Metrics for Given's Rotation SVD example

analyze505.0ms (4.8%)

Memory

25.8MiB live, 958.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.3s (22.2%)

Memory

-60.8MiB live, 3 656.3MiB allocated

Samples

948.0ms	6 286×	0	valid
533.0ms	871×	2	valid
197.0ms	655×	1	valid
186.0ms	370×	3	valid
30.0ms	74×	4	valid
19.0ms	39×	5	exit

Precisions

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

ival-mult: 600.0ms (38.5% of total)

const: 317.0ms (20.3% of total)

ival-sqrt: 195.0ms (12.5% of total)

ival-add: 148.0ms (9.5% of total)

ival-div: 93.0ms (6% of total)

ival-fabs: 64.0ms (4.1% of total)

adjust: 59.0ms (3.8% of total)

ival-<: 56.0ms (3.6% of total)

exact: 12.0ms (0.8% of total)

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

ival-assert: 4.0ms (0.3% of total)

Bogosity

preprocess64.0ms (0.6%)

Memory

-1.9MiB live, 37.5MiB allocated

Algorithm

2×	egg-herbie

Rules

248×	`distribute-lft-neg-in`
218×	`unsub-neg`
196×	`associate-r`
196×	`associate-l`
166×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	108
1	102	104
2	202	104
3	407	104
4	666	104
5	1003	104
6	1335	104
7	1547	104
8	1699	104
9	1935	104
10	2002	104
11	2030	104
12	2032	104
0	14	17
1	29	17
2	36	17
3	38	17
4	39	17
0	39	15

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

Outputs

(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

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

Call 2

Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))

Outputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(sqrt (+ 1/2 (/ (* x -1/2) (sqrt (+ (* 4 (* p p)) (* x x))))))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(neg (sqrt (+ 1/2 (/ (* x -1/2) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))
(sqrt (+ 1/2 (/ (* 1/2 p) (sqrt (+ (* x (* x 4)) (* p p))))))

Symmetry

(abs p)

explain262.0ms (2.5%)

Memory

-47.8MiB live, 367.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
71	0	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
37	0	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
20	2	(1.9342651075044092e-205 -3.7562558239553044e+117)	1	(3.2653385133116575e-103 -3.0228257348631004e+57)	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
0	0	-	0	-	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	0	-	0	-	`#s(literal 4 binary64)`
0	0	-	0	-	`(*.f64 x x)`
0	0	-	0	-	`p`
0	0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	0	-	0	-	`#s(literal 1/2 binary64)`
0	0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`	oflow-rescue	71	0
↳	`(*.f64 #s(literal 4 binary64) p)`	overflow	1
↳	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`	overflow	71
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	overflow	71
`+.f64`	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	cancellation	37	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	uflow-rescue	21	0
↳	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`	underflow	4
↳	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`	underflow	25
↳	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`	underflow	25
↳	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`	underflow	9
↳	`(.f64 (.f64 #s(literal 4 binary64) p) p)`	underflow	60

Confusion

	Predicted +	Predicted -
+	56	0
-	73	127

Precision

0.43410852713178294

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	56	0	0
-	73	0	127

Precision?

0.43410852713178294

Recall?

1.0

Freqs

test

number	freq
0	127
1	129

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

54.0ms	48×	2	valid
41.0ms	390×	0	valid
8.0ms	48×	1	valid
7.0ms	20×	3	valid
2.0ms	6×	4	valid

Compiler

Compiled 230 to 60 computations (73.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 20.0ms (42% of total)

ival-sqrt: 10.0ms (21% of total)

ival-add: 8.0ms (16.8% of total)

ival-div: 5.0ms (10.5% of total)

adjust: 3.0ms (6.3% of total)

exact: 1.0ms (2.1% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.3%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify5.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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×	`-lowering-.f32`
32×	`-lowering-.f64`
18×	`accelerator-lowering-fma.f32`
18×	`accelerator-lowering-fma.f64`
12×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	94
1	29	94
2	36	94
3	38	94
4	39	94
0	39	86

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(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)))))
1
(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
x
(sqrt (+ (* (* 4 p) p) (* x x)))
(+ (* (* 4 p) p) (* x x))
(* (* 4 p) p)
(* 4 p)
4
p
(* x x)

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

localize56.0ms (0.5%)

Memory

-13.0MiB live, 104.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
✓	accuracy	92.8%	(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)))))))
✓	accuracy	86.8%	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
✓	accuracy	74.1%	(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))

Samples

19.0ms	195×	0	valid
6.0ms	24×	2	valid
5.0ms	24×	1	valid
3.0ms	10×	3	valid
1.0ms	3×	4	valid

Compiler

Compiled 96 to 16 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 7.0ms (31.8% of total)

ival-sqrt: 6.0ms (27.3% of total)

ival-div: 3.0ms (13.6% of total)

ival-add: 3.0ms (13.6% of total)

adjust: 2.0ms (9.1% of total)

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

exact: 0.0ms (0% of total)

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

series22.0ms (0.2%)

Memory

10.3MiB live, 46.9MiB allocated

Counts

5 → 120

Calls

Call 1

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

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

30 calls:

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

rewrite299.0ms (2.9%)

Memory

-19.2MiB live, 458.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 862×	`accelerator-lowering-fma.f32`
4 862×	`accelerator-lowering-fma.f64`
3 532×	`-lowering-.f32`
3 532×	`-lowering-.f64`
2 388×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	68	66
2	492	66
3	6948	66
0	8473	59

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 276

Calls

Call 1

Inputs
(* 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)))

Outputs
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (/.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) x #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
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(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))))
(.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 3 binary64)))) (fma.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) (-.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) (.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)) (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64)))))) (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))))) (+.f64 (fma.f64 x (/.f64 x (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (*.f64 p p))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x))) (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))))))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 p p) #s(literal -4 binary64) (*.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 #s(literal -16 binary64) (.f64 p (.f64 p (.f64 p p)))))) (sqrt.f64 (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p))))))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (*.f64 p p) #s(literal 16 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))))
(pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))))
(.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 p (.f64 p p)) (.f64 #s(literal 64 binary64) (.f64 p (.f64 p p)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 p p) #s(literal -4 binary64))) (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64)))))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) #s(literal -4 binary64) (.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) #s(literal 16 binary64))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x)))))
(.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 x x (.f64 p (*.f64 #s(literal 4 binary64) p))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))

simplify530.0ms (5.1%)

Memory

24.9MiB live, 539.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 590×	`accelerator-lowering-fma.f32`
9 590×	`accelerator-lowering-fma.f64`
6 900×	`-lowering-.f32`
6 900×	`-lowering-.f64`
4 472×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	2482
1	1325	2377
2	4606	2304
0	8075	2141

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval74.0ms (0.7%)

Memory: 2.8MiB live, 116.9MiB allocated
Compiler: Compiled 15 528 to 1 955 computations (87.4% saved)

prune188.0ms (1.8%)

Memory

-17.8MiB live, 186.0MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	387	9	396
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	388	9	397

Accuracy

99.8%

Counts

397 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.9%	(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) p)) (neg.f64 x))
▶	79.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	26.4%	(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
▶	52.0%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
	14.5%	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x)))
	16.6%	(sqrt.f64 (/.f64 (.f64 p p) (.f64 x x)))
▶	75.7%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
	36.3%	(sqrt.f64 #s(literal 1 binary64))
▶	55.7%	(sqrt.f64 #s(literal 1/2 binary64))

Compiler

Compiled 220 to 148 computations (32.7% saved)

simplify556.0ms (5.3%)

Memory

42.2MiB live, 419.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

9 926×	`accelerator-lowering-fma.f32`
9 926×	`accelerator-lowering-fma.f64`
2 300×	`-lowering-.f32`
2 300×	`-lowering-.f64`
1 654×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	212
1	76	210
2	125	210
3	194	210
4	256	210
5	311	210
6	438	210
7	671	210
8	1128	210
9	2680	210
10	4469	210
11	6103	210
12	7359	210
0	8031	194

