Metrics for Given's Rotation SVD example

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze712.0ms (8.2%)

Memory

-182.6MiB live, 734.4MiB 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)

sample1.9s (21.5%)

Memory

48.1MiB live, 2 366.9MiB allocated

Samples

849.0ms	6 224×	0	valid
294.0ms	996×	2	valid
158.0ms	406×	3	valid
124.0ms	630×	1	valid

Precisions

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

const: 261.0ms (22.4% of total)

ival-mult: 246.0ms (21.1% of total)

ival-sqrt: 172.0ms (14.8% of total)

ival-add: 161.0ms (13.8% of total)

ival-div: 132.0ms (11.3% of total)

adjust: 74.0ms (6.3% of total)

ival-fabs: 52.0ms (4.5% of total)

ival-<: 42.0ms (3.6% of total)

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

exact: 11.0ms (0.9% of total)

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

Bogosity

explain284.0ms (3.3%)

Memory

6.4MiB live, 290.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
53	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
39	-	39	(-3.632113693611749e-66 -7249672130311.135)	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
27	-	27	(-5.250710637758046e-74 -1.1045900672675562e+139)	`(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	-	0	-	`(/.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	-	`#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	53	0
↳	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	overflow	1
↳	`(*.f64 #s(literal 4 binary64) p)`	overflow	1
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	54
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	54

Confusion

	Predicted +	Predicted -
+	0	64
-	53	139

Precision

0.0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	64
-	53	0	139

Precision?

0.0

Recall?

0.0

Freqs

test

number	freq
0	203
1	53

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms	34×	3	valid
38.0ms	366×	0	valid
15.0ms	62×	2	valid
9.0ms	50×	1	valid

Compiler

Compiled 303 to 101 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-sqrt: 35.0ms (44.1% of total)

ival-mult: 23.0ms (29% of total)

ival-add: 8.0ms (10.1% of total)

ival-div: 6.0ms (7.6% of total)

adjust: 5.0ms (6.3% of total)

exact: 1.0ms (1.3% of total)

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

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

preprocess67.0ms (0.8%)

Memory

6.0MiB live, 44.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs p)

Compiler

Compiled 17 to 14 computations (17.6% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.8%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (0.6%)

Memory

-3.3MiB live, 79.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.24851041444094796	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
accuracy	5.728522722387457	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
accuracy	8.97876987652354	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
accuracy	12.344307368833768	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

17.0ms	183×	0	valid
10.0ms	31×	2	valid
10.0ms	17×	3	valid
4.0ms	25×	1	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 7.0ms (24.2% of total)

adjust: 6.0ms (20.8% of total)

ival-sqrt: 6.0ms (20.8% of total)

ival-add: 6.0ms (20.8% of total)

ival-div: 3.0ms (10.4% of total)

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.3%)

Memory

3.6MiB live, 42.2MiB 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 (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 4 (pow p 2)) (pow x 2)) (taylor 0 p) (#s(alt (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) (patch (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt 2)) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2)))))))) (taylor 0 p) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* -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 (/ (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>) () ())) ())
#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 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#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 (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2))))) (taylor -inf x) (#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 (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2))))) (taylor -inf x) (#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 (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2))))) (taylor -inf x) (#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 (* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (/ (pow p 2) (pow x 2))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) (patch (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))) #<representation binary64>) () ())) ())
#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>) () ())) ())

Calls

6 calls:

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

simplify196.0ms (2.3%)

Memory

-7.4MiB live, 177.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	472	2997
1	1444	2876
2	4984	2834
0	8537	2634

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

Calls

Call 1

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

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

rewrite191.0ms (2.2%)

Memory

30.5MiB live, 185.1MiB 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 (/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 x (-.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 x (-.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal -1/2 binary64))))))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (.f64 x (-.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 x (-.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)))) (-.f64 (.f64 x (-.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 3 binary64)))) (fma.f64 x (+.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 x) (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64))) (fma.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 x (-.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
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(-.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (fma.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal -1/2 binary64)) x #s(literal -1 binary64))))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #s(literal -1 binary64)) (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))))
(-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))))))
(+.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -4 binary64) (.f64 p p) (.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -4 binary64) (.f64 p p) (.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (pow.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (*.f64 p #s(literal 4 binary64)) p)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)))) (sqrt.f64 (fma.f64 x x (.f64 #s(literal -4 binary64) (*.f64 p p)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 #s(literal -4 binary64) (.f64 p p) (*.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 p #s(literal 4 binary64)) p)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (*.f64 p #s(literal 4 binary64)) p))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 p #s(literal 4 binary64)) p))) (sqrt.f64 (-.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (*.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(exp.f64 (.f64 (log.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (/.f64 x (sqrt.f64 (-.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 (.f64 p #s(literal 4 binary64)) p))))
(.f64 (/.f64 x (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 16 binary64) (fma.f64 #s(literal -4 binary64) (pow.f64 (.f64 p x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 x (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) (neg.f64 x))
(.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal -1/2 binary64)) x)
(.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1 binary64)))
(.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1 binary64))
(.f64 x (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)) #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
(/.f64 (/.f64 x (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal 1/4 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) x))
(/.f64 (pow.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x))
(neg.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x))) x)) #s(literal -1 binary64)))

eval123.0ms (1.4%)

Memory: -29.0MiB live, 169.9MiB allocated
Compiler: Compiled 13 679 to 2 259 computations (83.5% saved)

prune123.0ms (1.4%)

