 1 (pow p 2))))) (* 1/2 (/ 1 p)))))
(* -1 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1 (pow p 2)) (* 1/24 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2)))) (pow x 2))
(/ (+ (* -1 (pow p 2)) (+ (* 1/720 (/ (+ (* -240 (pow p 6)) (+ (* -180 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -180 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (pow x 4))) (* 1/24 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2))))) (pow x 2))
(/ (+ (* -1 (pow p 2)) (+ (* 1/40320 (/ (+ (* -10080 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (+ (* -10080 (* (pow p 4) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -10080 (+ (* -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)))))))) (+ (* -10080 (pow p 8)) (* -1260 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)))))) (pow x 6))) (+ (* 1/720 (/ (+ (* -240 (pow p 6)) (+ (* -180 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* -180 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))) (pow x 4))) (* 1/24 (/ (+ (* -12 (pow p 4)) (* -6 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 2)))))) (pow x 2))
(+ (log (pow p 2)) (* 2 (log (/ -1 x))))
(+ (log (pow p 2)) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 2 (log (/ -1 x)))))
(+ (log (pow p 2)) (+ (* 1/24 (/ (+ (* -3/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 4))) (* 6 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))) (pow x 4))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 2 (log (/ -1 x))))))
(+ (log (pow p 2)) (+ (* 1/720 (/ (+ (* -45 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 4))) (+ (* 15/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 3) (pow p 6))) (* 180 (/ (+ (* -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))) (+ (* 1/24 (/ (+ (* -3/4 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 4))) (* 6 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 2)))) (pow x 4))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 2) (pow x 2)))) (* 2 (log (/ -1 x)))))))
(* -1 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 5/2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (- (* (pow p 2) (+ (* -22/3 (/ (pow p 2) (pow x 6))) (* 5/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 93/4 (/ (pow p 2) (pow x 8))) (* 22/3 (/ 1 (pow x 6))))) (* 5/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(log 1/2)
(+ (log 1/2) (* 1/2 (/ x p)))
(+ (log 1/2) (+ (* -1/8 (/ (pow x 2) (pow p 2))) (* 1/2 (/ x p))))
(+ (log 1/2) (+ (* -1/8 (/ (pow x 2) (pow p 2))) (+ (* 1/6 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3))) (* 1/2 (/ x p)))))
(log 1/2)
(+ (log 1/2) (* -1/2 (/ x p)))
(+ (log 1/2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) p)) (* 1/2 x)) p)))
(+ (log 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) p)) (* -1/8 (pow x 2))) p)) (* 1/2 x)) p)))
(+ (log (/ 1 p)) (* 2 (log x)))
(+ (log (/ 1 p)) (* 2 (log x)))
(+ (log (/ 1 p)) (* 2 (log x)))
(+ (log (/ 1 p)) (* 2 (log x)))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(+ (log (pow x 2)) (* -1 (log p)))
(+ (log (pow x 2)) (* -1 (log p)))
(+ (log (pow x 2)) (* -1 (log p)))
(+ (log (pow x 2)) (* -1 (log p)))
(+ (log (/ 1 p)) (log (pow x 2)))
(+ (log (/ 1 p)) (log (pow x 2)))
(+ (log (/ 1 p)) (log (pow x 2)))
(+ (log (/ 1 p)) (log (pow x 2)))
(+ (log (* -1 (pow x 2))) (log (/ -1 p)))
(+ (log (* -1 (pow x 2))) (log (/ -1 p)))
(+ (log (* -1 (pow x 2))) (log (/ -1 p)))
(+ (log (* -1 (pow x 2))) (log (/ -1 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 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #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))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/2 binary64) p (*.f64 #s(literal 1/4 binary64) x)) p)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(+ 1/2 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #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
#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 (* 1/4 (/ x p)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #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))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(fma.f64 x (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(fma.f64 x (fma.f64 #s(literal -1/128 binary64) (/.f64 x (.f64 p (.f64 #s(literal 1/2 binary64) (.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/8 binary64) (.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) (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 p (.f64 #s(literal 1/2 binary64) (.f64 p (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1/8 binary64) (.