Metrics for Given's Rotation SVD example

analyze658.0ms (5.9%)

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 28 to 20 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 398.0ms

...c/correct-round.rkt:119:19: 122.0ms (30.6% of total)

ival-mult: 107.0ms (26.9% of total)

ival-sqrt: 43.0ms (10.8% of total)

ival-add: 36.0ms (9% of total)

ival-fabs: 29.0ms (7.3% of total)

ival-div: 26.0ms (6.5% of total)

ival-<: 24.0ms (6% of total)

ival-and: 6.0ms (1.5% of total)

const: 4.0ms (1% of total)

backward-pass: 1.0ms (0.3% of total)

sample2.6s (23.3%)

Results

1.2s	6315×	0	valid
568.0ms	1131×	2	valid
202.0ms	596×	1	valid
133.0ms	214×	3	valid

Precisions

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

ival-mult: 454.0ms (27.6% of total)

...c/correct-round.rkt:119:19: 369.0ms (22.4% of total)

ival-sqrt: 238.0ms (14.4% of total)

ival-add: 162.0ms (9.8% of total)

ival-fabs: 123.0ms (7.5% of total)

ival-div: 117.0ms (7.1% of total)

ival-<: 77.0ms (4.7% of total)

backward-pass: 74.0ms (4.5% of total)

ival-and: 18.0ms (1.1% of total)

const: 17.0ms (1% of total)

Bogosity

preprocess179.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

2100×	`fnmadd-define`
1558×	`fma-define`
1450×	`fnmsub-define`
1444×	`fmsub-define`
1054×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	96
1	109	86
2	226	80
3	513	80
4	1096	80
5	2091	80
6	3454	80
7	4627	80
8	5340	80
9	5908	80
10	6193	80
11	6346	80
12	6404	80
13	6408	80
0	14	15
1	31	14
2	42	13
3	47	13
4	49	13
5	50	13
0	50	13

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

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 (fnmsub (* x -1/2) (rsqrt (fma 4 (square p) (square x))) -1/2))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (fnmsub (* x -1/2) (rsqrt (fma 4 (square p) (square x))) -1/2))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(sqrt (fnmsub (* 1/2 x) (rsqrt (fma 4 (square p) (square x))) -1/2))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (fnmsub (* x -1/2) (rsqrt (fma 4 (square p) (square x))) -1/2)))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(neg (sqrt (fnmsub (* 1/2 x) (rsqrt (fma 4 (square p) (square x))) -1/2)))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))
(sqrt (fnmsub (* p -1/2) (rsqrt (fma 4 (square x) (square p))) -1/2))

Symmetry

(abs p)

explain236.0ms (2.1%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
66	-	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
33	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
26	-	-	`(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	-	-	`x`
0	-	-	`#s(literal 1/2 binary64)`
0	-	-	`(*.f64 #s(literal 4 binary64) p)`
0	-	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	-	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	-	-	`p`
0	-	-	`(*.f64 x x)`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	-	-	`#s(literal 1 binary64)`
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))))))`

Results

87.0ms	382×	0	valid
60.0ms	78×	2	valid
17.0ms	42×	1	valid
8.0ms	10×	3	valid

Compiler

Compiled 213 to 44 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-sqrt: 29.0ms (39.3% of total)

ival-mult: 21.0ms (28.5% of total)

ival-add: 8.0ms (10.8% of total)

backward-pass: 7.0ms (9.5% of total)

ival-div: 6.0ms (8.1% of total)

const: 2.0ms (2.7% of total)

eval0.0ms (0%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.4%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

32×	`-lowering-.f32`
32×	`-lowering-.f64`
18×	`fma-lowering-fma.f32`
18×	`fma-define`
18×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	24	64
2	34	64
3	41	64
4	46	64
5	48	64
0	48	64

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize136.0ms (1.2%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 #s(literal 4 binary64) (.f64 p p))
✓	accuracy	90.7%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))
✓	accuracy	87.8%	(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
✓	accuracy	75.9%	(sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))

Results

51.0ms	191×	0	valid
25.0ms	39×	2	valid
7.0ms	20×	1	valid
4.0ms	6×	3	valid

Compiler

Compiled 87 to 14 computations (83.9% saved)

Precisions

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

ival-mult: 31.0ms (64.2% of total)

ival-sqrt: 6.0ms (12.4% of total)

backward-pass: 4.0ms (8.3% of total)

ival-add: 4.0ms (8.3% of total)

ival-div: 3.0ms (6.2% of total)

const: 1.0ms (2.1% of total)

series16.0ms (0.1%)

Counts

6 → 120

Calls

Call 1

Inputs
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))>
#<alt (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))>
#<alt (* 1/2 x)>
#<alt (sqrt (+ (* 4 (* p p)) (* x x)))>
#<alt (* 4 (* p p))>

Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (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)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (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)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<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)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<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))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<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))>
#<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))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)>
#<alt (- (+ (* 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)))) 1/2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -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)>
#<alt (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)>
#<alt (* -1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))>
#<alt (* -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))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>

Calls

30 calls:

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

rewrite269.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4058×	`-lowering-.f32`
4058×	`-lowering-.f64`
2612×	`/-lowering-/.f32`
2612×	`/-lowering-/.f64`
1718×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	64	50
2	528	50
3	7676	50
0	8682	50

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 178

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))))) (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 #s(literal -1/4 binary64) x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 #s(literal -1/4 binary64) x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64))) #s(literal -1/8 binary64))) (sqrt.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))) #s(literal -1/4 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal -1/4 binary64))) (sqrt.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 #s(literal -1/4 binary64) x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 #s(literal -1/4 binary64) x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 #s(literal -1/4 binary64) x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 #s(literal -1/4 binary64) x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))) #s(literal 1/2 binary64))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64))) (+.f64 (neg.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))) #s(literal -1/4 binary64))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 #s(literal -1/4 binary64) x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))))
(neg.f64 (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 3/2 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) #s(literal 1 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (sqrt.f64 (-.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (+.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal -4 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 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 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal -4 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 #s(literal -16 binary64) (.f64 p (.f64 p (.f64 p p)))))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal -4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal -4 binary64))))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (sqrt.f64 (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -4 binary64)))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 64 binary64) (.f64 (.f64 p p) (.f64 p (.f64 p (.f64 p p))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 p (.f64 (.f64 p p) #s(literal 16 binary64)))) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 p (.f64 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 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 4 binary64) (.f64 p p))
(.f64 p (.f64 #s(literal 4 binary64) p))
(.f64 (.f64 p p) #s(literal 4 binary64))
(.f64 (.f64 #s(literal 4 binary64) p) p)

simplify371.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

6082×	`-lowering-.f32`
6082×	`-lowering-.f64`
3762×	`+-lowering-+.f64`
3762×	`+-lowering-+.f32`
1706×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	381	2053
1	1209	1828
2	4341	1780
0	8565	1780

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(* 1/4 (/ x p))
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)
(- (+ (* 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)))) 1/2)
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -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 (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(* -1/4 (/ x p))
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
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))))))))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))

Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (.f64 p p)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))
(+ (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)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/512 binary64) (.f64 p (.f64 p p))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/128 binary64) (.f64 p (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 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)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (.f64 x x))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 3 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 (.f64 p p) (.f64 p p))))) (.f64 (.f64 x x) (*.f64 x x))))
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(+.f64 (/.f64 (.f64 p p) (.f64 x x)) (+.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 1/4 binary64)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/2 binary64)))
(- (+ (* 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)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal 1/4 binary64)) #s(literal -12 binary64)) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -12 binary64)))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 6 binary64)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 3 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -10 binary64)) (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)))))
(* 1/4 (/ x p))
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64))) (.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) p)
(/ (+ (* -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 (+.f64 (+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64))) (.f64 p p)) (.f64 x #s(literal 1/4 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)))) (.f64 (.f64 p p) (.f64 p p)))) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64))) (.f64 p p)) (.f64 x #s(literal 1/4 binary64))) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (+.f64 (.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) p)
(* -1/4 (/ x p))
(/.f64 (*.f64 x #s(literal -1/4 binary64)) p)
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64))) (.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) p))
(* -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 (+.f64 (+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64))) (.f64 p p)) (.f64 x #s(literal 1/4 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64)))) (.f64 (.f64 p p) (.f64 p p)))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64))) (.f64 p p)) (.f64 x #s(literal 1/4 binary64))) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (.f64 (.f64 p p) (.f64 p p))) (/.f64 (+.f64 (.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) p))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(+ x (* 2 (/ (pow p 2) x)))
(+.f64 x (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (.f64 x x)))))))))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 p (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 p p) (.f64 p p))))))
(* 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 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 p p) (.f64 p p))))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)) (-.f64 #s(literal 0 binary64) p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 p p) (.f64 p p))))) (-.f64 #s(literal 0 binary64) 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 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 p p) (.f64 p p))))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (*.f64 p 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)))))
(+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal 1/512 binary64) (.f64 x x)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p))))))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 x (+.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(.f64 (+.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 (.f64 p p) (.f64 p p)) #s(literal -2 binary64)) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(.f64 (.f64 p p) #s(literal 4 binary64))

eval41.0ms (0.4%)

Compiler: Compiled 9951 to 1186 computations (88.1% saved)

prune40.0ms (0.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	288	10	298
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	288	11	299

Accuracy

100.0%

Counts

299 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	27.7%	(-.f64 #s(literal 0 binary64) (/.f64 p x))
▶	24.6%	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
	19.3%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
	17.2%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
▶	57.3%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
▶	68.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))
	49.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x))))))))))))
✓	78.4%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))
	52.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
▶	56.7%	(sqrt.f64 #s(literal 1/2 binary64))
▶	34.4%	#s(literal 1 binary64)

Compiler

Compiled 413 to 253 computations (38.7% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

746×	`-lowering-.f32`
746×	`-lowering-.f64`
594×	`fma-define`
528×	`fma-lowering-fma.f32`
528×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	252
1	86	237
2	219	237
3	521	234
4	982	225
5	1116	225
6	1166	225
7	1200	225
8	1204	225
0	1204	225

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize179.0ms (1.6%)

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
✓	accuracy	99.7%	(.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))
✓	accuracy	99.6%	(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
✓	accuracy	91.5%	(/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	100.0%	(.f64 (.f64 p p) #s(literal -1/2 binary64))
✓	accuracy	88.4%	(/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	98.4%	(/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))
✓	accuracy	95.6%	(.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
✓	accuracy	76.4%	(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x)))

Results

132.0ms

256×

valid

Compiler

Compiled 302 to 34 computations (88.7% saved)

Precisions

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

ival-mult: 17.0ms (38.8% of total)

ival-div: 12.0ms (27.4% of total)

ival-add: 7.0ms (16% of total)

ival-sqrt: 6.0ms (13.7% of total)

const: 1.0ms (2.3% of total)

backward-pass: 0.0ms (0% of total)

series45.0ms (0.4%)

Counts

18 → 348

Calls

Call 1

Inputs
#<alt (* (* p p) (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))>
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (+ x (* (* p p) (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (+ x (* (* p p) (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))>
#<alt (/ (* 1/2 x) (+ x (* (* p p) (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))>
#<alt (+ 1 (/ (* (* p p) -1/2) (* x x)))>
#<alt (/ (* (* p p) -1/2) (* x x))>
#<alt (* (* p p) -1/2)>
#<alt (* p p)>
#<alt (sqrt 1/2)>
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p))))))>
#<alt (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))>
#<alt (* 1/2 x)>
#<alt (/ (* (* p p) -2) (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (* x (/ 1/4 p))>
#<alt (* x (* x (/ 1/4 p)))>

Outputs
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* -2 (/ (pow p 4) (pow x 3)))>
#<alt (* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* -2 (/ (pow p 4) (pow x 3)))>
#<alt (* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* -2 (/ (pow p 4) (pow x 3)))>
#<alt (/ (+ (* -2 (pow p 4)) (* 2 (* (pow p 2) (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -2 (pow p 4)) (* 2 (* (pow p 2) (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -2 (pow p 4)) (* 2 (* (pow p 2) (pow x 2)))) (pow x 3))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (/ (+ (* -2 (/ (pow p 4) (pow x 2))) (* 2 (pow p 2))) x)>
#<alt (/ (+ (* -2 (/ (pow p 4) (pow x 2))) (* 2 (pow p 2))) x)>
#<alt (/ (+ (* -2 (/ (pow p 4) (pow x 2))) (* 2 (pow p 2))) x)>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* -1 (/ (+ (* -2 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -2 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -2 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))) x))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow x 4) (- (* -1/8 (/ (pow x 2) (* (pow p 6) (sqrt 1/2)))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow x 4) (- (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 8) (pow (sqrt 1/2) 2)))) (* 3/8 (/ 1 (pow p 8))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 6) (sqrt 1/2)))))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/2 (+ (* -2 (* (pow p 2) (+ (* -4 (pow p 4)) (* -2 (pow p 4))))) (* 4 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* -4 (pow p 6)) (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (* 4 (pow p 4))))))) (* 1/2 (* (pow p 2) (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -53/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))>
#<alt (+ 1/2 (* (pow x 4) (- (* -1/4 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))))>
#<alt (+ 1/2 (* (pow x 4) (- (* (pow x 2) (- (* -3/8 (/ (pow x 2) (pow p 8))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -4 (pow p 4)) (* -2 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -4 (pow p 4)) (* -2 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* -2 (* (pow p 2) (+ (* -4 (pow p 4)) (* -2 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 1/2 (/ (+ (* 2 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* 1/2 (/ (+ (* -4 (pow p 6)) (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (* 4 (pow p 4)))))) (pow x 6)))) (+ (* -1/2 (/ (+ (* 2 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))>
#<alt (+ 1/2 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6)))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 8))) (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))>
#<alt (+ 1/2 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6)))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 8))) (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6))))))>
#<alt (* -1/4 (/ (pow x 4) (pow p 4)))>
#<alt (* (pow x 4) (- (* -1/4 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt (* (pow x 4) (- (* (pow x 2) (- (* -3/8 (/ (pow x 2) (pow p 8))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt (* (pow x 4) (- (* (pow x 2) (- (* (pow x 2) (- (* -1/2 (/ (pow x 2) (pow p 10))) (* 3/8 (/ 1 (pow p 8))))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (pow p 4)) (* -1 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (* (pow p 2) (+ (* -2 (pow p 4)) (* -1 (pow p 4))))) (* 2 (pow p 6))) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* -1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (pow p 4)) (* -1 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (* (pow p 2) (+ (* -2 (pow p 4)) (* -1 (pow p 4))))) (* 2 (pow p 6))) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* -1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt (* -1/4 (/ (pow x 4) (pow p 4)))>
#<alt (/ (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4)))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/2 (/ (+ (* 1/4 (pow x 10)) (* (pow x 2) (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))))) (pow p 6))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))))) (pow p 4))>
#<alt (* -1/4 (/ (pow x 4) (pow p 4)))>
#<alt (/ (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4)))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/2 (/ (+ (* 1/4 (pow x 10)) (* (pow x 2) (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))))) (pow p 6))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))))) (pow p 4))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ p (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- (* -16 (pow p 3)) (* -1 (/ (pow p 3) (pow (sqrt 1/2) 4)))) (* (pow x 3) (sqrt 1/2)))) (/ p (* x (sqrt 1/2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ p (sqrt 1/2))) (* 1/2 (/ (pow p 2) (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ p (sqrt 1/2))) (* -1 (/ (+ (* -1/2 (/ (pow p 2) (pow (sqrt 1/2) 3))) (* 1/2 (/ (+ (* -16 (pow p 3)) (/ (pow p 3) (pow (sqrt 1/2) 4))) (* x (sqrt 1/2))))) x))) x)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* p (+ (* -1/2 (/ p (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ 1 (* x (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* p (+ (* p (- (* 1/2 (/ (* p (- (/ 1 (* (pow x 3) (pow (sqrt 1/2) 4))) (* 16 (/ 1 (pow x 3))))) (sqrt 1/2))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (/ 1 (* x (sqrt 1/2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (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)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (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)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (+ (* -16 (/ (pow p 3) (pow x 3))) (* 2 (/ p x))))>
#<alt (+ 1/2 (+ (* -16 (/ (pow p 3) (pow x 3))) (+ (* 2 (/ p x)) (* 128 (/ (pow p 5) (pow x 5))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 16 (/ (pow p 3) (pow x 2))) (* 2 p)) x)))>
#<alt (+ 1/2 (* -1 (/ (- (* -128 (/ (pow p 5) (pow x 4))) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 2 p))) x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ 1/2 (* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (+ (* 1/256 (/ (pow x 5) (pow p 5))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (* 1/32 (/ (pow x 3) (pow p 2))))) p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2048 (/ (pow x 2) (pow p 7))) (* 1/256 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* 2 (/ p x))>
#<alt (/ (+ (* -16 (/ (pow p 3) (pow x 2))) (* 2 p)) x)>
#<alt (/ (- (+ (* 2 p) (* 128 (/ (pow p 5) (pow x 4)))) (* 16 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1024 (/ (pow p 7) (pow x 6))) (* 2 p)) (+ (* -128 (/ (pow p 5) (pow x 4))) (* 16 (/ (pow p 3) (pow x 2))))) x)>
#<alt (* 2 (/ p x))>
#<alt (* -1 (/ (+ (* -2 p) (* 16 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -128 (/ (pow p 5) (pow x 4))) (* -2 p)) (* -16 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -2 p) (* 1024 (/ (pow p 7) (pow x 6)))) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 128 (/ (pow p 5) (pow x 4))))) x))>
#<alt (* 2 (/ p x))>
#<alt (* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -1024 (/ (pow p 2) (pow x 7))) (* 128 (/ 1 (pow x 5))))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* -1/2048 (/ (pow x 7) (pow p 6))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x)))) p)>
#<alt (* 1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (* 1/32 (/ (pow x 3) (pow p 2))))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (+ (* 1/2048 (/ (pow x 7) (pow p 6))) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>