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
(+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
x
(sqrt (+ (* x x) (* p (* 4 p))))
(+ (* x x) (* p (* 4 p)))
(* p (* 4 p))
p
(* 4 p)
4
1/2
(sqrt 1/2)
1/2
(sqrt (+ (* 1/4 (/ x p)) 1/2))
(+ (* 1/4 (/ x p)) 1/2)
1/4
(/ x p)
x
p
1/2
(sqrt (+ (* (neg p) (/ p (* x x))) 1))
(+ (* (neg p) (/ p (* x x))) 1)
(neg p)
p
(/ p (* x x))
(* x x)
x
1
(sqrt (* 1/2 (+ 1 (/ x (+ (* p (* p (/ 2 x))) x)))))
(* 1/2 (+ 1 (/ x (+ (* p (* p (/ 2 x))) x))))
1/2
(+ 1 (/ x (+ (* p (* p (/ 2 x))) x)))
1
(/ x (+ (* p (* p (/ 2 x))) x))
x
(+ (* p (* p (/ 2 x))) x)
p
(* p (/ 2 x))
(/ 2 x)
2

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

localize234.0ms (2.2%)

Memory

-3.7MiB live, 226.9MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (.f64 p (/.f64 #s(literal 2 binary64) x)) x)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x)))
✓	accuracy	100.0%	(/.f64 x (fma.f64 p (*.f64 p (/.f64 #s(literal 2 binary64) x)) x))
✓	accuracy	99.9%	(*.f64 p (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (neg.f64 p) (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(neg.f64 p)
✓	accuracy	99.9%	(/.f64 p (*.f64 x x))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 x p)
✓	accuracy	96.3%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))
✓	accuracy	100.0%	(fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p)))))

Samples

87.0ms	191×	0	invalid
62.0ms	65×	0	valid

Compiler

Compiled 198 to 36 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-div: 37.0ms (55% of total)

ival-mult: 13.0ms (19.3% of total)

ival-sqrt: 9.0ms (13.4% of total)

ival-add: 7.0ms (10.4% of total)

exact: 1.0ms (1.5% of total)

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

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

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

series70.0ms (0.7%)

Memory

18.7MiB live, 90.7MiB allocated

Counts

18 → 384

Calls

Call 1

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

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

Calls

96 calls:

Time	Variable		Point	Expression
15.0ms	p	@	0	(+ (* (neg p) (/ p (* x x))) 1)
4.0ms	x	@	-inf	(/ x (+ (* p (* p (/ 2 x))) x))
3.0ms	x	@	inf	(sqrt (+ (* 1/4 (/ x p)) 1/2))
2.0ms	x	@	inf	(sqrt (* 1/2 (+ 1 (/ x (+ (* p (* p (/ 2 x))) x)))))
1.0ms	x	@	0	(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))

rewrite344.0ms (3.3%)

Memory

0.4MiB live, 571.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 628×	`/-lowering-/.f32`
4 628×	`/-lowering-/.f64`
4 464×	`accelerator-lowering-fma.f32`
4 464×	`accelerator-lowering-fma.f64`
4 212×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	166
1	184	164
2	1389	164
0	8255	150

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 538

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2))
(+ (* (/ x (sqrt (+ (* x x) (* p (* 4 p))))) 1/2) 1/2)
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
(sqrt (+ (* x x) (* p (* 4 p))))
(sqrt 1/2)
(sqrt (+ (* 1/4 (/ x p)) 1/2))
(+ (* 1/4 (/ x p)) 1/2)
(/ x p)
(sqrt (+ (* (neg p) (/ p (* x x))) 1))
(+ (* (neg p) (/ p (* x x))) 1)
(neg p)
(/ p (* x x))
(* 1/2 (+ 1 (/ x (+ (* p (* p (/ 2 x))) x))))
(* p (/ 2 x))
(sqrt (* 1/2 (+ 1 (/ x (+ (* p (* p (/ 2 x))) x)))))
(+ 1 (/ x (+ (* p (* p (/ 2 x))) x)))
(* x x)
(/ x (+ (* p (* p (/ 2 x))) x))

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

simplify402.0ms (3.9%)

Memory

-18.3MiB live, 748.3MiB allocated

Algorithm

1×	egg-herbie

Rules

9 904×	`accelerator-lowering-fma.f32`
9 904×	`accelerator-lowering-fma.f64`
7 620×	`-lowering-.f32`
7 620×	`-lowering-.f64`
4 044×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	843	5952
1	2563	5820
0	8264	5467

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(* 1/2 (/ x p))
(* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/2048 (/ (pow x 2) (pow p 7))) (* 3/256 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1
(- (* 2 (/ (pow p 2) (pow x 2))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))) 1)
(- (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (* 2 (/ (pow p 2) (pow x 2))))) 1)
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p)
(/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p)
(* -1/2 (/ x p))
(* -1 (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x))) p))
(* -1 (/ (+ (* -1 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)))) p))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* 1/2 (sqrt (/ x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))
(* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))
(* 1/2 (sqrt (/ x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* -1/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (- (* -1/16 (/ (pow p 2) (pow x 6))) (* 1/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(/ (* p (sqrt -1)) x)
(* p (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))
(* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))
(* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow x 5) (* (pow p 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))))
(* -1 (/ (* p (sqrt -1)) x))
(* -1 (* p (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))
(* -1 (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x)))))
(* -1 (* p (+ (* -1/8 (/ (pow x 3) (* (pow p 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow x 5) (* (pow p 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ x (* (pow p 2) (sqrt -1)))) (/ (sqrt -1) x))))))
(/ (* p (sqrt -1)) x)
(/ (+ (* 1/2 (/ (pow x 2) (* p (sqrt -1)))) (* p (sqrt -1))) x)
(/ (+ (* p (sqrt -1)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* p (sqrt -1))))))) x)
(/ (+ (* p (sqrt -1)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (* (pow p 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow p 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* p (sqrt -1))))))) x)
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* -1/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/8 (/ (pow p 4) (pow x 4))) (* -1/16 (/ (pow p 6) (pow x 6))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* -1/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* -1/8 (/ (pow p 4) (pow x 4))) (* -1/16 (/ (pow p 6) (pow x 6))))))
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 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* -1 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* (pow p 2) (- (/ 1 (pow p 2)) (/ 1 (pow x 2))))
(* -1 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1 (pow p 2)) (pow x 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
(+ 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)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(* -1 p)
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
(/ p (pow x 2))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))
(+ 1/2 (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -4 (/ (pow p 6) (pow x 6))) (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -4 (/ (pow p 6) (pow x 6))) (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(* 2 (/ p x))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* -5/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 4))) (* 1/4 (/ (sqrt 1/2) (pow p 2))))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (pow p 2))) (* (pow x 2) (+ (* -5/32 (/ (sqrt 1/2) (pow p 4))) (* 13/128 (/ (* (pow x 2) (sqrt 1/2)) (pow p 6))))))))
(* (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) (+ (* -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) (+ (* -4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 8 (pow p 6)) (/ (* (pow p 2) (+ (* -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)))))
(* (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) (- (* 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) (- (* -8 (pow p 6)) (* -1 (/ (* (pow p 2) (- (* 4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 4 (pow p 4)) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 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) (- (* 4 (/ 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 (/ (- (* 4 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 8 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 4 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/4 (* (pow x 2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4))))) (* -1/8 (pow x 6)))) (pow p 6))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/4 (* (pow x 2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4))))) (* -1/8 (pow x 6)))) (pow p 6))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/16 (pow x 4)) (* 1/4 (pow x 4)))) (pow p 4))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))))))
1
(+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))
(+ 1 (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2))))))
(+ 1 (* (pow x 2) (+ (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2))))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 2 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 4) (pow x 4)))))
(+ 2 (+ (* -8 (/ (pow p 6) (pow x 6))) (+ (* -2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 4) (pow x 4))))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))
(+ 1 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* 1/2 (/ (pow x 2) (pow p 2)))))
(- (+ 1 (+ (* 1/8 (/ (pow x 6) (pow p 6))) (* 1/2 (/ (pow x 2) (pow p 2))))) (* 1/4 (/ (pow x 4) (pow p 4))))
1
(+ 1 (* 1/2 (/ (pow x 2) (pow p 2))))
(+ 1 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* 1/2 (/ (pow x 2) (pow p 2)))))
(- (+ 1 (+ (* 1/8 (/ (pow x 6) (pow p 6))) (* 1/2 (/ (pow x 2) (pow p 2))))) (* 1/4 (/ (pow x 4) (pow p 4))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 8))) (* 1/8 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))