Memory

19.5MiB live, 143.0MiB allocated

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	434	10	444
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	435	10	445

Accuracy

99.9%

Counts

445 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.6%	(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 x (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
▶	76.8%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	71.2%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* 4 p) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))))))
▶	7.5%	(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)))))
	45.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
▶	28.1%	(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))))
	23.2%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (*.f64 (/.f64 p x) (/.f64 p x))))
	36.8%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1 binary64)))
▶	50.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	30.2%	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x)))

Compiler

Compiled 234 to 192 computations (17.9% saved)

simplify128.0ms (1.5%)

Memory

-12.9MiB live, 141.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

7 330×	`lower-fma.f32`
7 324×	`lower-fma.f64`
1 718×	`lower-*.f32`
1 708×	`lower-*.f64`
1 416×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	309
0	65	295
1	115	295
2	186	295
3	374	295
4	628	295
5	799	295
6	1073	295
7	1352	295
8	1839	295
9	3669	295
10	5533	295
11	7445	295
0	8036	293

Stop Event

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

Calls

Call 1

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

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

localize179.0ms (2.1%)

Memory

35.2MiB live, 192.8MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.421875	(*.f64 p (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.642887144517588	(.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	44.42001394453295	#s(approx (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/.f64 (.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 x)))
accuracy	0.05078125	(fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64))
accuracy	0.16796875	(/.f64 p (*.f64 x x))
accuracy	5.728522722387457	(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))))
accuracy	46.00434333057217	#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)))
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ ( (* 4 p) p) (* x x)))) #s(literal -1 binary64))))
accuracy	5.728522722387457	(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	8.97876987652354	(+.f64 #s(literal 1 binary64) #s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64)))
accuracy	44.351716763579546	#s(approx (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) #s(literal -1 binary64))
accuracy	5.728522722387457	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	32.383996040288885	#s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.24851041444094796	(/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x))))
accuracy	5.728522722387457	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	8.970102071502458	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	12.344307368833768	(sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))

Samples

91.0ms	183×	0	valid
43.0ms	31×	2	valid
12.0ms	17×	3	valid
9.0ms	25×	1	valid

Compiler

Compiled 276 to 36 computations (87% saved)

Precisions

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

adjust: 27.0ms (31.4% of total)

ival-mult: 23.0ms (26.8% of total)

ival-sqrt: 14.0ms (16.3% of total)

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

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

ival-neg: 2.0ms (2.3% of total)

exact: 1.0ms (1.2% of total)

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

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

series58.0ms (0.7%)

Memory

-20.6MiB live, 75.7MiB allocated

Counts

20 → 432

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	x	@	-inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (/ p (* x x)) (neg x))
10.0ms	p	@	0	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (/ p (* x x)) (neg x))
6.0ms	p	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (/ p (* x x)) (neg x))
3.0ms	p	@	-inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (/ p (* x x)) (neg x))
3.0ms	x	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))) (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (+ (* (neg p) (/ p (* x x))) 1) (neg p) (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x))))))) (/ (* (* p (sqrt 2)) (sqrt 1/2)) (neg x)) (* (* p (sqrt 2)) (sqrt 1/2)) (* p (sqrt 2)) (/ p (* x x)) (neg x))

simplify237.0ms (2.7%)

Memory

-6.5MiB live, 258.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 658×	`lower-fma.f64`
7 658×	`lower-fma.f32`
6 510×	`lower-*.f64`
6 510×	`lower-*.f32`
2 820×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	606	8752
1	1849	8267
2	6404	8143
0	8054	7658

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 430

Calls

Call 1

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

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

rewrite213.0ms (2.4%)

Memory

3.2MiB live, 243.5MiB allocated

Rules

6 168×	`lower-fma.f32`
6 162×	`lower-fma.f64`
4 170×	`lower-*.f32`
4 160×	`lower-*.f64`
3 822×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	273
0	65	259
1	226	243
2	1271	241
0	8583	239

Stop Event

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

Counts

20 → 497

Calls

Call 1

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

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

eval161.0ms (1.9%)

Memory: -36.7MiB live, 251.2MiB allocated
Compiler: Compiled 19 518 to 2 716 computations (86.1% saved)

prune100.0ms (1.1%)

Memory

-18.2MiB live, 218.9MiB allocated

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	921	6	927
Fresh	5	0	5
Picked	3	2	5
Done	0	0	0
Total	929	8	937

Accuracy

100.0%

Counts

937 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.0%	(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
✓	76.8%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	71.2%	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	45.8%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
✓	50.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
▶	28.4%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))
▶	30.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
▶	36.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 168 to 126 computations (25% saved)

simplify354.0ms (4.1%)

Memory

40.2MiB live, 111.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

2 504×	`lower-fma.f32`
2 496×	`lower-fma.f64`
1 920×	`lower-*.f32`
1 918×	`lower-*.f64`
838×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	270
0	54	270
1	93	270
2	143	270
3	196	270
4	224	270
5	239	270
6	314	270
7	373	270
8	414	270
9	487	270
10	605	270
11	836	270
12	1328	270
13	2235	270
14	3352	270
15	4074	270
16	4478	270
17	4677	270
18	4763	270
19	4789	270
20	4813	270
21	4813	270
22	4813	270
23	4893	270
24	5009	270
25	5057	270
26	5057	270
27	5057	270
28	5081	270
29	5293	270
30	5293	270
31	5421	270
32	6239	270
33	6239	270
0	6239	256