Calls

87 calls:

Time	Variable		Point	Expression
5.0ms	p	@	inf	(* x (/ 1/4 p))
3.0ms	x	@	0	(sqrt (+ 1/2 (/ (* 1/2 x) (+ x (* (* p p) (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))
3.0ms	p	@	inf	(* (* p p) (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))
2.0ms	x	@	inf	(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p))))))
1.0ms	p	@	0	(* (* p p) (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))

rewrite391.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4860×	`/-lowering-/.f32`
4860×	`/-lowering-/.f64`
4524×	`-lowering-.f32`
4524×	`-lowering-.f64`
2042×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	178
1	207	166
2	2297	166
0	9390	166

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 502

Calls

Call 1

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

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

simplify307.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

5148×	`-lowering-.f32`
5148×	`-lowering-.f64`
2234×	`/-lowering-/.f32`
2234×	`/-lowering-/.f64`
2076×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	582	4238
1	1812	3725
2	5954	3630
0	8325	3630

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(* 2 (/ (pow p 2) x))
(* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(* -2 (/ (pow p 4) (pow x 3)))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(* -2 (/ (pow p 4) (pow x 3)))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
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(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))

Outputs
(* 2 (/ (pow p 2) x))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)
(* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(* -2 (/ (pow p 4) (pow x 3)))
(/.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x (*.f64 x x)))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (pow.f64 p #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 p p) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (pow.f64 p #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 p p) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (pow.f64 p #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 p p) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* -2 (/ (pow p 4) (pow x 3)))
(/.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x (*.f64 x x)))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (pow.f64 p #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 p p) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (pow.f64 p #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 p p) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* (pow p 4) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (pow.f64 p #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 p p) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* -2 (/ (pow p 4) (pow x 3)))
(/.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x (*.f64 x x)))
(/ (+ (* -2 (pow p 4)) (* 2 (* (pow p 2) (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 (.f64 p p) (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 x (*.f64 x x)))
(/ (+ (* -2 (pow p 4)) (* 2 (* (pow p 2) (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 (.f64 p p) (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 x (*.f64 x x)))
(/ (+ (* -2 (pow p 4)) (* 2 (* (pow p 2) (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 (.f64 p p) (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 x (*.f64 x x)))
(* 2 (/ (pow p 2) x))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)
(/ (+ (* -2 (/ (pow p 4) (pow x 2))) (* 2 (pow p 2))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x)) (.f64 #s(literal 2 binary64) (.f64 p p))) x)
(/ (+ (* -2 (/ (pow p 4) (pow x 2))) (* 2 (pow p 2))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x)) (.f64 #s(literal 2 binary64) (.f64 p p))) x)
(/ (+ (* -2 (/ (pow p 4) (pow x 2))) (* 2 (pow p 2))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x)) (.f64 #s(literal 2 binary64) (.f64 p p))) x)
(* 2 (/ (pow p 2) x))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)
(* -1 (/ (+ (* -2 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))) x))
(/.f64 (+.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (neg.f64 x))
(* -1 (/ (+ (* -2 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))) x))
(/.f64 (+.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (neg.f64 x))
(* -1 (/ (+ (* -2 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))) x))
(/.f64 (+.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (neg.f64 x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* (pow x 4) (- (* -1/8 (/ (pow x 2) (* (pow p 6) (sqrt 1/2)))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 x (pow.f64 p #s(literal 6 binary64)))) (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 p #s(literal 4 binary64))))))
(+ (sqrt 1/2) (* (pow x 4) (- (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 8) (pow (sqrt 1/2) 2)))) (* 3/8 (/ 1 (pow p 8))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 6) (sqrt 1/2)))))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) (-.f64 (/.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 p #s(literal 8 binary64))) (/.f64 #s(literal 3/8 binary64) (pow.f64 p #s(literal 8 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 p #s(literal 6 binary64))))) (/.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (.f64 x x)) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (pow.f64 x #s(literal 4 binary64)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/2 (+ (* -2 (* (pow p 2) (+ (* -4 (pow p 4)) (* -2 (pow p 4))))) (* 4 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (.f64 x x))) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 (.f64 (.f64 p p) #s(literal 1/2 binary64)) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64)))))) (pow.f64 x #s(literal 6 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* -4 (pow p 6)) (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (* 4 (pow p 4))))))) (* 1/2 (* (pow p 2) (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (+.f64 (+.f64 (.f64 #s(literal 2 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 (.f64 p p) (.f64 #s(literal -2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))))) (.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (.f64 (*.f64 p p) #s(literal 1/2 binary64)))) (pow.f64 x #s(literal 6 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 #s(literal 11/8 binary64) (*.f64 p (/.f64 p (pow.f64 x #s(literal 4 binary64))))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -53/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -53/16 binary64)) (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)))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -3/8 binary64)) (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 8 binary64))) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 8 binary64))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -3/8 binary64)) (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 8 binary64))) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 8 binary64))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 p #s(literal 4 binary64))))
(+ 1/2 (* (pow x 4) (- (* -1/4 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))))
(+.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 (.f64 (*.f64 x x) #s(literal -1/4 binary64)) (pow.f64 p #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64))))))
(+ 1/2 (* (pow x 4) (- (* (pow x 2) (- (* -3/8 (/ (pow x 2) (pow p 8))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))))
(+.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (*.f64 x x) #s(literal -3/8 binary64)) (pow.f64 p #s(literal 8 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 6 binary64))))) (/.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -4 (pow p 4)) (* -2 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 p p) (*.f64 x x))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -4 (pow p 4)) (* -2 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* -2 (* (pow p 2) (+ (* -4 (pow p 4)) (* -2 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))))))
(+.f64 #s(literal 1 binary64) (+.f64 (-.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 p p) (.f64 x x))) (/.f64 (+.f64 (.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64))) (.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(- (+ 1 (* 1/2 (/ (+ (* 2 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x))))
(- (+ 1 (* 1/2 (/ (+ (* -4 (pow p 6)) (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (* 4 (pow p 4)))))) (pow x 6)))) (+ (* -1/2 (/ (+ (* 2 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -4 binary64)) (.f64 (.f64 p p) (.f64 #s(literal -2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)))))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 (.f64 p p) (.f64 x x)) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (pow.f64 x #s(literal 4 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (.f64 (*.f64 p p) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p (/.f64 p (pow.f64 x #s(literal 6 binary64)))) #s(literal -8 binary64)) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
1/2
#s(literal 1/2 binary64)
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1/2
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1/2
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1/2
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1/2
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1/2
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(/.f64 (+.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/32 binary64)) (.f64 p p))) (/.f64 (.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/256 binary64)) (pow.f64 p #s(literal 4 binary64)))) (neg.f64 p))
(* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (+ (* 1/2048 (/ (pow x 7) (pow p 6))) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))
(/.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/32 binary64)) (.f64 p p)) (+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/256 binary64)) (pow.f64 p #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/2048 binary64)) (pow.f64 p #s(literal 6 binary64)))))) (neg.f64 p))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(* -2 (/ (pow p 2) (pow x 3)))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x (.f64 x x)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) p)