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

eval118.0ms (1.1%)

Memory: -6.0MiB live, 271.2MiB allocated
Compiler: Compiled 21 687 to 2 821 computations (87% saved)

prune107.0ms (1%)

Memory

-4.2MiB live, 276.8MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	918	4	922
Fresh	3	1	4
Picked	2	3	5
Done	0	0	0
Total	923	8	931

Accuracy

100.0%

Counts

931 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	26.8%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
▶	26.2%	(/.f64 p (neg.f64 x))
▶	75.7%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	79.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	52.0%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
▶	14.5%	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x)))
✓	55.7%	(sqrt.f64 #s(literal 1/2 binary64))
▶	36.3%	#s(literal 1 binary64)

Compiler

Compiled 154 to 96 computations (37.7% saved)

simplify287.0ms (2.8%)

Memory

27.5MiB live, 432.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)))
✓	cost-diff	0	(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x))
✓	cost-diff	0	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x)))
✓	cost-diff	640	(fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	0	(/.f64 (.f64 p p) (.f64 x x))
✓	cost-diff	0	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
✓	cost-diff	0	(neg.f64 x)
✓	cost-diff	0	(/.f64 p (neg.f64 x))
✓	cost-diff	0	(fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)
✓	cost-diff	0	(/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x))
✓	cost-diff	0	(fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Rules

5 732×	`-lowering-.f32`
5 732×	`-lowering-.f64`
5 268×	`accelerator-lowering-fma.f32`
5 268×	`accelerator-lowering-fma.f64`
2 520×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	201
1	76	191
2	185	175
3	422	175
4	899	175
5	1550	175
6	1741	175
7	2038	175
8	2557	175
9	3167	175
10	4875	175
11	7625	171
0	8176	161

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2))
(+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)
(/ x (+ (* p (/ (* p 2) x)) x))
x
(+ (* p (/ (* p 2) x)) x)
p
(/ (* p 2) x)
(* p 2)
2
1/2
1
(/ p (neg x))
p
(neg x)
x
(+ (* -1/2 (/ (* p p) (* x x))) 1)
-1/2
(/ (* p p) (* x x))
(* p p)
p
(* x x)
x
1
(sqrt (/ (+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p)) (* x x)))
(/ (+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p)) (* x x))
(+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p))
1/4
(* (* (* p p) (* p p)) (/ -12 (* x x)))
(* (* p p) (* p p))
(* p p)
p
(/ -12 (* x x))
-12
(* x x)
x

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

localize236.0ms (2.3%)

Memory

-34.7MiB live, 163.9MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 #s(literal -12 binary64) (*.f64 x x))
✓	accuracy	96.7%	(.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x)))
✓	accuracy	93.1%	(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x))
✓	accuracy	85.1%	(sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 p p) (.f64 p p)) (/.f64 #s(literal -12 binary64) (.f64 x x))) (.f64 p p)) (*.f64 x x)))
✓	accuracy	100.0%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	93.1%	(/.f64 (.f64 p p) (.f64 x x))
✓	accuracy	100.0%	(/.f64 p (neg.f64 x))
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(*.f64 p #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x))

Samples

85.0ms	129×	0	invalid
29.0ms	127×	0	valid

Compiler

Compiled 193 to 32 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-add: 43.0ms (43.6% of total)

ival-mult: 35.0ms (35.5% of total)

ival-div: 16.0ms (16.2% of total)

ival-sqrt: 3.0ms (3% of total)

exact: 1.0ms (1% of total)

ival-neg: 1.0ms (1% of total)

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

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

series47.0ms (0.5%)

Memory

21.8MiB live, 60.9MiB allocated

Counts

16 → 324

Calls

Call 1

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

Outputs
#s(alt (sqrt 1/2) (taylor 0 x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2))))) (taylor 0 x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2))))))) (taylor 0 x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* -1/2 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow x 2) (- (* 1/16 (/ 1 (pow p 6))) (* -1/8 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2))))))) (taylor 0 x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor inf x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) 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 inf x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) 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))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))))) (taylor inf x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) 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))) (+ (* 1/2 (/ (- (* -4 (pow p 6)) (* -1/2 (* (pow p 2) (- (* 2 (pow p 4)) (* 1/4 (pow p 4)))))) (pow x 6))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4)))))) (taylor inf x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) 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 -inf x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/2 (/ (+ (* -2 (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 (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (+ (* -1/2 (/ (+ (* 1/2 (* (pow p 2) (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))) (* -1/2 (/ (pow p 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 p) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) 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 (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* 7/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -25/16 (/ (pow p 2) (pow x 6))) (* 7/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2)))))) (taylor 0 p) (#s(alt (sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)) (patch (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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Calls

81 calls:

Time	Variable		Point	Expression
19.0ms	p	@	inf	(* p 2)
1.0ms	x	@	0	(sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2))
1.0ms	p	@	inf	(sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2))
1.0ms	x	@	0	(+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p))
1.0ms	p	@	inf	(sqrt (/ (+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p)) (* x x)))

rewrite462.0ms (4.4%)

Memory

-36.3MiB live, 581.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 880×	`accelerator-lowering-fma.f32`
5 880×	`accelerator-lowering-fma.f64`
4 582×	`-lowering-.f32`
4 582×	`-lowering-.f64`
3 860×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	160
1	169	147
2	1246	140
0	8318	130

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 656

Calls

Call 1

Inputs
(sqrt (+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2))
(+ (* (/ x (+ (* p (/ (* p 2) x)) x)) 1/2) 1/2)
(/ x (+ (* p (/ (* p 2) x)) x))
(+ (* p (/ (* p 2) x)) x)
(/ p (neg x))
(neg x)
(+ (* -1/2 (/ (* p p) (* x x))) 1)
(/ (* p p) (* x x))
(* p p)
(* x x)
(+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p))
(sqrt (/ (+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p)) (* x x)))
(/ (+ (* 1/4 (* (* (* p p) (* p p)) (/ -12 (* x x)))) (* p p)) (* x x))
(* (* (* p p) (* p p)) (/ -12 (* x x)))
(* p 2)
(/ -12 (* x x))

Outputs
(exp.f64 (.f64 (log.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/4 binary64)))) (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/4 binary64))) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/4 binary64)))) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/4 binary64))))))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal 1/4 binary64)) (.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal -1/4 binary64))))))
(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))
(+.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64))
(+.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)))))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 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 (neg.f64 x) (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 x (fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (fma.f64 x (.f64 x x) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) #s(literal 8 binary64)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (.f64 p (.f64 (/.f64 p x) #s(literal -2 binary64)))) (/.f64 (.f64 (.f64 p (.f64 p (.f64 p p))) #s(literal 4 binary64)) (.f64 x x))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (-.f64 (/.f64 (.f64 (.f64 p (.f64 p (.f64 p p))) #s(literal 4 binary64)) (.f64 x x)) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 p (*.f64 (/.f64 p x) #s(literal -2 binary64)) x))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) (fma.f64 x (.f64 x x) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) #s(literal 8 binary64)) (.f64 x (.f64 x x))))) (fma.f64 x (+.f64 x (.f64 p (.f64 (/.f64 p x) #s(literal -2 binary64)))) (/.f64 (.f64 (.f64 p (.f64 p (.f64 p p))) #s(literal 4 binary64)) (*.f64 x x))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (/.f64 (.f64 (.f64 p (.f64 p (.f64 p p))) #s(literal 4 binary64)) (.f64 x x)) (.f64 x x))) (fma.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x) (neg.f64 x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 x (.f64 x x) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) #s(literal 8 binary64)) (.f64 x (.f64 x x))))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (.f64 p (.f64 (/.f64 p x) #s(literal -2 binary64)))) (/.f64 (.f64 (.f64 p (.f64 p (.f64 p p))) #s(literal 4 binary64)) (.f64 x x))))) #s(literal 1/2 binary64))
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simplify516.0ms (4.9%)