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize119.0ms (1.4%)

Memory

-20.3MiB live, 233.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 p p)
accuracy	2.0896663296123155	(fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64))
accuracy	2.437807110782863	(/.f64 (*.f64 p p) x)
accuracy	45.80305517884302	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))
accuracy	0	(fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
accuracy	0	(/.f64 x p)
accuracy	5.728522722387457	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
accuracy	34.621037140548566	#s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))
accuracy	0	(/.f64 (neg.f64 p) x)
accuracy	0	(neg.f64 p)
accuracy	44.42001394453295	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
accuracy	40.46432845994683	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))
accuracy	1.2233066139162627	(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
accuracy	5.728522722387457	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	8.970102071502458	(fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	45.4986588647892	#s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))

Samples

40.0ms	183×	0	valid
15.0ms	25×	1	valid
14.0ms	31×	2	valid
10.0ms	17×	3	valid

Compiler

Compiled 209 to 32 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 16.0ms (27.6% of total)

ival-div: 14.0ms (24.2% of total)

ival-sqrt: 13.0ms (22.4% of total)

ival-add: 8.0ms (13.8% of total)

adjust: 5.0ms (8.6% of total)

exact: 1.0ms (1.7% of total)

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

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

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

series66.0ms (0.8%)

Memory

-9.5MiB live, 28.8MiB allocated

Counts

18 → 396

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))) (taylor 0 p) (#s(alt (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) (patch (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) (patch (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) 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 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) (patch (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) 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 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x))) (patch (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x)) (patch #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 2 (/ (pow p 2) x))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x)) (patch #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x)) (patch #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x)) (patch #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (patch #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/.f64 (neg.f64 p) x) (patch (/.f64 (neg.f64 p) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 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 (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ x p)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ x p) (taylor -inf x) (#s(alt (/.f64 x p) (patch (/.f64 x p) #<representation binary64>) () ())) ())
#s(alt (/ x p) (taylor -inf x) (#s(alt (/.f64 x p) (patch (/.f64 x p) #<representation binary64>) () ())) ())
#s(alt (/ x p) (taylor -inf x) (#s(alt (/.f64 x p) (patch (/.f64 x p) #<representation binary64>) () ())) ())
#s(alt (/ x p) (taylor -inf x) (#s(alt (/.f64 x p) (patch (/.f64 x p) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64))) (patch #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64))) #<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 #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64))) (patch #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x)) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64))) (patch #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x)) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64))) (patch #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 2) x) (taylor -inf x) (#s(alt (/.f64 (.f64 p p) x) (patch (/.f64 (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) (patch (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) (patch (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) (patch (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) (patch (fma.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	x	@	0	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ -1/2 x) (/ (* p p) x) (+ (* (/ 2 x) (* p p)) x) (* p p))
3.0ms	x	@	-inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ -1/2 x) (/ (* p p) x) (+ (* (/ 2 x) (* p p)) x) (* p p))
2.0ms	x	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ -1/2 x) (/ (* p p) x) (+ (* (/ 2 x) (* p p)) x) (* p p))
2.0ms	p	@	inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ -1/2 x) (/ (* p p) x) (+ (* (/ 2 x) (* p p)) x) (* p p))
2.0ms	p	@	-inf	((sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (/ x (sqrt (+ (* (* p 4) p) (* x x)))) (sqrt (+ (* (* p 4) p) (* x x))) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/ (neg p) x) (neg p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* (/ x p) 1/4) 1/2) (/ x p) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ -1/2 x) (/ (* p p) x) (+ (* (/ 2 x) (* p p)) x) (* p p))

simplify194.0ms (2.2%)

Memory

18.0MiB live, 248.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10 252×	`lower-fma.f64`
10 252×	`lower-fma.f32`
6 992×	`lower-*.f64`
6 992×	`lower-*.f32`
4 286×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	443	6285
1	1300	6120
2	4181	5899
0	8032	5492

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 391

Calls

Call 1

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

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

rewrite196.0ms (2.3%)

Memory

29.5MiB live, 248.9MiB allocated

Rules

4 844×	`lower-/.f32`
4 832×	`lower-/.f64`
4 124×	`lower-fma.f32`
4 116×	`lower-fma.f64`
3 838×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	249
0	54	249
1	209	249
2	1436	249
0	8375	235