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) (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)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal 3 binary64) (.f64 (.f64 p p) (.f64 p p)))) (pow.f64 x #s(literal 4 binary64))) (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))) (* 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 #s(literal 3 binary64) (.f64 (.f64 p p) (.f64 p p)))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p)) (.f64 #s(literal 3 binary64) (.f64 (.f64 p p) (.f64 p p))))) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 #s(literal 3 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (*.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 (+.f64 p (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 (.f64 p p) (.f64 p p))) (.f64 p (.f64 x x)))) (neg.f64 x))
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(* (pow p 2) (- (* 5/2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (.f64 p p) (fma.f64 (.f64 p p) (/.f64 #s(literal 5/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(* (pow p 2) (- (* (pow p 2) (+ (* -22/3 (/ (pow p 2) (pow x 6))) (* 5/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (pow.f64 x #s(literal 6 binary64))) #s(literal -22/3 binary64) (/.f64 #s(literal 5/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow p 2) (- (* (pow p 2) (+ (* (pow p 2) (- (* 93/4 (/ (pow p 2) (pow x 8))) (* 22/3 (/ 1 (pow x 6))))) (* 5/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 (.f64 p p) (fma.f64 #s(literal 93/4 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 8 binary64)))) (/.f64 #s(literal -22/3 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 5/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(log 1/2)
(log.f64 #s(literal 1/2 binary64))
(+ (log 1/2) (* 1/2 (/ x p)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x p) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (+ (* -1/8 (/ (pow x 2) (pow p 2))) (* 1/2 (/ x p))))
(fma.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 x (*.f64 p p)) (/.f64 #s(literal 1/2 binary64) p)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (+ (* -1/8 (/ (pow x 2) (pow p 2))) (+ (* 1/6 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3))) (* 1/2 (/ x p)))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 x (.f64 p p)) (/.f64 #s(literal 1/2 binary64) p)) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64)))) #s(literal 1/6 binary64)) (.f64 p (*.f64 p p)))))
(log 1/2)
(log.f64 #s(literal 1/2 binary64))
(+ (log 1/2) (* -1/2 (/ x p)))
(fma.f64 (/.f64 x p) #s(literal -1/2 binary64) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) p)) (* 1/2 x)) p)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal 1/8 binary64) (.f64 x (/.f64 x p)))) p))
(+ (log 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (+ (* -3/8 (pow x 3)) (* 1/4 (pow x 3))) p)) (* -1/8 (pow x 2))) p)) (* 1/2 x)) p)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 #s(literal -1/6 binary64) (/.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64)))) p) (.f64 x (*.f64 x #s(literal -1/8 binary64)))) (neg.f64 p))) p))
(+ (log (/ 1 p)) (* 2 (log x)))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* 2 (log x)))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* 2 (log x)))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* 2 (log x)))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* -2 (log (/ 1 x))))
(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 p))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 p)))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 p)))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 p)))
(+ (log (/ 1 p)) (* -2 (log (/ -1 x))))
(fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 p)))
(+ (log (pow x 2)) (* -1 (log p)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (pow x 2)) (* -1 (log p)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (pow x 2)) (* -1 (log p)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (pow x 2)) (* -1 (log p)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (/ 1 p)) (log (pow x 2)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (/ 1 p)) (log (pow x 2)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (/ 1 p)) (log (pow x 2)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (/ 1 p)) (log (pow x 2)))
(-.f64 (log.f64 (*.f64 x x)) (log.f64 p))
(+ (log (* -1 (pow x 2))) (log (/ -1 p)))
(+.f64 (neg.f64 (log.f64 (neg.f64 p))) (log.f64 (*.f64 x (neg.f64 x))))
(+ (log (* -1 (pow x 2))) (log (/ -1 p)))
(+.f64 (neg.f64 (log.f64 (neg.f64 p))) (log.f64 (*.f64 x (neg.f64 x))))
(+ (log (* -1 (pow x 2))) (log (/ -1 p)))
(+.f64 (neg.f64 (log.f64 (neg.f64 p))) (log.f64 (*.f64 x (neg.f64 x))))
(+ (log (* -1 (pow x 2))) (log (/ -1 p)))
(+.f64 (neg.f64 (log.f64 (neg.f64 p))) (log.f64 (*.f64 x (neg.f64 x))))