Memory

27.2MiB live, 846.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 924×	`accelerator-lowering-fma.f32`
10 924×	`accelerator-lowering-fma.f64`
6 184×	`-lowering-.f32`
6 184×	`-lowering-.f64`
3 338×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	402	3896
1	1158	3843
2	3522	3769
0	8248	3563

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 324

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
(+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* -1/2 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow x 2) (- (* 1/16 (/ 1 (pow p 6))) (* -1/8 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -4 (pow p 6)) (* -1/2 (* (pow p 2) (- (* 2 (pow p 4)) (* 1/4 (pow p 4)))))) (pow x 6))) (* 1/2 (/ (- (* 2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (/ (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))) (pow x 4))) (+ (* -1/2 (/ (+ (* 1/2 (* (pow p 2) (+ (* -2 (pow p 4)) (* 1/4 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))) (* -1/2 (/ (pow p 2) (pow x 2))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 7/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -25/16 (/ (pow p 2) (pow x 6))) (* 7/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))) (+ (* 1/2 (/ (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* 1/2 (/ (- (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (- (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))
(+ 1/2 (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -4 (/ (pow p 6) (pow x 6))) (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 2 (/ (pow p 4) (pow x 4)))) (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -4 (/ (pow p 6) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
1/2
(+ 1/2 (* 1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(+ 1/2 (+ (* -1/8 (/ (pow x 4) (pow p 4))) (+ (* 1/16 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow p 4))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 8))) (* 1/8 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))) (* 1/2 (/ 1 (pow p 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* 4 (/ (pow p 4) (pow x 4)))) (* 2 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -8 (/ (pow p 6) (pow x 6)))) (+ (* -4 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))
1
(+ 1 (* -2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 4 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
(* 1/2 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (/ (pow x 4) (pow p 2))) (* 1/2 (pow x 2))) (pow p 2))
(/ (- (+ (* 1/8 (/ (pow x 6) (pow p 4))) (* 1/2 (pow x 2))) (* 1/4 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* 2 (/ (pow p 2) x)))
(* 2 (/ (pow p 2) x))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* 2 (/ (pow p 2) x))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* (pow p 2) (+ (* 2 (/ 1 x)) (/ x (pow p 2))))
(* 2 (/ (pow p 2) x))
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/ (+ (* 2 (pow p 2)) (pow x 2)) x)
(/ (+ (* 2 (pow p 2)) (pow x 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)))))
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)))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 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 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 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 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow p 2)
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(* (pow p 2) (+ 1 (* -3 (/ (pow p 2) (pow x 2)))))
(* -3 (/ (pow p 4) (pow x 2)))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* -3 (/ (pow p 4) (pow x 2)))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* (pow p 4) (- (/ 1 (pow p 2)) (* 3 (/ 1 (pow x 2)))))
(* -3 (/ (pow p 4) (pow x 2)))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 2))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 2))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 2))
(pow p 2)
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(pow p 2)
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2))
(/ p x)
(* p (+ (* -3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* -9/8 (/ (pow p 2) (pow x 5))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* (pow p 2) (- (* -27/16 (/ (pow p 2) (pow x 7))) (* 9/8 (/ 1 (pow x 5))))) (* 3/2 (/ 1 (pow x 3))))) (/ 1 x)))
(/ (* (pow p 2) (sqrt -3)) (pow x 2))
(* (pow p 2) (+ (* 1/2 (/ 1 (* (pow p 2) (sqrt -3)))) (/ (sqrt -3) (pow x 2))))
(* (pow p 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 4) (pow (sqrt -3) 3)))) (+ (/ 1/2 (* (pow p 2) (sqrt -3))) (/ (sqrt -3) (pow x 2)))))
(* (pow p 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (pow x 4) (* (pow p 6) (pow (sqrt -3) 5)))) (+ (/ 1/2 (* (pow p 2) (sqrt -3))) (/ (sqrt -3) (pow x 2))))))
(/ (* (pow p 2) (sqrt -3)) (pow x 2))
(* (pow p 2) (+ (* 1/2 (/ 1 (* (pow p 2) (sqrt -3)))) (/ (sqrt -3) (pow x 2))))
(* (pow p 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 4) (pow (sqrt -3) 3)))) (+ (/ 1/2 (* (pow p 2) (sqrt -3))) (/ (sqrt -3) (pow x 2)))))
(* (pow p 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (pow x 4) (* (pow p 6) (pow (sqrt -3) 5)))) (+ (/ 1/2 (* (pow p 2) (sqrt -3))) (/ (sqrt -3) (pow x 2))))))
(/ (* (pow p 2) (sqrt -3)) (pow x 2))
(/ (+ (* 1/2 (/ (pow x 2) (sqrt -3))) (* (pow p 2) (sqrt -3))) (pow x 2))
(/ (+ (* (pow p 2) (sqrt -3)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt -3) 3)))) (* 1/2 (/ 1 (sqrt -3)))))) (pow x 2))
(/ (+ (* (pow p 2) (sqrt -3)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (* (pow p 4) (pow (sqrt -3) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt -3) 3)))))) (* 1/2 (/ 1 (sqrt -3)))))) (pow x 2))
(/ p x)
(/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4))))) x)
(/ (+ p (+ (* -27/16 (/ (pow p 7) (pow x 6))) (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4)))))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4))))) x))
(* -1 (/ (+ p (+ (* -27/16 (/ (pow p 7) (pow x 6))) (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4)))))) x))
(/ (pow p 2) (pow x 2))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* -3 (/ (pow p 4) (pow x 4)))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* -3 (/ (pow p 4) (pow x 4)))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(* -3 (/ (pow p 4) (pow x 4)))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
(/ (pow p 2) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* -12 (/ (pow p 4) (pow x 2)))
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(* 2 p)
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))
(/ -12 (pow x 2))

Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(fma.f64 x (/.f64 (.f64 x #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 p p) (.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* (pow x 2) (+ (* (pow x 2) (+ (* -1/2 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (sqrt 1/2))) (* 1/2 (/ (* (pow x 2) (- (* 1/16 (/ 1 (pow p 6))) (* -1/8 (/ (+ (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))) (* 1/8 (/ 1 (pow p 4)))) (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (.f64 (.f64 p p) (.f64 p p))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 p p) (.f64 p p)))) (.f64 p p)) (/.f64 #s(literal 1/16 binary64) (pow.f64 p #s(literal 6 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -1/64 binary64) (.f64 (.f64 p p) (.f64 p p))) (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 p p) (.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
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1
#s(literal 1 binary64)
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(sqrt 1/2)
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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1/2
#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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(/ (- (+ (* -1/16 (/ (pow x 8) (pow p 6))) (* 1/2 (pow x 2))) (+ (* -1/8 (/ (pow x 6) (pow p 4))) (* 1/4 (/ (pow x 4) (pow p 2))))) (pow p 2))
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(fma.f64 (.f64 p p) (fma.f64 #s(literal 1/24 binary64) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 p p) (.f64 p p)))) (/.f64 (sqrt.f64 #s(literal -3 binary64)) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))
(* (pow p 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (pow x 4) (* (pow p 6) (pow (sqrt -3) 5)))) (+ (/ 1/2 (* (pow p 2) (sqrt -3))) (/ (sqrt -3) (pow x 2))))))
(fma.f64 (.f64 p p) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)))) (fma.f64 #s(literal 1/24 binary64) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 p p) (.f64 p p)))) (/.f64 (sqrt.f64 #s(literal -3 binary64)) (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))))
(/ (* (pow p 2) (sqrt -3)) (pow x 2))
(/.f64 (.f64 (.f64 p p) (sqrt.f64 #s(literal -3 binary64))) (*.f64 x x))
(/ (+ (* 1/2 (/ (pow x 2) (sqrt -3))) (* (pow p 2) (sqrt -3))) (pow x 2))
(/.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (.f64 p p) (sqrt.f64 #s(literal -3 binary64)))) (.f64 x x))
(/ (+ (* (pow p 2) (sqrt -3)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt -3) 3)))) (* 1/2 (/ 1 (sqrt -3)))))) (pow x 2))
(/.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (/.f64 (.f64 x x) (.f64 (.f64 p p) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64)))) (.f64 (.f64 p p) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 x x))
(/ (+ (* (pow p 2) (sqrt -3)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (* (pow p 4) (pow (sqrt -3) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt -3) 3)))))) (* 1/2 (/ 1 (sqrt -3)))))) (pow x 2))
(/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (.f64 (.f64 (.f64 p p) (.f64 p p)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64)))) (.f64 (.f64 p p) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 x x))
(/ p x)
(/.f64 p x)
(/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)
(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) x)
(/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4))))) x)
(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) (fma.f64 #s(literal -9/8 binary64) (/.f64 (pow.f64 p #s(literal 5 binary64)) (.f64 (.f64 x x) (.f64 x x))) p)) x)
(/ (+ p (+ (* -27/16 (/ (pow p 7) (pow x 6))) (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal -9/8 binary64) (/.f64 (pow.f64 p #s(literal 5 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -27/16 binary64) (/.f64 (pow.f64 p #s(literal 7 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) p))) x)
(* -1 (/ p x))
(/.f64 (neg.f64 p) x)
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x))
(* -1 (/ (+ p (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4))))) x))
(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) (fma.f64 #s(literal -9/8 binary64) (/.f64 (pow.f64 p #s(literal 5 binary64)) (.f64 (.f64 x x) (.f64 x x))) p)) (neg.f64 x))
(* -1 (/ (+ p (+ (* -27/16 (/ (pow p 7) (pow x 6))) (+ (* -3/2 (/ (pow p 3) (pow x 2))) (* -9/8 (/ (pow p 5) (pow x 4)))))) x))
(/.f64 (fma.f64 #s(literal -9/8 binary64) (/.f64 (pow.f64 p #s(literal 5 binary64)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -27/16 binary64) (/.f64 (pow.f64 p #s(literal 7 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) p))) (neg.f64 x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (.f64 (.f64 x x) (.f64 x x))) #s(literal -3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (.f64 (.f64 x x) (.f64 x x))) #s(literal -3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(* (pow p 2) (+ (* -3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(.f64 (.f64 p p) (fma.f64 (/.f64 (.f64 p p) (.f64 (.f64 x x) (.f64 x x))) #s(literal -3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(* -3 (/ (pow p 4) (pow x 4)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -3 binary64)) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 p p) x) x)) (/.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 p p) x) x)) (/.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 p p) x) x)) (/.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(* -3 (/ (pow p 4) (pow x 4)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -3 binary64)) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 p p) x) x)) (/.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 p p) x) x)) (/.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(* (pow p 4) (- (/ 1 (* (pow p 2) (pow x 2))) (* 3 (/ 1 (pow x 4)))))
(.f64 (.f64 (.f64 p p) (.f64 p p)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 p p) x) x)) (/.f64 #s(literal -3 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(* -3 (/ (pow p 4) (pow x 4)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -3 binary64)) (.f64 (.f64 x x) (*.f64 x x)))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
(/.f64 (fma.f64 x (.f64 x (.f64 p p)) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -3 binary64))) (.f64 (.f64 x x) (*.f64 x x)))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
(/.f64 (fma.f64 x (.f64 x (.f64 p p)) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -3 binary64))) (.f64 (.f64 x x) (*.f64 x x)))
(/ (+ (* -3 (pow p 4)) (* (pow p 2) (pow x 2))) (pow x 4))
(/.f64 (fma.f64 x (.f64 x (.f64 p p)) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -3 binary64))) (.f64 (.f64 x x) (*.f64 x x)))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (.f64 p (fma.f64 p (/.f64 (.f64 (.f64 p p) #s(literal -3 binary64)) (.f64 x x)) p)) (*.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (.f64 p (fma.f64 p (/.f64 (.f64 (.f64 p p) #s(literal -3 binary64)) (.f64 x x)) p)) (*.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (.f64 p (fma.f64 p (/.f64 (.f64 (.f64 p p) #s(literal -3 binary64)) (.f64 x x)) p)) (*.f64 x x))
(/ (pow p 2) (pow x 2))
(/.f64 (.f64 p p) (.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (.f64 p (fma.f64 p (/.f64 (.f64 (.f64 p p) #s(literal -3 binary64)) (.f64 x x)) p)) (*.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (.f64 p (fma.f64 p (/.f64 (.f64 (.f64 p p) #s(literal -3 binary64)) (.f64 x x)) p)) (*.f64 x x))
(/ (+ (* -3 (/ (pow p 4) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (.f64 p (fma.f64 p (/.f64 (.f64 (.f64 p p) #s(literal -3 binary64)) (.f64 x x)) p)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* -12 (/ (pow p 4) (pow x 2)))
(/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(* 2 p)
(*.f64 #s(literal 2 binary64) p)
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))
(/ -12 (pow x 2))
(/.f64 #s(literal -12 binary64) (*.f64 x x))

eval149.0ms (1.4%)

Memory: 31.3MiB live, 335.5MiB allocated
Compiler: Compiled 29 701 to 2 948 computations (90.1% saved)

prune119.0ms (1.1%)

Memory

-33.5MiB live, 271.2MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	1 118	2	1 120
Fresh	0	0	0
Picked	1	4	5
Done	0	3	3
Total	1 119	9	1 128

Accuracy

100.0%

Counts

1 128 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	26.8%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
▶	26.0%	(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x))
✓	26.2%	(/.f64 p (neg.f64 x))
▶	6.1%	(/.f64 p x)
✓	75.7%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	79.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	52.0%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓	55.7%	(sqrt.f64 #s(literal 1/2 binary64))
✓	36.3%	#s(literal 1 binary64)

Compiler

Compiled 89 to 60 computations (32.6% saved)

simplify391.0ms (3.8%)

Memory

26.9MiB live, 261.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 p (.f64 p p))
✓	cost-diff	0	(/.f64 (.f64 p (.f64 p p)) (*.f64 x x))
✓	cost-diff	0	(fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p)
✓	cost-diff	128	(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x))
✓	cost-diff	0	(/.f64 p x)

Rules

3 440×	`accelerator-lowering-fma.f32`
3 440×	`accelerator-lowering-fma.f64`
2 592×	`-lowering-.f32`
2 592×	`-lowering-.f64`
1 724×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	31	51
2	73	51
3	154	50
4	292	50
5	673	50
6	1421	50
7	2485	48
8	3494	48
9	4722	48
10	5136	48
11	5294	48
12	5301	48
13	5309	48
14	5463	48
15	5539	48
16	5539	48
17	6553	48
18	7029	48
19	7029	48
20	7029	48
21	7029	48
22	7136	48
23	7762	48
24	7794	48
25	7794	48
0	7794	47

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ p x)
p
x
(/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x))
(+ (* -3/2 (/ (* p (* p p)) (* x x))) p)
-3/2
(/ (* p (* p p)) (* x x))
(* p (* p p))
p
(* p p)
(* x x)
x
(neg x)

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

localize37.0ms (0.4%)

Memory

-3.3MiB live, 76.2MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p)
✓	accuracy	99.8%	(.f64 p (.f64 p p))
✓	accuracy	98.9%	(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x))
✓	accuracy	91.7%	(/.f64 (.f64 p (.f64 p p)) (*.f64 x x))
✓	accuracy	100.0%	(/.f64 p x)

Samples

23.0ms

256×

valid

Compiler

Compiled 59 to 14 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 6.0ms (44.1% of total)

ival-div: 5.0ms (36.7% of total)

ival-add: 1.0ms (7.3% of total)

ival-neg: 1.0ms (7.3% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Memory

-24.8MiB live, 12.9MiB allocated

Counts

5 → 108

Calls

Call 1

Inputs
#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())
#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())
#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())