Stop Event

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

Counts

18 → 325

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (sqrt.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (pow.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))))) (sqrt.f64 #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (+.f64 (log1p.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) (log.f64 #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)))))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -2 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64))) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x #s(approx (sqrt (+ ( (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) x) #s(literal -3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 2 binary64)) (.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64))))))
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(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 (/.f64 x p) p) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64)) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 (/.f64 x p) p) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64)) (.f64 x (-.f64 x (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)))))))
(/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64)) (.f64 (neg.f64 x) x)) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 (/.f64 x p) p) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64)) x))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 (/.f64 x p) p) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64)) (.f64 x (-.f64 x (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64))) (-.f64 (.f64 x x) (pow.f64 (.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (pow.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64)) x))) (fma.f64 #s(literal 8 binary64) (pow.f64 (/.f64 (/.f64 x p) p) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))
(fma.f64 (/.f64 (*.f64 p p) #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) x) x)
(fma.f64 (/.f64 (*.f64 p p) #s(literal 1/2 binary64)) (pow.f64 x #s(literal -1 binary64)) x)
(fma.f64 (/.f64 p #s(literal 1/2 binary64)) (/.f64 p x) x)
(fma.f64 (.f64 (.f64 p p) #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64)) x)
(fma.f64 (*.f64 (/.f64 #s(literal 2 binary64) x) p) p x)
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (*.f64 p p) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 p x) (/.f64 p #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) x)
(fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)
(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p p) x) x)
(fma.f64 p (*.f64 (/.f64 #s(literal 2 binary64) x) p) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 x (.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal 2 binary64) (neg.f64 x))))
(+.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)) x)
(+.f64 x (.f64 (/.f64 (.f64 p p) x) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 p)) (exp.f64 (log.f64 p)))
(*.f64 (neg.f64 p) (neg.f64 p))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 p) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 p p))
(*.f64 p p)
(pow.f64 (exp.f64 (log.f64 p)) #s(literal 2 binary64))
(pow.f64 (*.f64 p p) #s(literal 1 binary64))
(pow.f64 p #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 p) #s(literal 2 binary64)))

eval152.0ms (1.8%)

Memory: -17.4MiB live, 227.3MiB allocated
Compiler: Compiled 14 053 to 1 878 computations (86.6% saved)

prune65.0ms (0.7%)

Memory

7.8MiB live, 165.6MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	735	2	737
Fresh	0	1	1
Picked	1	4	5
Done	0	2	2
Total	736	9	745

Accuracy

100.0%

Counts

745 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.0%	(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
✓	76.8%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	71.2%	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	45.8%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
✓	50.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	28.4%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 p p) x) #s(literal 1 binary64)))
✓	30.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
▶	28.4%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) x) x)))
✓	36.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 107 to 81 computations (24.3% saved)

simplify301.0ms (3.5%)

Memory

-9.3MiB live, 102.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

3 076×	`lower-fma.f32`
3 070×	`lower-fma.f64`
2 192×	`lower-*.f32`
2 180×	`lower-*.f64`
1 764×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	343
0	68	340
1	118	340
2	188	340
3	313	340
4	473	340
5	656	340
6	831	340
7	1005	340
8	2088	340
9	4479	337
10	5815	337
11	6074	337
12	6378	337
13	6494	337
14	6503	337
15	6776	337
16	6880	337
17	6880	337
18	6880	337
19	7000	336
20	7209	336
21	7747	336
0	8093	321

Stop Event

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

Calls

Call 1

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

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

localize310.0ms (3.6%)

Memory

29.2MiB live, 425.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	7.613881272634325	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64))))
accuracy	12.344307368833768	(sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))
accuracy	13.338497745021783	(sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x))))))
accuracy	15.245969583810755	(-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 4 binary64) p) p (.f64 x x)))))
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	5.728522722387457	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
accuracy	34.621037140548566	#s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64)))
accuracy	0.00390625	(.f64 (.f64 p p) #s(literal -1/2 binary64))
accuracy	1.2582560352311458	(/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) x)
accuracy	2.0740413296123155	(/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) x) x)
accuracy	45.80305517884302	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -1/2 binary64))) x) x)))

Samples

172.0ms	116×	0	valid
56.0ms	70×	2	valid
31.0ms	30×	3	valid
21.0ms	40×	1	valid

Compiler

Compiled 309 to 43 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-div: 110.0ms (43.8% of total)

ival-sqrt: 77.0ms (30.6% of total)

ival-mult: 26.0ms (10.3% of total)

ival-add: 19.0ms (7.6% of total)

adjust: 14.0ms (5.6% of total)

ival-sub: 5.0ms (2% of total)

exact: 1.0ms (0.4% of total)

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

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

series65.0ms (0.8%)

Memory

-26.7MiB live, 132.9MiB allocated

Counts

15 → 336

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	p	@	0	((/ (+ (* x x) (* (* p p) -1/2)) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ (/ (+ (* x x) (* (* p p) -1/2)) x) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* x (/ 1/4 p)) 1/2) (/ 1/4 p) (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x))))) (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)) (/ (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)))) (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (* (* p p) -1/2) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2))))
8.0ms	x	@	inf	((/ (+ (* x x) (* (* p p) -1/2)) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ (/ (+ (* x x) (* (* p p) -1/2)) x) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* x (/ 1/4 p)) 1/2) (/ 1/4 p) (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x))))) (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)) (/ (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)))) (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (* (* p p) -1/2) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2))))
7.0ms	x	@	-inf	((/ (+ (* x x) (* (* p p) -1/2)) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ (/ (+ (* x x) (* (* p p) -1/2)) x) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* x (/ 1/4 p)) 1/2) (/ 1/4 p) (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x))))) (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)) (/ (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)))) (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (* (* p p) -1/2) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2))))
4.0ms	p	@	inf	((/ (+ (* x x) (* (* p p) -1/2)) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ (/ (+ (* x x) (* (* p p) -1/2)) x) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* x (/ 1/4 p)) 1/2) (/ 1/4 p) (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x))))) (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)) (/ (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)))) (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (* (* p p) -1/2) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2))))
4.0ms	p	@	-inf	((/ (+ (* x x) (* (* p p) -1/2)) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/ (/ (+ (* x x) (* (* p p) -1/2)) x) x) (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (+ (* x (/ 1/4 p)) 1/2) (/ 1/4 p) (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x))))) (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)) (/ (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2)))) (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) (* (* p p) -1/2) (sqrt (+ (* (* 4 p) p) (* x x))) (sqrt (- 1/2 (* (/ x (sqrt (+ (* (* 4 p) p) (* x x)))) 1/2))))

simplify288.0ms (3.3%)