eval135.0ms (1.2%)

Compiler: Compiled 27141 to 3023 computations (88.9% saved)

prune91.0ms (0.8%)

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	924	4	928
Fresh	1	4	5
Picked	1	4	5
Done	0	1	1
Total	926	13	939

Accuracy

100.0%

Counts

939 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	27.7%	(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓	24.6%	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
▶	19.3%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
▶	17.2%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
	10.4%	(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
▶	57.3%	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))))
	52.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
✓	57.3%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
	49.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x))))))))))))
✓	78.4%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))
▶	68.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))))
✓	56.7%	(sqrt.f64 #s(literal 1/2 binary64))
✓	34.4%	#s(literal 1 binary64)

Compiler

Compiled 511 to 283 computations (44.6% saved)

simplify210.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))))
✓	cost-diff	128	(/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64))))
✓	cost-diff	0	(+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	0	(.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
✓	cost-diff	0	(+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
✓	cost-diff	256	(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))))
✓	cost-diff	0	(/.f64 p x)
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓	cost-diff	0	(.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))))))))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))))
✓	cost-diff	128	(.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))

Rules

3982×	`-lowering-.f32`
3982×	`-lowering-.f64`
2272×	`+-lowering-+.f64`
2272×	`+-lowering-+.f32`
1280×	`distribute-lft-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	617
1	169	548
2	526	548
3	1534	538
4	3234	534
5	4292	534
6	7429	534
0	8105	534

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))))
(+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))))
1/2
(* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))
x
(/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))
(+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))
(* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))
p
(* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))
(+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))
(/ (* (* p p) -2) (* x (* x x)))
(* (* p p) -2)
(* p p)
-2
(* x (* x x))
(* x x)
(/ 2 x)
2
(- 0 (/ p x))
0
(/ p x)
p
x
(+ 1 (* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))))
1
(* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x)))))
(* p p)
p
(+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))
(/ -1/2 (* x x))
-1/2
(* x x)
x
(/ (* (* p p) 11/8) (* (* x x) (* x x)))
(* (* p p) 11/8)
11/8
(* (* x x) (* x x))
(+ 1 (* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))))
1
(* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x))))
(* p p)
p
(+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))
(* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x)))))
(+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))
(/ (* (* p p) -69/16) (pow x 6))
(* (* p p) -69/16)
-69/16
(pow x 6)
x
6
(/ 11/8 (* (* x x) (* x x)))
11/8
(* (* x x) (* x x))
(* x x)
(/ -1/2 (* x x))
-1/2
(sqrt (/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2)))
(/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2))
(- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4)
(* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4))))
(* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4))))
1/4
(/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))
x
(+ (* p 2) (* (/ (* x x) p) 1/4))
(* p 2)
p
2
(* (/ (* x x) p) 1/4)
(/ (* x x) p)
(* x x)
(- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2)
(/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4)))
(/ x 2)
1/2

Outputs
(sqrt (+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 (/.f64 (.f64 p p) x) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x))))))))
(+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 (/.f64 (.f64 p p) x) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x)))))))
1/2
#s(literal 1/2 binary64)
(* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))
(/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 (/.f64 (.f64 p p) x) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x))))))
x
(/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))
(/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (/.f64 (.f64 p p) x) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (*.f64 x x))))))
(+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))
(+.f64 x (.f64 (/.f64 (.f64 p p) x) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (*.f64 x x)))))
(* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))
(.f64 (/.f64 (.f64 p p) x) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (*.f64 x x))))
p
(* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))
(.f64 (/.f64 p x) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x))))
(+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))
(+.f64 (.f64 p (/.f64 (.f64 #s(literal -2 binary64) (/.f64 (/.f64 p x) x)) x)) (/.f64 #s(literal 2 binary64) x))
(/ (* (* p p) -2) (* x (* x x)))
(.f64 p (/.f64 (.f64 #s(literal -2 binary64) (/.f64 (/.f64 p x) x)) x))
(* (* p p) -2)
(.f64 p (.f64 p #s(literal -2 binary64)))
(* p p)
(*.f64 p p)
-2
#s(literal -2 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
(- 0 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
0
#s(literal 0 binary64)
(/ p x)
(/.f64 p x)
p
x
(+ 1 (* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))))
(+.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 p p) (.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)))))
1
#s(literal 1 binary64)
(* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x)))))
(.f64 (/.f64 (.f64 p p) (.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x))))
(* p p)
(*.f64 p p)
p
(+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))
(+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) x) (.f64 x (*.f64 x x))))
(/ -1/2 (* x x))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
x
(/ (* (* p p) 11/8) (* (* x x) (* x x)))
(/.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) x) (.f64 x (.f64 x x)))
(* (* p p) 11/8)
(.f64 (.f64 p p) #s(literal 11/8 binary64))
11/8
#s(literal 11/8 binary64)
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(+ 1 (* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 11/8 binary64) x) (.f64 x (*.f64 x x))))))))
1
#s(literal 1 binary64)
(* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x))))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 11/8 binary64) x) (.f64 x (*.f64 x x)))))))
(* p p)
(*.f64 p p)
p
(+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 11/8 binary64) x) (.f64 x (*.f64 x x))))))
(* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x)))))
(.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 11/8 binary64) x) (.f64 x (.f64 x x)))))
(+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))
(+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 11/8 binary64) x) (.f64 x (.f64 x x))))
(/ (* (* p p) -69/16) (pow x 6))
(/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64)))
(* (* p p) -69/16)
(.f64 (.f64 p p) #s(literal -69/16 binary64))
-69/16
#s(literal -69/16 binary64)
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
x
6
#s(literal 6 binary64)
(/ 11/8 (* (* x x) (* x x)))
(/.f64 (/.f64 #s(literal 11/8 binary64) x) (.f64 x (.f64 x x)))
11/8
#s(literal 11/8 binary64)
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
(/ -1/2 (* x x))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(sqrt (/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2)))
(sqrt.f64 (/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))))) #s(literal -1/4 binary64)) (+.f64 #s(literal -1/2 binary64) (/.f64 x (+.f64 (.f64 (/.f64 (.f64 x x) p) #s(literal 1/2 binary64)) (.f64 p #s(literal 4 binary64)))))))
(/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))))) #s(literal -1/4 binary64)) (+.f64 #s(literal -1/2 binary64) (/.f64 x (+.f64 (.f64 (/.f64 (.f64 x x) p) #s(literal 1/2 binary64)) (.f64 p #s(literal 4 binary64))))))
(- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4)
(+.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))))) #s(literal -1/4 binary64))
(* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4))))
(/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))))
(* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4))))
(/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))))
1/4
#s(literal 1/4 binary64)
(/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))
(/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))))
x
(+ (* p 2) (* (/ (* x x) p) 1/4))
(+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(* (/ (* x x) p) 1/4)
(.f64 x (/.f64 (.f64 x #s(literal 1/4 binary64)) p))
(/ (* x x) p)
(/.f64 (*.f64 x x) p)
(* x x)
(*.f64 x x)
(- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 x (+.f64 (.f64 (/.f64 (.f64 x x) p) #s(literal 1/2 binary64)) (*.f64 p #s(literal 4 binary64)))))
(/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4)))
(/.f64 x (+.f64 (.f64 (/.f64 (.f64 x x) p) #s(literal 1/2 binary64)) (*.f64 p #s(literal 4 binary64))))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
1/2
#s(literal 1/2 binary64)