Outputs
#s(alt (/ p x) (taylor 0 p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor 0 p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor 0 p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor 0 p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf p) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor 0 x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor 0 x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor 0 x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor 0 x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (/ p x) (taylor -inf x) (#s(alt (/ p x) (patch (/.f64 p x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor 0 p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x))) (taylor 0 p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x))) (taylor 0 p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x))) (taylor 0 p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 3/2 (/ (pow p 3) (pow x 3))) (taylor inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x)))) (taylor inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x)))) (taylor inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x)))) (taylor inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 3/2 (/ (pow p 3) (pow x 3))) (taylor -inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3)))))) (taylor -inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3)))))) (taylor -inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3)))))) (taylor -inf p) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 3/2 (/ (pow p 3) (pow x 3))) (taylor 0 x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3)) (taylor 0 x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3)) (taylor 0 x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3)) (taylor 0 x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x) (taylor inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x) (taylor inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x) (taylor inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ p x)) (taylor -inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)) (taylor -inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)) (taylor -inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x)) (taylor -inf x) (#s(alt (/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x)) (patch (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt p (taylor 0 p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2))))) (taylor 0 p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2))))) (taylor 0 p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2))))) (taylor 0 p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* -3/2 (/ (pow p 3) (pow x 2))) (taylor inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))) (taylor inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))) (taylor inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))) (taylor inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* -3/2 (/ (pow p 3) (pow x 2))) (taylor -inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))) (taylor -inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))) (taylor -inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))) (taylor -inf p) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (* -3/2 (/ (pow p 3) (pow x 2))) (taylor 0 x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2)) (taylor 0 x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2)) (taylor 0 x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2)) (taylor 0 x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt p (taylor inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) (taylor inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) (taylor inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) (taylor inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt p (taylor -inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) (taylor -inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) (taylor -inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) (taylor -inf x) (#s(alt (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (patch (fma.f64 #s(literal -3/2 binary64) (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf p) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor 0 x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (pow p 3) (pow x 2)) (taylor -inf x) (#s(alt (/ (* p (* p p)) (* x x)) (patch (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor 0 p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor 0 p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor 0 p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor 0 p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor -inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor -inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor -inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())
#s(alt (pow p 3) (taylor -inf p) (#s(alt (* p (* p p)) (patch (.f64 p (.f64 p p)) #<representation binary64>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	p	@	0	(/ (* p (* p p)) (* x x))
1.0ms	x	@	0	(/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x))
1.0ms	p	@	inf	(/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x))
1.0ms	p	@	0	(/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x))
1.0ms	x	@	inf	(/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x))

rewrite254.0ms (2.4%)

Memory

0.3MiB live, 402.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 296×	`-lowering-.f32`
4 296×	`-lowering-.f64`
3 698×	`accelerator-lowering-fma.f32`
3 698×	`accelerator-lowering-fma.f64`
3 034×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	65	38
2	457	37
3	6670	37
0	8151	36

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 404

Calls

Call 1

Inputs
(/ p x)
(/ (+ (* -3/2 (/ (* p (* p p)) (* x x))) p) (neg x))
(+ (* -3/2 (/ (* p (* p p)) (* x x))) p)
(/ (* p (* p p)) (* x x))
(* p (* p p))