Memory

-36.8MiB live, 287.8MiB allocated

Algorithm

1×	egg-herbie

Rules

8 554×	`lower-fma.f64`
8 554×	`lower-fma.f32`
6 466×	`lower-*.f64`
6 466×	`lower-*.f32`
3 558×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	757	6550
1	2314	6356
2	7862	6342
0	8201	5923

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 331

Calls

Call 1

Inputs
x
(+ x (* -1/2 (/ (pow p 2) x)))
(+ x (* -1/2 (/ (pow p 2) x)))
(+ x (* -1/2 (/ (pow p 2) x)))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ (pow p 2) (pow x 2))
(* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 8))) (* 16 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(/ (pow p 2) (pow x 2))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* (pow p 2) (- (* 10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -35 (/ (pow p 2) (pow x 8))) (* 10 (/ 1 (pow x 6))))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(/ p x)
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 7))) (* 6 (/ 1 (pow x 5))))) (* 2 (/ 1 (pow x 3))))) (/ 1 x)))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(/ p x)
(* p (+ (* -3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* 31/8 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -187/16 (/ (pow p 2) (pow x 7))) (* 31/8 (/ 1 (pow x 5))))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(* -1/2 (/ (pow p 2) x))
(* (pow p 2) (- (/ x (pow p 2)) (* 1/2 (/ 1 x))))
(* (pow p 2) (- (/ x (pow p 2)) (* 1/2 (/ 1 x))))
(* (pow p 2) (- (/ x (pow p 2)) (* 1/2 (/ 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
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x
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1
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x
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(/ (+ p (+ (* -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)))) (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))))) x)
x
(* -1 (* x (- (* 1/2 (/ (pow p 2) (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ (pow p 2) (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ (pow p 2) (pow x 2))) 1)))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(* 1/4 (/ 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))))
(/ (pow p 2) (pow x 2))
(/ (- (* -4 (/ (pow p 4) (pow x 2))) (* -1 (pow p 2))) (pow x 2))
(/ (- (* 16 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 4 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (- (* -64 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 4 (/ (pow p 4) (pow x 2)))))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -1/4 (/ (+ (* 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 4))) (/ (pow p 2) (pow x 2))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/2 (/ (- (* -4 (pow p 4)) (* -1 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/2 (/ (- (* -4 (pow p 4)) (* -1 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -4 (pow p 4)) (* -1 (pow p 4))) 2) (pow p 2)))))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/2 (/ (- (* -64 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* 1/2 (/ (* (- (* -4 (pow p 4)) (* -1 (pow p 4))) (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -4 (pow p 4)) (* -1 (pow p 4))) 2) (pow p 2))))))) (pow p 2))))))) (* p (pow x 6)))) (+ (* 1/2 (/ (- (* -4 (pow p 4)) (* -1 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -4 (pow p 4)) (* -1 (pow p 4))) 2) (pow p 2)))))) (* p (pow x 4))))))) x))
(* -1 (/ p x))
(* -1 (/ (+ p (* -2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (+ (* -2 (/ (pow p 3) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 6)) (* 4 (pow p 6))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* -2 (/ (pow p 3) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 6)) (* 4 (pow p 6))) (* p (pow x 4)))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 6)) (* 4 (pow p 6))))) (* 64 (pow p 8))) (* p (pow x 6))))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (+ (* 1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(+ 1 (+ (* -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))) (* -1/2 (/ (pow p 2) (pow x 2))))))