localize333.0ms (3%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 (*.f64 x x) p)
✓	accuracy	99.6%	(.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64)))))
✓	accuracy	91.5%	(/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64))))
✓	accuracy	91.5%	(/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64))))
✓	accuracy	90.7%	(.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	accuracy	81.8%	(.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
✓	accuracy	80.9%	(+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (*.f64 x x))))
✓	accuracy	74.1%	(/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64)))
✓	accuracy	99.6%	(.f64 (.f64 x x) (*.f64 x x))
✓	accuracy	99.6%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	89.7%	(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))))
✓	accuracy	72.4%	(/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (*.f64 x x)))
✓	accuracy	100.0%	(/.f64 p x)
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓	accuracy	99.7%	(.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x))))))
✓	accuracy	98.4%	(.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))
✓	accuracy	76.4%	(/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x)))

Results

227.0ms

256×

valid

Compiler

Compiled 778 to 58 computations (92.5% saved)

Precisions

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

ival-mult: 28.0ms (35.5% of total)

ival-div: 25.0ms (31.7% of total)

ival-add: 12.0ms (15.2% of total)

ival-sub: 4.0ms (5.1% of total)

ival-sqrt: 4.0ms (5.1% of total)

ival-pow: 4.0ms (5.1% of total)

const: 2.0ms (2.5% of total)

backward-pass: 0.0ms (0% of total)

series48.0ms (0.4%)

Counts

28 → 636

Calls

Call 1

Inputs
#<alt (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))>
#<alt (sqrt (+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))))>
#<alt (+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))))>
#<alt (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))>
#<alt (- 0 (/ p x))>
#<alt (/ p x)>
#<alt (* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x)))))>
#<alt (+ 1 (* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))))>
#<alt (* p p)>
#<alt (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))>
#<alt (+ 1 (* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))))>
#<alt (* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x))))>
#<alt (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))>
#<alt (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4)))>
#<alt (sqrt (/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2)))>
#<alt (/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2))>
#<alt (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4)>
#<alt (/ (* (* p p) -2) (* x (* x x)))>
#<alt (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))>
#<alt (/ (* (* p p) 11/8) (* (* x x) (* x x)))>
#<alt (/ -1/2 (* x x))>
#<alt (* (* x x) (* x x))>
#<alt (/ (* (* p p) -69/16) (pow x 6))>
#<alt (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))>
#<alt (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x)))))>
#<alt (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))>
#<alt (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4))))>
#<alt (/ (* x x) p)>