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 x p)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 p (neg.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 p (neg.f64 x)))
(neg.f64 (/.f64 p (neg.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 x p)))
(/.f64 p x)
(/.f64 (neg.f64 p) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 x p))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (neg.f64 p) #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) p))
(/.f64 #s(literal -1 binary64) (/.f64 x (neg.f64 p)))
(/.f64 (/.f64 p (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 p) #s(literal -1 binary64)) x)
(/.f64 (*.f64 (neg.f64 p) #s(literal 1 binary64)) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 p)) (neg.f64 x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 p) #s(literal -1 binary64))) x)
(/.f64 (neg.f64 (*.f64 (neg.f64 p) #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (/.f64 p #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (/.f64 (*.f64 (neg.f64 p) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/.f64 (/.f64 (*.f64 (neg.f64 p) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(pow.f64 (/.f64 x p) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p x) #s(literal 1 binary64))
(*.f64 (neg.f64 p) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 p x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 p))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 p #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) p)
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) p) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 p (neg.f64 x)))
(.f64 (.f64 (neg.f64 p) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 p (.f64 x x)) x)
(.f64 (.f64 (neg.f64 p) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 p)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 x p) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x p) #s(literal -1/2 binary64)))
(.f64 (/.f64 (neg.f64 p) (neg.f64 (.f64 x (.f64 x x)))) (.f64 x x))
(+.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p) x)))
(+.f64 (/.f64 p (neg.f64 x)) (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) x) p) (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x))) (.f64 (/.f64 #s(literal -1 binary64) x) p))
(+.f64 (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x)) (/.f64 p (neg.f64 x)))
(exp.f64 (.f64 (log.f64 (neg.f64 (/.f64 x (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (.f64 p #s(literal -3/2 binary64)) p)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p) x))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p) x))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) #s(literal 9/4 binary64)) (.f64 (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 x (.f64 x (.f64 x x))))) (neg.f64 x)) (/.f64 (/.f64 (.f64 p p) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (*.f64 x x)))) (neg.f64 p))) (neg.f64 x)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) #s(literal 9/4 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (fma.f64 (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) #s(literal 3/2 binary64) p))) (/.f64 (.f64 p p) (.f64 x (fma.f64 (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) #s(literal 3/2 binary64) p))))
(fma.f64 p (/.f64 #s(literal -1 binary64) x) (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (/.f64 #s(literal -1 binary64) x) (/.f64 p (neg.f64 x)))
(fma.f64 (neg.f64 p) (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (/.f64 p (neg.f64 x)) (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) p (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x))))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (*.f64 (/.f64 #s(literal -1 binary64) x) p))
(fma.f64 #s(literal -1 binary64) (/.f64 p x) (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (/.f64 p (neg.f64 (.f64 x x))) x (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (/.f64 p (neg.f64 (.f64 x (.f64 x x)))) (.f64 x x) (.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(neg.f64 (/.f64 (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p) x))
(/.f64 (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p) (neg.f64 x))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) p) x)
(/.f64 (fma.f64 p (.f64 p p) (/.f64 (.f64 #s(literal -27/8 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (neg.f64 x) (fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 p p))))
(/.f64 (fma.f64 p (.f64 p p) (/.f64 (.f64 #s(literal -27/8 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (neg.f64 (fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 p p))) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 p p)) (/.f64 (fma.f64 p (.f64 p p) (/.f64 (.f64 #s(literal -27/8 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))) (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (/.f64 (fma.f64 #s(literal 9/4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 p (neg.f64 p))) (neg.f64 x))))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p)))
(/.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p)))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (.f64 p #s(literal -3/2 binary64)) p)) x))
(/.f64 (fma.f64 #s(literal 9/4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 p (neg.f64 p))) (.f64 x (fma.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64) p)))
(/.f64 (fma.f64 #s(literal 9/4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 p (neg.f64 p))) (.f64 (fma.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64) p) x))
(/.f64 (/.f64 (fma.f64 (.f64 p (/.f64 p (.f64 x x))) (*.f64 p #s(literal -3/2 binary64)) p) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (fma.f64 p (.f64 p p) (/.f64 (.f64 #s(literal -27/8 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 x (fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 p p))))
(/.f64 (neg.f64 (fma.f64 p (.f64 p p) (/.f64 (.f64 #s(literal -27/8 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (neg.f64 x) (neg.f64 (fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 p p)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 9/4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 p (neg.f64 p)))) (.f64 x (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (*.f64 x x)))) (neg.f64 p))))
(/.f64 (neg.f64 (fma.f64 #s(literal 9/4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 p (neg.f64 p)))) (.f64 (neg.f64 x) (fma.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) #s(literal 3/2 binary64) p)))
(/.f64 (fma.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (pow.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) #s(literal 9 binary64))) (.f64 (.f64 (neg.f64 x) (fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 p p))) (fma.f64 (.f64 p (.f64 p p)) (-.f64 (.f64 p (.f64 p p)) (/.f64 (.f64 #s(literal -27/8 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (pow.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (*.f64 x x)) #s(literal 6 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) #s(literal 6 binary64)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 (neg.f64 x) (fma.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (fma.f64 p (.f64 #s(literal -3/2 binary64) (.f64 p (/.f64 p (.f64 x x)))) (neg.f64 p)) (.f64 p p))) (-.f64 (/.f64 (.f64 #s(literal -27/8 binary64) (.f64 (.f64 p (.f64 p p)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 p (*.f64 p p)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal -3/2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) #s(literal 6 binary64)) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x (fma.f64 (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) #s(literal 3/2 binary64) p)) (fma.f64 (.f64 p p) (fma.f64 #s(literal 9/4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 p p)) (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) #s(literal 9/4 binary64)) (.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) #s(literal 9/4 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (fma.f64 p p (.f64 #s(literal -9/4 binary64) (/.f64 (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p)))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (neg.f64 x) (+.f64 p (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)))))
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(/.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal -1 binary64)) (/.f64 x (neg.f64 p)))
(/.f64 (neg.f64 (/.f64 (*.f64 p p) x)) (/.f64 x (neg.f64 p)))
(/.f64 (/.f64 (neg.f64 (.f64 p (.f64 p p))) #s(literal -1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (/.f64 (.f64 p (.f64 p p)) x) #s(literal 1 binary64)) x)
(/.f64 (/.f64 (/.f64 (.f64 p (.f64 p p)) x) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (.f64 (/.f64 p x) (.f64 p (neg.f64 p))) (neg.f64 x))
(pow.f64 (.f64 x (/.f64 x (.f64 p (*.f64 p p)))) #s(literal -1 binary64))
(.f64 p (.f64 p (/.f64 p (*.f64 x x))))
(.f64 (/.f64 p x) (/.f64 (.f64 p p) x))
(.f64 (.f64 p p) (/.f64 p (*.f64 x x)))
(.f64 (.f64 p p) (*.f64 (/.f64 p x) (/.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 p p) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 p x)))
(.f64 (.f64 p p) (.f64 (neg.f64 p) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(.f64 (.f64 p (.f64 p p)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 p (.f64 p p)) (.f64 x x)) #s(literal 1 binary64))
(.f64 (neg.f64 p) (/.f64 (.f64 p p) (neg.f64 (*.f64 x x))))
(.f64 (neg.f64 p) (/.f64 (/.f64 (.f64 p p) x) (neg.f64 x)))
(.f64 (neg.f64 p) (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 p p) x)))
(.f64 (neg.f64 p) (.f64 (.f64 p p) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(.f64 (neg.f64 (.f64 p (.f64 p p))) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 p (.f64 p p)) (.f64 x x)))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 p (*.f64 p p)) (neg.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 p (*.f64 p p)) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 (.f64 p p) x) (/.f64 #s(literal 1 binary64) p)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 p (.f64 p p))) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 p p)) (neg.f64 (.f64 x x))))
(.f64 (/.f64 (.f64 p (*.f64 p p)) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 p (/.f64 p (*.f64 x x))) p)
(.f64 (.f64 p (neg.f64 p)) (.f64 p (/.f64 #s(literal -1 binary64) (.f64 x x))))
(.f64 (.f64 p (neg.f64 p)) (/.f64 p (neg.f64 (*.f64 x x))))
(.f64 (/.f64 (.f64 p (*.f64 p p)) (neg.f64 x)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (neg.f64 (.f64 p (.f64 p p))))
(.f64 (pow.f64 p #s(literal 3/2 binary64)) (/.f64 (pow.f64 p #s(literal 3/2 binary64)) (.f64 x x)))
(.f64 (pow.f64 p #s(literal 3/2 binary64)) (.f64 (pow.f64 p #s(literal 3/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (/.f64 p (neg.f64 x)) (/.f64 (.f64 p (neg.f64 p)) x))
(.f64 (/.f64 p (neg.f64 x)) (/.f64 (.f64 p p) (neg.f64 x)))
(.f64 (/.f64 p (neg.f64 x)) (/.f64 (/.f64 (.f64 p p) x) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 p p) x) (/.f64 p x))
(.f64 (.f64 (neg.f64 p) #s(literal -1 binary64)) (.f64 p (/.f64 p (.f64 x x))))
(.f64 (/.f64 p (.f64 x x)) (*.f64 p p))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 p (.f64 p p)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 (.f64 p (.f64 p p)) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 (.f64 p (neg.f64 p)) (*.f64 x x)))
(.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 (/.f64 (.f64 p p) x) (neg.f64 x)))
(.f64 (/.f64 (.f64 p p) #s(literal 1 binary64)) (/.f64 p (*.f64 x x)))
(.f64 (/.f64 (.f64 p p) #s(literal -1 binary64)) (/.f64 (/.f64 p x) (neg.f64 x)))
(.f64 (/.f64 (.f64 p p) #s(literal -1 binary64)) (/.f64 (neg.f64 p) (*.f64 x x)))
(*.f64 (/.f64 (pow.f64 p #s(literal 3/2 binary64)) x) (/.f64 (pow.f64 p #s(literal 3/2 binary64)) x))
(.f64 (/.f64 (.f64 p (neg.f64 p)) x) (/.f64 p (neg.f64 x)))
(.f64 (/.f64 (.f64 p p) (neg.f64 x)) (/.f64 p (neg.f64 x)))
(.f64 (/.f64 (.f64 p (neg.f64 p)) #s(literal -1 binary64)) (/.f64 p (*.f64 x x)))
(.f64 (/.f64 (.f64 p (.f64 p p)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 p (.f64 p p)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 (/.f64 (/.f64 p x) #s(literal 1 binary64)) (/.f64 (.f64 p p) x))
(.f64 (pow.f64 (.f64 x (/.f64 x (.f64 p (.f64 p p)))) #s(literal -1/2 binary64)) (pow.f64 (.f64 x (/.f64 x (.f64 p (*.f64 p p)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 (/.f64 (.f64 p p) x) (neg.f64 x)) (neg.f64 p))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 p #s(literal 3/2 binary64))) (pow.f64 p #s(literal 3/2 binary64)))
(.f64 (/.f64 (/.f64 (.f64 p p) x) #s(literal 1 binary64)) (/.f64 p x))
(.f64 (/.f64 (/.f64 (.f64 p (.f64 p p)) (neg.f64 x)) (neg.f64 (.f64 x x))) x)
(.f64 (/.f64 (/.f64 (.f64 p (.f64 p p)) (neg.f64 x)) (neg.f64 (.f64 x (.f64 x x)))) (.f64 x x))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 p)))
(-.f64 #s(literal 0 binary64) (neg.f64 (.f64 p (.f64 p p))))
(neg.f64 (neg.f64 (.f64 p (.f64 p p))))
(pow.f64 p #s(literal 3 binary64))
(pow.f64 (*.f64 p p) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 p #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 p)) #s(literal 3 binary64))
(.f64 p (.f64 p p))
(.f64 p (neg.f64 (.f64 p (neg.f64 p))))
(.f64 (.f64 p p) p)
(.f64 (.f64 p (*.f64 p p)) #s(literal 1 binary64))
(.f64 (neg.f64 p) (.f64 p (neg.f64 p)))
(.f64 #s(literal 1 binary64) (.f64 p (*.f64 p p)))
(.f64 #s(literal -1 binary64) (neg.f64 (.f64 p (*.f64 p p))))
(.f64 (.f64 p (neg.f64 p)) (neg.f64 p))
(*.f64 (pow.f64 p #s(literal 3/2 binary64)) (pow.f64 p #s(literal 3/2 binary64)))
(.f64 (pow.f64 p #s(literal 3/2 binary64)) (.f64 (pow.f64 p #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(.f64 (neg.f64 (.f64 p (neg.f64 p))) p)

simplify178.0ms (1.7%)

Memory

9.2MiB live, 323.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4 332×	`accelerator-lowering-fma.f32`
4 332×	`accelerator-lowering-fma.f64`
3 954×	`-lowering-.f32`
3 954×	`-lowering-.f64`
1 404×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	849
1	140	813
2	415	735
3	1549	735
4	4810	735
5	7180	735
0	8053	717

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(* -1 (/ p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
p
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(/ (pow p 3) (pow x 2))
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)

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

eval66.0ms (0.6%)

Memory: 11.8MiB live, 164.1MiB allocated
Compiler: Compiled 15 077 to 1 190 computations (92.1% saved)

prune87.0ms (0.8%)