Outputs
x
(+ x (* -1/2 (/ (pow p 2) x)))
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal -1/2 binary64) x)
(+ x (* -1/2 (/ (pow p 2) x)))
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal -1/2 binary64) x)
(+ x (* -1/2 (/ (pow p 2) x)))
(fma.f64 (/.f64 (*.f64 p p) x) #s(literal -1/2 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 6 binary64)))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 6 binary64)))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -10 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
(* 1/4 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/2 binary64) p)) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ (pow p 2) (pow x 2))
(/.f64 (/.f64 (*.f64 p p) x) x)
(* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (fma.f64 #s(literal -4 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* 16 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64))) p) p (/.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 8))) (* 16 (/ 1 (pow x 6))))) (* 4 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 8 binary64)))) #s(literal -64 binary64) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 p p))
(/ (pow p 2) (pow x 2))
(/.f64 (/.f64 (*.f64 p p) x) x)
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (fma.f64 #s(literal -3 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* 10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 10 binary64) (pow.f64 x #s(literal 6 binary64))) p) p (/.f64 #s(literal -3 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 p p))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -35 (/ (pow p 2) (pow x 8))) (* 10 (/ 1 (pow x 6))))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 8 binary64)))) (/.f64 #s(literal 10 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 p p) (/.f64 #s(literal -3 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 p p))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))) p) p (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (*.f64 p p) #s(literal 1 binary64))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 6 binary64)))) #s(literal -69/16 binary64) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 p p) #s(literal 1 binary64))
(/ p x)
(/.f64 p x)
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 3 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) x)) p)
(* p (+ (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (/ 1 x)))
(fma.f64 (pow.f64 p #s(literal 3 binary64)) (fma.f64 (.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 5 binary64))) p) p (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) x) p))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 7))) (* 6 (/ 1 (pow x 5))))) (* 2 (/ 1 (pow x 3))))) (/ 1 x)))
(fma.f64 (pow.f64 p #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 7 binary64)))) #s(literal -20 binary64) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 p p) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) x) p))
(* -1/2 (pow p 2))
(.f64 (.f64 p p) #s(literal -1/2 binary64))
(* -1/2 (pow p 2))
(.f64 (.f64 p p) #s(literal -1/2 binary64))
(* -1/2 (pow p 2))
(.f64 (.f64 p p) #s(literal -1/2 binary64))
(* -1/2 (pow p 2))
(.f64 (.f64 p p) #s(literal -1/2 binary64))
x
(+ x (* 2 (/ (pow p 2) x)))
(fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x)
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 3 binary64)))) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (.f64 p p) x)
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 5 binary64)))) #s(literal 4 binary64) (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 p p) (/.f64 #s(literal 2 binary64) x)) (*.f64 p p) x)
(/ p x)
(/.f64 p x)
(* p (+ (* -3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(.f64 (fma.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) x)) p)
(* p (+ (* (pow p 2) (- (* 31/8 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(fma.f64 (pow.f64 p #s(literal 3 binary64)) (fma.f64 (.f64 (/.f64 #s(literal 31/8 binary64) (pow.f64 x #s(literal 5 binary64))) p) p (/.f64 #s(literal -3/2 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) x) p))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -187/16 (/ (pow p 2) (pow x 7))) (* 31/8 (/ 1 (pow x 5))))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(fma.f64 (pow.f64 p #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -187/16 binary64) (.f64 p (/.f64 p (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 31/8 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 p p) (/.f64 #s(literal -3/2 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) x) p))
(* -1/2 (/ (pow p 2) x))
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1/2
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1/2
#s(literal 1/2 binary64)
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(/ 1/4 p)
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1/4
#s(literal 1/4 binary64)
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
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1/2
#s(literal 1/2 binary64)
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(* -1/2 (pow p 2))
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(sqrt 1/2)
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(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
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(sqrt 1/2)
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
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(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
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1/4
#s(literal 1/4 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (fma.f64 (+.f64 (/.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64))) (.f64 p p)))) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) (/.f64 #s(literal -12 binary64) p))) #s(literal -1/8 binary64) (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 1/4 binary64) (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -64 binary64)))) (.f64 (pow.f64 x #s(literal 6 binary64)) p)) (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64))) (.f64 p p)))) (.f64 (pow.f64 x #s(literal 4 binary64)) p))) #s(literal 1/2 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 (*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) p) p)) (neg.f64 x))
(/ (pow p 2) (pow x 2))
(/.f64 (/.f64 (*.f64 p p) x) x)
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (fma.f64 p p (/.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) x) x)) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (fma.f64 p p (+.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) x) x))) (.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))) (.f64 p p) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (fma.f64 (pow.f64 (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 8 binary64))))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64) (fma.f64 p p (+.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) x) x)))) (.f64 x x))
(* 1/4 (/ x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x)) x)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x)) x)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x)) x)
(/ (pow p 2) (pow x 2))
(/.f64 (/.f64 (*.f64 p p) x) x)
(/ (- (* -4 (/ (pow p 4) (pow x 2))) (* -1 (pow p 2))) (pow x 2))
(/.f64 (fma.f64 (/.f64 #s(literal -4 binary64) x) (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (.f64 p p)) (.f64 x x))
(/ (- (* 16 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 4 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 16 binary64) (.f64 p p)) (.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal 4 binary64) x))) (*.f64 x x))
(/ (- (* -64 (/ (pow p 8) (pow x 6))) (+ (* -16 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 4 (/ (pow p 4) (pow x 2)))))) (pow x 2))
(/.f64 (-.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) (/.f64 #s(literal -64 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) x) (/.f64 #s(literal 4 binary64) x) (.f64 (neg.f64 p) p))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))
(- (+ 1 (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))
(+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
(- (+ 1 (* -1/4 (/ (+ (* 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 4))) (/ (pow p 2) (pow x 2))))
(-.f64 (+.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ (+ p (* 1/2 (/ (- (* -4 (pow p 4)) (* -1 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) p) (/.f64 (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) x) x) p) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/2 (/ (- (* -4 (pow p 4)) (* -1 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -4 (pow p 4)) (* -1 (pow p 4))) 2) (pow p 2)))))) (* p (pow x 4)))))) x))
(/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) (/.f64 #s(literal -3 binary64) (.f64 x x)) (/.f64 (-.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) p) p)) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 p p) (.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) #s(literal 2 binary64)) p)))) (*.f64 (pow.f64 x #s(literal 4 binary64)) p))) #s(literal 1/2 binary64) p) (neg.f64 x))
(* -1 (/ (+ p (+ (* 1/2 (/ (- (* -64 (pow p 8)) (+ (* -1 (* (pow p 2) (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (+ (* -1/4 (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))) (* 1/2 (/ (* (- (* -4 (pow p 4)) (* -1 (pow p 4))) (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -4 (pow p 4)) (* -1 (pow p 4))) 2) (pow p 2))))))) (pow p 2))))))) (* p (pow x 6)))) (+ (* 1/2 (/ (- (* -4 (pow p 4)) (* -1 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 16 (pow p 6)) (+ (* -1 (* (pow p 2) (- (* -4 (pow p 4)) (* -1 (pow p 4))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 1/4 (/ (pow (- (* -4 (pow p 4)) (* -1 (pow p 4))) 2) (pow p 2)))))) (* p (pow x 4))))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -64 binary64) (.f64 (-.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) p) p)) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 p p))) (.f64 p p))) (fma.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal -3 binary64) (fma.f64 (.f64 (-.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) p) p)) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 p p) (.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) #s(literal 2 binary64)) p)))) (/.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) p) p)) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 p p))))) (.f64 (pow.f64 x #s(literal 6 binary64)) p)) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) (/.f64 #s(literal -3 binary64) (.f64 x x)) (/.f64 (-.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64) (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) p) p)) (fma.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 p p) (.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) #s(literal 2 binary64)) p)))) (*.f64 (pow.f64 x #s(literal 4 binary64)) p)))) p) (neg.f64 x))
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ (+ p (* -2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p) (neg.f64 x))
(* -1 (/ (+ p (+ (* -2 (/ (pow p 3) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 6)) (* 4 (pow p 6))) (* p (pow x 4)))))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 6 binary64))) p) (fma.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p)) (neg.f64 x))
(* -1 (/ (+ p (+ (* -2 (/ (pow p 3) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 6)) (* 4 (pow p 6))) (* p (pow x 4)))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 6)) (* 4 (pow p 6))))) (* 64 (pow p 8))) (* p (pow x 6))))))) x))
(/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) p) (/.f64 #s(literal -12 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 p p) (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal 64 binary64))) (*.f64 (pow.f64 x #s(literal 6 binary64)) p))) #s(literal -1/2 binary64) (fma.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (pow.f64 p #s(literal 3 binary64)) x) p)) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (fma.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p p) x) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(neg.f64 (fma.f64 (fma.f64 (pow.f64 p #s(literal 6 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -2 binary64) (.f64 (/.f64 (/.f64 (.f64 p p) x) x) #s(literal 2 binary64)))) x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 p p) x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (+ (* 1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(fma.f64 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 (fma.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (+ (* -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))) (* -1/2 (/ (pow p 2) (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) p) p) #s(literal 1/4 binary64)) (fma.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)) (pow.f64 p #s(literal 4 binary64))) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) p) p) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)))) (pow.f64 x #s(literal 6 binary64))))) #s(literal 1 binary64))