Outputs
#<alt (* 2 (/ p x))>
#<alt (* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* -2 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))>
#<alt (* -2 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))>
#<alt (* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))>
#<alt (* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))>
#<alt (* -2 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))>
#<alt (* 2 (/ p x))>
#<alt (/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)>
#<alt (/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)>
#<alt (/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)>
#<alt (* 2 (/ p x))>
#<alt (* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow x 4) (- (* -1/8 (/ (pow x 2) (* (pow p 6) (sqrt 1/2)))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow x 4) (- (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 8) (pow (sqrt 1/2) 2)))) (* 3/8 (/ 1 (pow p 8))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 6) (sqrt 1/2)))))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/2 (+ (* -2 (* (pow p 2) (+ (* -4 (pow p 4)) (* -2 (pow p 4))))) (* 4 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* -4 (pow p 6)) (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (* 4 (pow p 4))))))) (* 1/2 (* (pow p 2) (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -53/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))>
#<alt (+ 1/2 (* (pow x 4) (- (* -1/4 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))))>
#<alt (+ 1/2 (* (pow x 4) (- (* (pow x 2) (- (* -3/8 (/ (pow x 2) (pow p 8))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -4 (pow p 4)) (* -2 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -4 (pow p 4)) (* -2 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* -2 (* (pow p 2) (+ (* -4 (pow p 4)) (* -2 (pow p 4))))) (* 4 (pow p 6))) (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* 1/2 (/ (+ (* 2 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* 1/2 (/ (+ (* -4 (pow p 6)) (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (* 4 (pow p 4)))))) (pow x 6)))) (+ (* -1/2 (/ (+ (* 2 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))>
#<alt (+ 1/2 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6)))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 8))) (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))>
#<alt (+ 1/2 (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6)))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 8))) (+ (* -1/4 (/ (pow x 4) (pow p 4))) (* -1/4 (/ (pow x 6) (pow p 6))))))>
#<alt (* -1/4 (/ (pow x 4) (pow p 4)))>
#<alt (* (pow x 4) (- (* -1/4 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt (* (pow x 4) (- (* (pow x 2) (- (* -3/8 (/ (pow x 2) (pow p 8))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt (* (pow x 4) (- (* (pow x 2) (- (* (pow x 2) (- (* -1/2 (/ (pow x 2) (pow p 10))) (* 3/8 (/ 1 (pow p 8))))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (pow p 4)) (* -1 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (* (pow p 2) (+ (* -2 (pow p 4)) (* -1 (pow p 4))))) (* 2 (pow p 6))) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* -1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (pow p 4)) (* -1 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1/2 (* -1 (/ (+ (* -2 (* (pow p 2) (+ (* -2 (pow p 4)) (* -1 (pow p 4))))) (* 2 (pow p 6))) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* -1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt (* -1/4 (/ (pow x 4) (pow p 4)))>
#<alt (/ (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4)))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/2 (/ (+ (* 1/4 (pow x 10)) (* (pow x 2) (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))))) (pow p 6))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))))) (pow p 4))>
#<alt (* -1/4 (/ (pow x 4) (pow p 4)))>
#<alt (/ (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4)))) (pow p 4))>
#<alt (/ (+ (* -1/2 (/ (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))) (pow p 4))) (+ (* -1/2 (/ (+ (* 1/4 (pow x 10)) (* (pow x 2) (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8))))) (pow p 6))) (+ (* -1/4 (/ (pow x 6) (pow p 2))) (* -1/4 (pow x 4))))) (pow p 4))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 11/8 (/ (pow p 4) (pow x 4)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* 11/8 (/ (pow p 4) (pow x 4)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* 11/8 (/ (pow p 4) (pow x 4)))>
#<alt (/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))>
#<alt (/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))>
#<alt (/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* 11/8 (/ (pow p 4) (pow x 4)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))>
#<alt (* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))>
#<alt (* 11/8 (/ (pow p 4) (pow x 4)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))>
#<alt (* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))>
#<alt (* 11/8 (/ (pow p 4) (pow x 4)))>
#<alt (/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))>
#<alt (/ (+ (* 11/8 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow p 2)) (pow x 2)))) (pow x 4))>
#<alt (/ (+ (* 11/8 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow p 2)) (pow x 2)))) (pow x 4))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -69/16 (/ (pow p 6) (pow x 6)))>
#<alt (* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))>
#<alt (* (pow p 6) (- (+ (/ 1 (pow p 6)) (/ 11/8 (* (pow p 2) (pow x 4)))) (+ (* 69/16 (/ 1 (pow x 6))) (* 1/2 (/ 1 (* (pow p 4) (pow x 2)))))))>
#<alt (* -69/16 (/ (pow p 6) (pow x 6)))>
#<alt (* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))>
#<alt (* (pow p 6) (- (+ (/ 1 (pow p 6)) (/ 11/8 (* (pow p 2) (pow x 4)))) (+ (* 69/16 (/ 1 (pow x 6))) (* 1/2 (/ 1 (* (pow p 4) (pow x 2)))))))>
#<alt (* -69/16 (/ (pow p 6) (pow x 6)))>
#<alt (/ (+ (* -69/16 (pow p 6)) (* 11/8 (* (pow p 4) (pow x 2)))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* 11/8 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow p 2)) (pow x 2)))))) (pow x 6))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -69/16 (/ (pow p 6) (pow x 6))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))>
#<alt (+ 1 (+ (* -69/16 (/ (pow p 6) (pow x 6))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4))))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (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)))))>
#<alt (* (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)))))>
#<alt (* -69/16 (/ (pow p 6) (pow x 6)))>
#<alt (* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))>
#<alt (* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))>
#<alt (* -69/16 (/ (pow p 6) (pow x 6)))>
#<alt (* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))>
#<alt (* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))>
#<alt (* -69/16 (/ (pow p 6) (pow x 6)))>
#<alt (/ (+ (* -69/16 (pow p 6)) (* 11/8 (* (pow p 4) (pow x 2)))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))))) (pow x 6))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))>
#<alt (* -69/16 (/ (pow p 4) (pow x 6)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))>
#<alt (* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))>
#<alt (* -69/16 (/ (pow p 4) (pow x 6)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))>
#<alt (* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))>
#<alt (* -69/16 (/ (pow p 4) (pow x 6)))>
#<alt (/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))))) (pow x 6))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))>
#<alt (/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))>
#<alt (/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))>
#<alt (/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2048 (/ (pow x 2) (pow p 7))) (* 1/256 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* 2 (/ p x))>
#<alt (/ (+ (* -16 (/ (pow p 3) (pow x 2))) (* 2 p)) x)>
#<alt (/ (- (+ (* 2 p) (* 128 (/ (pow p 5) (pow x 4)))) (* 16 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1024 (/ (pow p 7) (pow x 6))) (* 2 p)) (+ (* -128 (/ (pow p 5) (pow x 4))) (* 16 (/ (pow p 3) (pow x 2))))) x)>
#<alt (* 2 (/ p x))>
#<alt (* -1 (/ (+ (* -2 p) (* 16 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -128 (/ (pow p 5) (pow x 4))) (* -2 p)) (* -16 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -2 p) (* 1024 (/ (pow p 7) (pow x 6)))) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 128 (/ (pow p 5) (pow x 4))))) x))>
#<alt (* 2 (/ p x))>
#<alt (* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -1024 (/ (pow p 2) (pow x 7))) (* 128 (/ 1 (pow x 5))))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* -1/2048 (/ (pow x 7) (pow p 6))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x)))) p)>
#<alt (* 1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (* 1/32 (/ (pow x 3) (pow p 2))))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (+ (* 1/2048 (/ (pow x 7) (pow p 6))) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ p (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1 (/ (pow p 3) (pow (sqrt 1/2) 4))) (* 16 (pow p 3))) (* (pow x 3) (sqrt 1/2)))) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ p (* x (sqrt 1/2))))))>
#<alt (* (sqrt -1) (sqrt -1/2))>
#<alt (+ (* -1 (/ (* p (sqrt -1)) (* x (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/2 (/ (* (pow p 2) (sqrt -1)) (* x (pow (sqrt -1/2) 3)))) (/ (* p (sqrt -1)) (sqrt -1/2))) x)) (* (sqrt -1) (sqrt -1/2)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow p 2) (sqrt -1)) (pow (sqrt -1/2) 3))) (* 1/2 (/ (* (sqrt -1) (+ (* -1 (/ (pow p 3) (pow (sqrt -1/2) 4))) (* 16 (pow p 3)))) (* x (sqrt -1/2))))) x)) (/ (* p (sqrt -1)) (sqrt -1/2))) x)) (* (sqrt -1) (sqrt -1/2)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* p (+ (* -1/2 (/ p (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ 1 (* x (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* p (+ (* p (- (* 1/2 (/ (* p (- (/ 1 (* (pow x 3) (pow (sqrt 1/2) 4))) (* 16 (/ 1 (pow x 3))))) (sqrt 1/2))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (/ 1 (* x (sqrt 1/2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4))) (* 1/32 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/2 (/ (+ (* -1/32 (pow x 3)) (* 1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (- (+ 1/2 (* -16 (/ (pow p 3) (pow x 3)))) (* -2 (/ p x)))>