rewrite257.0ms (2.9%)

Memory

4.2MiB live, 323.0MiB allocated

Rules

3 530×	`lower-*.f32`
3 520×	`lower-*.f64`
3 450×	`lower-/.f32`
3 434×	`lower-/.f64`
2 732×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	440
0	93	386
1	353	345
2	2313	327
0	8242	305

Stop Event

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

Counts

27 → 771

Calls

Call 1

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

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

eval248.0ms (2.8%)

Memory: 16.7MiB live, 370.1MiB allocated
Compiler: Compiled 34 432 to 3 265 computations (90.5% saved)

prune177.0ms (2%)

Memory

-10.9MiB live, 307.7MiB allocated

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	1 451	3	1 454
Fresh	0	0	0
Picked	3	2	5
Done	0	6	6
Total	1 454	11	1 465

Accuracy

99.9%

Counts

1 465 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	19.5%	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x))))))
✓	76.1%	(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)))
✓	50.4%	(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))))
✓	50.4%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))))
✓	54.5%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	26.5%	#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)))
	10.7%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 p x) #s(literal 3 binary64))) (/.f64 (.f64 p p) (.f64 x x))))
✓	28.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 p (neg.f64 x)))
	25.5%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (/.f64 (exp.f64 (log.f64 (neg.f64 x))) p)) #s(literal -1 binary64))))
	25.7%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (log.f64 (/.f64 p (neg.f64 x)))))
✓	35.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 367 to 176 computations (52% saved)

regimes48.0ms (0.5%)

Memory

0.2MiB live, 76.6MiB allocated

Counts

23 → 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))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x)))
(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))))
(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)))))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 p x) #s(literal 3 binary64))) (/.f64 (.f64 p p) (.f64 x x))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (/.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))))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (log.f64 (/.f64 p (neg.f64 x)))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 x) p)) #s(literal -1 binary64))))
(exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (/.f64 p (.f64 x x))))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (.f64 p (/.f64 p (.f64 x x))))))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)) (exp.f64 (*.f64 (log.f64 (/.f64 (exp.f64 (log.f64 (neg.f64 x))) p)) #s(literal -1 binary64))))
(exp.f64 (.f64 (log.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (.f64 p (exp.f64 (.f64 (log.f64 (/.f64 (*.f64 x x) p)) #s(literal -1 binary64)))))) #s(literal 1/2 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:

9.0ms	p
8.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
7.0ms	x
6.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
6.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Results

Accuracy	Segments	Branch
79.3%	3	`p`
80.9%	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))))`
76.1%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes18.0ms (0.2%)

Memory

-8.8MiB live, 29.2MiB allocated

Counts

13 → 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))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x)))
(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 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 (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #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)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)) #s(literal 1 binary64)))

Calls

4 calls:

7.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
4.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
99.8%	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)))))))`
99.8%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.8%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.8%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes14.0ms (0.2%)

Memory

26.9MiB live, 26.9MiB allocated

Counts

12 → 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))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) #s(approx (+ 1 (/ x (sqrt (+ ( (* 4 p) p) (* x x))))) (/.f64 (.f64 p (.f64 p #s(literal 2 binary64))) (*.f64 x x)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.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:

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

Results

Accuracy	Segments	Branch
99.8%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.8%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.8%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.8%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes16.0ms (0.2%)

Memory

-39.0MiB live, 19.2MiB 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:

8.0ms	(.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
99.2%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.2%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.2%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.2%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes8.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB 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:

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

Results

Accuracy	Segments	Branch
99.1%	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)))))))`
99.1%	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))))))`
99.1%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.1%	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)

regimes14.0ms (0.2%)

Memory

-9.1MiB live, 29.4MiB 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:

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

Results

Accuracy	Segments	Branch
68.6%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
68.6%	2	`p`
60.7%	2	`x`
74.1%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
74.1%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
74.1%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
74.1%	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)

regimes8.0ms (0.1%)

Memory

21.4MiB live, 21.4MiB 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:

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

Results

Accuracy	Segments	Branch
35.8%	1	`x`
35.8%	1	`p`
35.8%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
35.8%	1	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
35.8%	1	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
35.8%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
35.8%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999882973	-1.5910018263522346e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	6.102074839650468e-5	0.9999999999995727
0.0ms	-0.9999999999882973	-1.5910018263522346e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	6.102074839650468e-5	0.9999999999995727
0.0ms	-0.9999999999882973	-1.5910018263522346e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	6.102074839650468e-5	0.9999999999995727
0.0ms	-0.9999999999882973	-1.5910018263522346e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	6.102074839650468e-5	0.9999999999995727
0.0ms	-0.9999999999882973	-1.5910018263522346e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch13.0ms (0.1%)

Memory

-18.2MiB live, 20.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	6.102074839650468e-5	0.9999999999995727

Samples

7.0ms

128×

valid

Compiler

Compiled 110 to 91 computations (17.3% saved)

Precisions

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

ival-add: 1.0ms (40.4% of total)

ival-mult: 1.0ms (40.4% of total)

ival-sqrt: 1.0ms (40.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB 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	69	525
1	80	525
2	86	525
3	91	525
4	94	525
5	95	525

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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #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)) (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 7378697629483821/73786976294838206464 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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* 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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* 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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #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)) (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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx (+ ( (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 #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)) (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 7378697629483821/73786976294838206464 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 7378697629483821/73786976294838206464 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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* 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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* 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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* 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 7378697629483821/73786976294838206464 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* 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))

soundness757.0ms (8.4%)

Memory

-26.1MiB live, 728.4MiB allocated

Rules

10 048×	`lower-fma.f64`
10 048×	`lower-fma.f32`
7 612×	`lower-fma.f64`
7 612×	`lower-fma.f32`
7 228×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	597	9337
1	1835	8860
2	6385	8715
0	8027	8163
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
0	41	263
0	58	261
1	219	246
2	1314	246
0	8379	228

Stop Event

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

Compiler

Compiled 1 220 to 484 computations (60.3% saved)

preprocess88.0ms (1%)

Memory: 3.6MiB live, 120.8MiB allocated
Compiler: Compiled 664 to 186 computations (72% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	41	287
0	58	285
1	102	284
2	148	284
3	191	284
4	210	284
5	223	284
6	256	284
7	318	284
8	384	284
9	398	284
10	399	284
0	399	266

Iter	Nodes	Cost
0	41	287
0	58	285
1	102	284
2	148	284
3	191	284
4	210	284
5	223	284
6	256	284
7	318	284
8	384	284
9	398	284
10	399	284
0	399	266

start0.0ms (0%)

analyze471.0ms (5.3%)

sample2.3s (25.9%)

explain252.0ms (2.8%)

preprocess65.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize58.0ms (0.7%)

series29.0ms (0.3%)

simplify270.0ms (3%)

rewrite257.0ms (2.9%)

eval118.0ms (1.3%)

prune64.0ms (0.7%)

simplify23.0ms (0.3%)

localize105.0ms (1.2%)

series34.0ms (0.4%)

simplify375.0ms (4.2%)

rewrite340.0ms (3.8%)

eval160.0ms (1.8%)

prune114.0ms (1.3%)

simplify19.0ms (0.2%)

localize181.0ms (2%)

series38.0ms (0.4%)

simplify279.0ms (3.1%)

rewrite207.0ms (2.3%)

eval102.0ms (1.1%)

prune82.0ms (0.9%)

simplify154.0ms (1.7%)

localize294.0ms (3.3%)

series537.0ms (6%)

simplify326.0ms (3.6%)

rewrite257.0ms (2.9%)

eval248.0ms (2.8%)

prune177.0ms (2%)

regimes48.0ms (0.5%)

regimes18.0ms (0.2%)

regimes14.0ms (0.2%)

regimes16.0ms (0.2%)

regimes8.0ms (0.1%)

regimes14.0ms (0.2%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch13.0ms (0.1%)

simplify9.0ms (0.1%)

soundness757.0ms (8.4%)

preprocess88.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	41	287
0	58	285
1	102	284
2	148	284
3	191	284
4	210	284
5	223	284
6	256	284
7	318	284
8	384	284
9	398	284
10	399	284
0	399	266