rewrite237.0ms (2.7%)

Memory

10.7MiB live, 237.5MiB allocated

Rules

4 984×	`lower-/.f32`
4 972×	`lower-/.f64`
4 254×	`lower-*.f32`
4 242×	`lower-*.f64`
3 946×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	256
0	68	252
1	285	252
2	1801	252
0	8752	241

Stop Event

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

Counts

15 → 340

Calls

Call 1

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

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

eval145.0ms (1.7%)

Memory: -3.3MiB live, 233.7MiB allocated
Compiler: Compiled 21 637 to 2 468 computations (88.6% saved)

prune104.0ms (1.2%)

Memory

18.2MiB live, 130.2MiB allocated

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	667	4	671
Fresh	0	0	0
Picked	2	1	3
Done	1	5	6
Total	670	10	680

Accuracy

100.0%

Counts

680 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	45.7%	(/.f64 #s(approx (sqrt (- 1/4 (* 1/4 (/ (* x x) (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 #s(literal 4 binary64) p) p (*.f64 x x)))) #s(literal 1/2 binary64)))))
✓	76.8%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	71.2%	(sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	45.8%	(sqrt.f64 #s(approx (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2) (fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))))
✓	50.1%	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64)))
✓	30.6%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x))
	28.4%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 (fma.f64 x x (.f64 #s(literal -1/2 binary64) (.f64 p p))) (*.f64 x x))))
	28.4%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 (/.f64 (fma.f64 (.f64 p p) #s(literal -1/2 binary64) (.f64 x x)) x) x)))
	28.4%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 #s(approx (/ (+ (* x x) (* (* p p) -1/2)) x) (fma.f64 (/.f64 (*.f64 p p) x) #s(literal -1/2 binary64) x)) x)))
✓	36.8%	#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

Compiler

Compiled 399 to 208 computations (47.9% saved)

regimes78.0ms (0.9%)

Memory

7.6MiB live, 98.8MiB allocated

Counts

23 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

31.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
13.0ms	(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)))))))
7.0ms	x
7.0ms	p
7.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)

Results

Accuracy	Segments	Branch
76.8%	1	`p`
85.3%	2	`x`
100.0%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
100.0%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
100.0%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
76.8%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 66 to 56 computations (15.2% saved)

regimes21.0ms (0.2%)

Memory

2.8MiB live, 40.7MiB allocated

Counts

18 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.3%	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)))))))`
98.3%	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))))))`
98.3%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.3%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 59 to 47 computations (20.3% saved)

regimes28.0ms (0.3%)

Memory

-5.1MiB live, 32.8MiB allocated

Counts

16 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

14.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
4.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
4.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
4.0ms	(+.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
99.0%	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)))))))`
99.0%	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))))))`
99.0%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.0%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 59 to 47 computations (20.3% saved)

regimes32.0ms (0.4%)

Memory

-21.1MiB live, 25.4MiB allocated

Counts

8 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

23.0ms	(.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 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
98.9%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
98.9%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.9%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.9%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 59 to 47 computations (20.3% saved)

regimes9.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.1%	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)))))))`
98.1%	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))))))`
98.1%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.1%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 59 to 47 computations (20.3% saved)

regimes29.0ms (0.3%)