#<alt (- (+ 1/2 (* 128 (/ (pow p 5) (pow x 5)))) (+ (* -2 (/ p x)) (* 16 (/ (pow p 3) (pow x 3)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -2 p) (* 16 (/ (pow p 3) (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -128 (/ (pow p 5) (pow x 4))) (+ (* -2 p) (* 16 (/ (pow p 3) (pow x 2))))) x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ 1/2 (* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (- (+ 1/2 (* -1/32 (/ (pow x 3) (pow p 3)))) (* -1/4 (/ x p)))>
#<alt (- (+ 1/2 (* 1/256 (/ (pow x 5) (pow p 5)))) (+ (* -1/4 (/ x p)) (* 1/32 (/ (pow x 3) (pow p 3)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (- (* -1/256 (/ (pow x 5) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt -1/4>
#<alt (- (* 1/16 (/ (pow x 2) (pow p 2))) 1/4)>
#<alt (- (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 4))) (* 1/16 (/ 1 (pow p 2))))) 1/4)>
#<alt (- (* (pow x 2) (+ (* (pow x 2) (- (* 3/1024 (/ (pow x 2) (pow p 6))) (* 1/64 (/ 1 (pow p 4))))) (* 1/16 (/ 1 (pow p 2))))) 1/4)>
#<alt -1/4>
#<alt (- (* 4 (/ (pow p 2) (pow x 2))) 1/4)>
#<alt (- (+ (* -64 (/ (pow p 4) (pow x 4))) (* 4 (/ (pow p 2) (pow x 2)))) 1/4)>
#<alt (- (+ (* -64 (/ (pow p 4) (pow x 4))) (+ (* -1/4 (/ (+ (* -4096 (pow p 6)) (* 1024 (pow p 6))) (pow x 6))) (* 4 (/ (pow p 2) (pow x 2))))) 1/4)>
#<alt -1/4>
#<alt (- (* 4 (/ (pow p 2) (pow x 2))) 1/4)>
#<alt (- (+ (* -64 (/ (pow p 4) (pow x 4))) (* 4 (/ (pow p 2) (pow x 2)))) 1/4)>
#<alt (- (+ (* -64 (/ (pow p 4) (pow x 4))) (+ (* -1/4 (/ (+ (* -4096 (pow p 6)) (* 1024 (pow p 6))) (pow x 6))) (* 4 (/ (pow p 2) (pow x 2))))) 1/4)>
#<alt -1/4>
#<alt (- (* 4 (/ (pow p 2) (pow x 2))) 1/4)>
#<alt (- (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2))))) 1/4)>
#<alt (- (* (pow p 2) (+ (* (pow p 2) (- (* 768 (/ (pow p 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2))))) 1/4)>
#<alt -1/4>
#<alt (- (* 1/16 (/ (pow x 2) (pow p 2))) 1/4)>
#<alt (- (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/16 (/ (pow x 2) (pow p 2)))) 1/4)>
#<alt (- (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 6))) (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/16 (/ (pow x 2) (pow p 2))))) 1/4)>
#<alt -1/4>
#<alt (- (* 1/16 (/ (pow x 2) (pow p 2))) 1/4)>
#<alt (- (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/16 (/ (pow x 2) (pow p 2)))) 1/4)>
#<alt (- (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 6))) (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/16 (/ (pow x 2) (pow p 2))))) 1/4)>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -2 (/ (pow p 2) (pow x 3)))>
#<alt (* -1/4 (/ (pow x 3) (pow p 4)))>
#<alt (* (pow x 3) (- (* -1/4 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt (* (pow x 3) (- (* (pow x 2) (- (* -3/8 (/ (pow x 2) (pow p 8))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -1/2 (/ (pow x 2) (pow p 10))) (* 3/8 (/ 1 (pow p 8))))) (* 1/4 (/ 1 (pow p 6))))) (* 1/4 (/ 1 (pow p 4)))))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (* -1 (/ (+ (* -2 (pow p 4)) (* -1 (pow p 4))) (pow x 4)))) (/ (pow p 2) (pow x 2))) x)>
#<alt (/ (- (+ 1/2 (* -1 (/ (+ (* -2 (* (pow p 2) (+ (* -2 (pow p 4)) (* -1 (pow p 4))))) (* 2 (pow p 6))) (pow x 6)))) (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* -1 (/ (pow p 4) (pow x 4))) (/ (pow p 2) (pow x 2))))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (/ (pow p 2) (pow x 2)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* 2 (pow p 4)) (pow p 4)) (pow x 4))) (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (pow p 4)))) (* -2 (pow p 6))) (pow x 6))) (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* 2 (/ (pow p 4) (pow x 4))) (/ (pow p 4) (pow x 4)))))) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* -1 (/ (pow p 2) (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 5))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))>
#<alt (+ (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 7))) (* 3 (/ 1 (pow x 5))))) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))>
#<alt (* -1/4 (/ (pow x 3) (pow p 4)))>
#<alt (/ (+ (* -1/4 (/ (pow x 5) (pow p 2))) (* -1/4 (pow x 3))) (pow p 4))>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/8 (pow x 7)) (* 1/4 (pow x 7))) (pow p 4))) (* -1/4 (pow x 3))) (* 1/4 (/ (pow x 5) (pow p 2)))) (pow p 4))>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/8 (pow x 9)) (* (pow x 2) (+ (* 1/8 (pow x 7)) (* 1/4 (pow x 7))))) (pow p 6))) (* -1/4 (pow x 3))) (+ (* 1/8 (/ (pow x 7) (pow p 4))) (+ (* 1/4 (/ (pow x 5) (pow p 2))) (* 1/4 (/ (pow x 7) (pow p 4)))))) (pow p 4))>
#<alt (* -1/4 (/ (pow x 3) (pow p 4)))>
#<alt (/ (+ (* -1/4 (/ (pow x 5) (pow p 2))) (* -1/4 (pow x 3))) (pow p 4))>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/8 (pow x 7)) (* 1/4 (pow x 7))) (pow p 4))) (* -1/4 (pow x 3))) (* 1/4 (/ (pow x 5) (pow p 2)))) (pow p 4))>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/8 (pow x 9)) (* (pow x 2) (+ (* 1/8 (pow x 7)) (* 1/4 (pow x 7))))) (pow p 6))) (* -1/4 (pow x 3))) (+ (* 1/8 (/ (pow x 7) (pow p 4))) (+ (* 1/4 (/ (pow x 5) (pow p 2))) (* 1/4 (/ (pow x 7) (pow p 4)))))) (pow p 4))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (/ 11/8 (pow x 4))>
#<alt (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))>
#<alt (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))>
#<alt (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))>
#<alt (/ 11/8 (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ 11/8 (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4)))))>
#<alt (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4)))))>
#<alt (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4)))))>
#<alt (* -69/16 (/ (pow p 4) (pow x 6)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* -69/16 (/ (pow p 4) (pow x 6)))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* -69/16 (/ (pow p 4) (pow x 6)))>
#<alt (/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (* 1/2 (/ x p))>
#<alt (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 1/128 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/1024 (/ (pow x 2) (pow p 7))) (* 1/128 (/ 1 (pow p 5))))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p))))>
#<alt (* 4 (/ p x))>
#<alt (/ (+ (* -32 (/ (pow p 3) (pow x 2))) (* 4 p)) x)>
#<alt (/ (- (+ (* 4 p) (* 256 (/ (pow p 5) (pow x 4)))) (* 32 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (- (+ (* -2048 (/ (pow p 7) (pow x 6))) (* 4 p)) (+ (* -256 (/ (pow p 5) (pow x 4))) (* 32 (/ (pow p 3) (pow x 2))))) x)>
#<alt (* 4 (/ p x))>
#<alt (* -1 (/ (+ (* -4 p) (* 32 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -256 (/ (pow p 5) (pow x 4))) (* -4 p)) (* -32 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -4 p) (* 2048 (/ (pow p 7) (pow x 6)))) (+ (* -32 (/ (pow p 3) (pow x 2))) (* 256 (/ (pow p 5) (pow x 4))))) x))>
#<alt (* 4 (/ p x))>
#<alt (* p (+ (* -32 (/ (pow p 2) (pow x 3))) (* 4 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))) (* 4 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -2048 (/ (pow p 2) (pow x 7))) (* 256 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))) (* 4 (/ 1 x))))>
#<alt (* 1/2 (/ x p))>
#<alt (/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)>
#<alt (/ (- (+ (* 1/128 (/ (pow x 5) (pow p 4))) (* 1/2 x)) (* 1/16 (/ (pow x 3) (pow p 2)))) p)>
#<alt (/ (- (+ (* -1/1024 (/ (pow x 7) (pow p 6))) (* 1/2 x)) (+ (* -1/128 (/ (pow x 5) (pow p 4))) (* 1/16 (/ (pow x 3) (pow p 2))))) p)>
#<alt (* 1/2 (/ x p))>
#<alt (* -1 (/ (+ (* -1/2 x) (* 1/16 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (- (+ (* -1/2 x) (* -1/128 (/ (pow x 5) (pow p 4)))) (* -1/16 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (- (+ (* -1/2 x) (* 1/1024 (/ (pow x 7) (pow p 6)))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/128 (/ (pow x 5) (pow p 4))))) p))>
#<alt (* 1/16 (/ (pow x 2) (pow p 2)))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 4))) (* 1/16 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* 3/1024 (/ (pow x 2) (pow p 6))) (* 1/64 (/ 1 (pow p 4))))) (* 1/16 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2048 (/ (pow x 2) (pow p 8))) (* 3/1024 (/ 1 (pow p 6))))) (* 1/64 (/ 1 (pow p 4))))) (* 1/16 (/ 1 (pow p 2)))))>
#<alt (* 4 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -64 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1024 (pow p 6)) (* 256 (pow p 6))) (pow x 4))) (* 4 (pow p 2))) (* 64 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -4096 (pow p 8)) (* -16 (* (pow p 2) (+ (* -1024 (pow p 6)) (* 256 (pow p 6)))))) (pow x 6))) (* 4 (pow p 2))) (+ (* -1024 (/ (pow p 6) (pow x 4))) (+ (* 64 (/ (pow p 4) (pow x 2))) (* 256 (/ (pow p 6) (pow x 4)))))) (pow x 2))>
#<alt (* 4 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -64 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1024 (pow p 6)) (* 256 (pow p 6))) (pow x 4))) (* 4 (pow p 2))) (* 64 (/ (pow p 4) (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -4096 (pow p 8)) (* -16 (* (pow p 2) (+ (* -1024 (pow p 6)) (* 256 (pow p 6)))))) (pow x 6))) (* 4 (pow p 2))) (+ (* -1024 (/ (pow p 6) (pow x 4))) (+ (* 64 (/ (pow p 4) (pow x 2))) (* 256 (/ (pow p 6) (pow x 4)))))) (pow x 2))>
#<alt (* 4 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (+ (* (pow p 2) (- (* 768 (/ (pow p 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -8192 (/ (pow p 2) (pow x 8))) (* 768 (/ 1 (pow x 6))))) (* 64 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))>
#<alt (* 1/16 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))) (pow p 2))>
#<alt (/ (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2)))) (pow p 2))>
#<alt (/ (+ (* -1/4 (/ (+ (* -1/4 (* (pow x 2) (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))))) (* -1/1024 (pow x 8))) (pow p 6))) (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))))) (pow p 2))>
#<alt (* 1/16 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))) (pow p 2))>
#<alt (/ (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2)))) (pow p 2))>
#<alt (/ (+ (* -1/4 (/ (+ (* -1/4 (* (pow x 2) (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))))) (* -1/1024 (pow x 8))) (pow p 6))) (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))))) (pow p 2))>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>