Memory

-1.5MiB live, 204.1MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	511	1	512
Fresh	0	0	0
Picked	1	1	2
Done	0	7	7
Total	512	9	521

Accuracy

100.0%

Counts

521 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	26.8%	(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))
	26.0%	(/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (*.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x)
✓	26.2%	(/.f64 p (neg.f64 x))
✓	6.1%	(/.f64 p x)
✓	75.7%	(sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	79.3%	(sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	52.0%	(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64)))
✓	55.7%	(sqrt.f64 #s(literal 1/2 binary64))
✓	36.3%	#s(literal 1 binary64)

Compiler

Compiled 260 to 134 computations (48.5% saved)

regimes41.0ms (0.4%)

Memory

4.4MiB live, 81.1MiB allocated

Counts

17 → 2

Calls

Call 1

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

Outputs

(/.f64 (*.f64 p (fma.f64 (/.f64 p (*.f64 x x)) (*.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x)

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

Calls

7 calls:

8.0ms	x
8.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
5.0ms	p
5.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
5.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Results

Accuracy	Segments	Branch
79.3%	1	`p`
84.7%	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))))`
79.3%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes20.0ms (0.2%)

Memory

9.5MiB live, 47.9MiB allocated

Counts

14 → 2

Calls

Call 1

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

Outputs

(/.f64 (*.f64 p (fma.f64 (/.f64 p (*.f64 x x)) (*.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x)

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

Calls

4 calls:

7.0ms	(.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 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
98.6%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
98.6%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.6%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.6%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes17.0ms (0.2%)

Memory

-6.5MiB live, 38.0MiB allocated

Counts

12 → 3

Calls

Call 1

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

Outputs

(/.f64 (*.f64 p (fma.f64 (/.f64 p (*.f64 x x)) (*.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x)

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.6%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.6%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.6%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.6%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes51.0ms (0.5%)

Memory

-1.2MiB live, 37.8MiB allocated

Counts

9 → 3

Calls

Call 1

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

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

Calls

4 calls:

42.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
3.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
3.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
3.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))

Results

Accuracy	Segments	Branch
99.5%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.5%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.5%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.5%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes43.0ms (0.4%)

Memory

-21.0MiB live, 18.4MiB allocated

Counts

6 → 3

Calls

Call 1

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

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

Calls

4 calls:

36.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
2.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
2.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
2.0ms	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))

Results

Accuracy	Segments	Branch
99.4%	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)))))))`
99.4%	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))))))`
99.4%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.4%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes8.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

5 → 3

Calls

Call 1

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

Outputs
(/.f64 p (neg.f64 x))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1 binary64)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.3%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
98.3%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
98.3%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
98.3%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes21.0ms (0.2%)

Memory

-7.0MiB live, 32.1MiB allocated

Counts

4 → 3

Calls

Call 1

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

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

Calls

7 calls:

9.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
2.0ms	x
2.0ms	p
2.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
2.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))

Results

Accuracy	Segments	Branch
71.2%	2	`p`
71.2%	2	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
60.1%	2	`x`
77.3%	3	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
77.3%	3	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
77.3%	3	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
77.3%	3	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes7.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1 binary64))

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

Results

Accuracy	Segments	Branch
75.5%	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)))))))`
75.5%	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))))))`
75.5%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
75.5%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 67 to 47 computations (29.9% saved)

regimes10.0ms (0.1%)

Memory

-17.1MiB live, 26.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

7 calls:

3.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
1.0ms	p
1.0ms	x
1.0ms	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))
1.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Results

Accuracy	Segments	Branch
36.3%	1	`x`
36.3%	1	`p`
36.3%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
36.3%	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)))))))`
36.3%	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))))))`
36.3%	1	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
36.3%	1	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`

Compiler

Compiled 80 to 56 computations (30% saved)

bsearch0.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999977186	-3.0240274370208155e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999977186	-3.0240274370208155e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.000244573021143614	0.9590781541398488
0.0ms	-0.9999999999977186	-3.0240274370208155e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.000244573021143614	0.9590781541398488
0.0ms	-0.9999999999977186	-3.0240274370208155e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.000244573021143614	0.9590781541398488
0.0ms	-0.9999999999977186	-3.0240274370208155e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.000244573021143614	0.9590781541398488
0.0ms	-0.9999999999977186	-3.0240274370208155e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.000244573021143614	0.9590781541398488
0.0ms	-1.0	-0.9999999999977186

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch11.0ms (0.1%)

Memory

21.5MiB live, 21.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.000244573021143614	0.9590781541398488

Samples

5.0ms

128×

valid

Compiler

Compiled 94 to 91 computations (3.2% saved)

Precisions

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

ival-add: 1.0ms (40.1% of total)

ival-mult: 1.0ms (40.1% of total)

ival-sqrt: 1.0ms (40.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify12.0ms (0.1%)

Memory

-11.0MiB live, 28.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	333
1	72	333
2	78	333
3	83	333
4	86	333
5	87	333

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) 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 -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #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)) (/.f64 p x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 #s(literal 4 binary64) p))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) x) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (sqrt.f64 (fma.f64 (/.f64 x (fma.f64 p (/.f64 (*.f64 p #s(literal 2 binary64)) 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 -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (.f64 p (fma.f64 (/.f64 p (.f64 x x)) (.f64 p #s(literal 3/2 binary64)) #s(literal -1 binary64))) x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (neg.f64 p) x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (neg.f64 p) x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 p (neg.f64 x)) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (neg.f64 p) x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #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)) (/.f64 p x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 p x) (if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal 7378697629483821/18446744073709551616 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 8286623314361713/18014398509481984 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.1s (10.9%)

Memory

-15.9MiB live, 1 105.8MiB allocated

Rules

10 924×	`accelerator-lowering-fma.f32`
10 924×	`accelerator-lowering-fma.f64`
9 904×	`accelerator-lowering-fma.f32`
9 904×	`accelerator-lowering-fma.f64`
9 590×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	402	3896
1	1158	3843
2	3522	3769
0	8248	3563
0	434	2482
1	1325	2377
2	4606	2304
0	8075	2141
0	14	66
1	68	66
2	492	66
3	6948	66
0	8473	59
0	59	849
1	140	813
2	415	735
3	1549	735
4	4810	735
5	7180	735
0	8053	717
0	34	166
1	184	164
2	1389	164
0	8255	150
0	843	5952
1	2563	5820
0	8264	5467

Stop Event

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

Compiler

Compiled 807 to 359 computations (55.5% saved)

preprocess66.0ms (0.6%)

Memory: 1.3MiB live, 159.3MiB allocated
Compiler: Compiled 832 to 220 computations (73.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze505.0ms (4.8%)

sample2.3s (22.2%)

preprocess64.0ms (0.6%)

explain262.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

localize56.0ms (0.5%)

series22.0ms (0.2%)

rewrite299.0ms (2.9%)

simplify530.0ms (5.1%)

eval74.0ms (0.7%)

prune188.0ms (1.8%)

simplify556.0ms (5.3%)

localize234.0ms (2.2%)

series70.0ms (0.7%)

rewrite344.0ms (3.3%)

simplify402.0ms (3.9%)

eval118.0ms (1.1%)

prune107.0ms (1%)

simplify287.0ms (2.8%)

localize236.0ms (2.3%)

series47.0ms (0.5%)

rewrite462.0ms (4.4%)

simplify516.0ms (4.9%)

eval149.0ms (1.4%)

prune119.0ms (1.1%)

simplify391.0ms (3.8%)

localize37.0ms (0.4%)

series10.0ms (0.1%)

rewrite254.0ms (2.4%)

simplify178.0ms (1.7%)

eval66.0ms (0.6%)

prune87.0ms (0.8%)

regimes41.0ms (0.4%)

regimes20.0ms (0.2%)

regimes17.0ms (0.2%)

regimes51.0ms (0.5%)

regimes43.0ms (0.4%)

regimes8.0ms (0.1%)

regimes21.0ms (0.2%)

regimes7.0ms (0.1%)

regimes10.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch11.0ms (0.1%)

simplify12.0ms (0.1%)

soundness1.1s (10.9%)

preprocess66.0ms (0.6%)

end0.0ms (0%)

Profiling