Memory

-5.9MiB live, 30.9MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

7 calls:

18.0ms	(.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	x
2.0ms	p
2.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
67.8%	2	`p`
67.8%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
60.9%	2	`x`
71.1%	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)))))))`
71.1%	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))))))`
71.1%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
71.1%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 66 to 56 computations (15.2% saved)

regimes47.0ms (0.5%)

Memory

-13.4MiB live, 23.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

39.0ms	p
1.0ms	x
1.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
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
36.8%	1	`x`
36.8%	1	`p`
36.8%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
36.8%	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)))))))`
36.8%	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))))))`
36.8%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
36.8%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 66 to 56 computations (15.2% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.18304497016642854

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.18304497016642854

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5630059748597973	0.7658627524086403
0.0ms	-1.0	-0.18304497016642854

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5630059748597973	0.7658627524086403
0.0ms	-1.0	-0.18304497016642854

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	4.7926473156510315e-6	0.5630059748597973
0.0ms	-1.0	-0.18304497016642854

Compiler

Compiled 20 to 19 computations (5% saved)

bsearch16.0ms (0.2%)

Memory

1.4MiB live, 36.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	4.7926473156510315e-6	0.5630059748597973

Samples

6.0ms

144×

valid

Compiler

Compiled 65 to 118 computations (-81.5% saved)

Precisions

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

ival-add: 1.0ms (33.4% of total)

ival-mult: 1.0ms (33.4% of total)

ival-sqrt: 1.0ms (33.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify33.0ms (0.4%)

Memory

-8.9MiB live, 74.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	489
1	91	489
2	97	489
3	102	489
4	105	489
5	106	489

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 (fma.f64 x x (.f64 #s(literal -1/2 binary64) (.f64 p p))) (*.f64 x x))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 p #s(literal 4 binary64)) p (.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (sqrt.f64 (fma.f64 (/.f64 x #s(approx (sqrt (+ (* (* p 4) p) (* x x))) (fma.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 p p) x))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 (fma.f64 x x (.f64 #s(literal -1/2 binary64) (.f64 p p))) (*.f64 x x))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(approx (+ (* (/ -1/2 x) (/ (* p p) x)) 1) (/.f64 (fma.f64 x x (.f64 #s(literal -1/2 binary64) (.f64 p p))) (*.f64 x x))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 5404319552844595/9007199254740992 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) (fma.f64 (/.f64 x p) #s(literal 1/4 binary64) #s(literal 1/2 binary64)))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal -1 binary64)) #s(approx (sqrt (+ ( (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) (/.f64 (neg.f64 p) x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p #s(literal 4 binary64)) p)))) #s(literal 8106479329266893/18014398509481984 binary64)) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))) #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* (/ x (sqrt (+ (* (* p 4) p) (* x x)))) 1/2) 1/2)) #s(literal 1 binary64))

soundness892.0ms (10.3%)

Memory

49.8MiB live, 753.0MiB allocated

Rules

10 252×	`lower-fma.f64`
10 252×	`lower-fma.f32`
10 048×	`lower-fma.f64`
10 048×	`lower-fma.f32`
7 658×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	443	6285
1	1300	6120
2	4181	5899
0	8032	5492
0	14	78
0	23	78
1	77	78
2	501	78
3	6967	78
0	8492	70
0	606	8752
1	1849	8267
2	6404	8143
0	8054	7658
0	45	256
0	68	252
1	285	252
2	1801	252
0	8752	241
0	472	2997
1	1444	2876
2	4984	2834
0	8537	2634

Stop Event

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

Compiler

Compiled 1 070 to 466 computations (56.4% saved)

preprocess175.0ms (2%)

Memory: -23.7MiB live, 260.6MiB allocated
Compiler: Compiled 600 to 210 computations (65% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze712.0ms (8.2%)

sample1.9s (21.5%)

explain284.0ms (3.3%)

preprocess67.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize51.0ms (0.6%)

series26.0ms (0.3%)

simplify196.0ms (2.3%)

rewrite191.0ms (2.2%)

eval123.0ms (1.4%)

prune123.0ms (1.4%)

simplify128.0ms (1.5%)

localize179.0ms (2.1%)

series58.0ms (0.7%)

simplify237.0ms (2.7%)

rewrite213.0ms (2.4%)

eval161.0ms (1.9%)

prune100.0ms (1.1%)

simplify354.0ms (4.1%)

localize119.0ms (1.4%)

series66.0ms (0.8%)

simplify194.0ms (2.2%)

rewrite196.0ms (2.3%)

eval152.0ms (1.8%)

prune65.0ms (0.7%)

simplify301.0ms (3.5%)

localize310.0ms (3.6%)

series65.0ms (0.8%)

simplify288.0ms (3.3%)

rewrite237.0ms (2.7%)

eval145.0ms (1.7%)

prune104.0ms (1.2%)

regimes78.0ms (0.9%)

regimes21.0ms (0.2%)

regimes28.0ms (0.3%)

regimes32.0ms (0.4%)

regimes9.0ms (0.1%)

regimes29.0ms (0.3%)

regimes47.0ms (0.5%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch16.0ms (0.2%)

simplify33.0ms (0.4%)

soundness892.0ms (10.3%)

preprocess175.0ms (2%)

end0.0ms (0%)

Profiling