Calls

159 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(+ 1 (* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))))
2.0ms	x	@	inf	(/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))
2.0ms	p	@	0	(- 0 (/ p x))
1.0ms	p	@	0	(* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x)))))
1.0ms	p	@	inf	(* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x)))))

rewrite372.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3752×	`-lowering-.f32`
3752×	`-lowering-.f64`
2596×	`/-lowering-/.f32`
2596×	`/-lowering-/.f64`
1486×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	454
1	413	389
2	4937	387
0	8250	387

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 657

Calls

Call 1

Inputs
(* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))
(sqrt (+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))))
(+ 1/2 (* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))))
(* x (/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x)))))))
(- 0 (/ p x))
(/ p x)
(* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x)))))
(+ 1 (* (* p p) (+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))))
(* p p)
(+ (/ -1/2 (* x x)) (/ (* (* p p) 11/8) (* (* x x) (* x x))))
(+ 1 (* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))))
(* (* p p) (+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x))))
(+ (* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))) (/ -1/2 (* x x)))
(/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4)))
(sqrt (/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2)))
(/ (- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4) (- (/ (/ x 2) (+ (* p 2) (* (/ (* x x) p) 1/4))) 1/2))
(- (* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) 1/4)
(/ (* (* p p) -2) (* x (* x x)))
(/ 1/2 (+ x (* p (* p (+ (/ (* (* p p) -2) (* x (* x x))) (/ 2 x))))))
(/ (* (* p p) 11/8) (* (* x x) (* x x)))
(/ -1/2 (* x x))
(* (* x x) (* x x))
(/ (* (* p p) -69/16) (pow x 6))
(+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x))))
(* (* p p) (+ (/ (* (* p p) -69/16) (pow x 6)) (/ 11/8 (* (* x x) (* x x)))))
(/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))
(* (* 1/4 (/ x (+ (* p 2) (* (/ (* x x) p) 1/4)))) (/ x (+ (* p 2) (* (/ (* x x) p) 1/4))))
(/ (* x x) p)

Outputs
(+.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (*.f64 x x))) (/.f64 p (/.f64 x #s(literal 2 binary64))))
(+.f64 (/.f64 p (/.f64 x #s(literal 2 binary64))) (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (*.f64 x x))))
(fma.f64 p (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 p (/.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) p (/.f64 p (/.f64 x #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 p (/.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (.f64 x x))) (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (.f64 x x)))) (-.f64 (.f64 (/.f64 p (/.f64 x #s(literal 2 binary64))) (/.f64 p (/.f64 x #s(literal 2 binary64)))) (.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (*.f64 x x))) (/.f64 p (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (.f64 x x))) (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (.f64 x x)))) (.f64 (/.f64 p (/.f64 x #s(literal 2 binary64))) (/.f64 p (/.f64 x #s(literal 2 binary64))))) (-.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -2 binary64))) (.f64 x (*.f64 x x))) (/.f64 p (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 p (+.f64 (.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64)))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 p (+.f64 (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 p p) #s(literal -2 binary64))))) (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (+.f64 (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 p p) #s(literal -2 binary64)))) (.f64 (/.f64 #s(literal 2 binary64) x) (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 p (-.f64 (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 p p) #s(literal -2 binary64)))) (/.f64 #s(literal 4 binary64) (.f64 x x)))) (-.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2 binary64))) p) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 (+.f64 (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 p p) #s(literal -2 binary64))))) (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) p) (+.f64 (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 p p) #s(literal -2 binary64)))) (.f64 (/.f64 #s(literal 2 binary64) x) (-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (-.f64 (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 p p) #s(literal -2 binary64)))) (/.f64 #s(literal 4 binary64) (.f64 x x))) p) (-.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)) p)
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (/.f64 x (/.f64 (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 x (/.f64 (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64))) (-.f64 (/.f64 x (/.f64 (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) x))))))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64))))))
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(/.f64 (.f64 (.f64 p p) (+.f64 (.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 p (.f64 p #s(literal -69/16 binary64)))))) (.f64 (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)) (/.f64 #s(literal 121/64 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))))) (+.f64 (/.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 p (.f64 p #s(literal -69/16 binary64))))) (.f64 (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)) (-.f64 (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)) (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))))
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(/.f64 (.f64 (+.f64 (.f64 p (.f64 (.f64 p #s(literal -69/16 binary64)) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 11/8 binary64)))) (.f64 p p)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))) x)
(.f64 (/.f64 x (+.f64 (.f64 (.f64 p #s(literal 2 binary64)) (.f64 (.f64 p p) #s(literal 4 binary64))) (.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (.f64 x x) p) (/.f64 (.f64 x x) p)))))) (+.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))) (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))) (*.f64 p #s(literal 2 binary64))))))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))))))
(/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x)) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x))
(/.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))))
(/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/4 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))))
(/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))))
(/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x)))) x)))
(/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x)))))))
(/.f64 (neg.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))))
(/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x)) #s(literal 1 binary64)) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x)))) x))
(/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x)) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x))) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x)))) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))))
(/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))))) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))))
(pow.f64 (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))))) #s(literal -1 binary64))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x)))) x))))
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(.f64 (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x)))) x)))
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(.f64 (/.f64 (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))) (/.f64 (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x)))) x)) #s(literal 1/4 binary64))
(.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (*.f64 x x))))))
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(.f64 (/.f64 (/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) (+.f64 (.f64 p #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (/.f64 p (.f64 x x))))) (-.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (.f64 x x) p) (/.f64 (.f64 x x) p))))) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 x x) p))))
(exp.f64 (.f64 (log.f64 (/.f64 p (.f64 x x))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) p)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) p))
(/.f64 (*.f64 x x) p)
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) p))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 p (*.f64 x x))))
(/.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) p)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 0 binary64) p)))
(pow.f64 (/.f64 p (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 x p))
(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) p))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) p))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)))
(*.f64 (/.f64 x p) x)
(.f64 (/.f64 #s(literal 1 binary64) p) (.f64 x x))

simplify392.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

6356×	`-lowering-.f32`
6356×	`-lowering-.f64`
3984×	`+-lowering-+.f64`
3984×	`+-lowering-+.f32`
1414×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	999	9327
1	3228	8402
0	8137	8402

Stop Event

1×	iter limit
1×	node limit

Counts

636 → 636

Calls

Call 1

Inputs
(* 2 (/ p x))
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(* -2 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(* -2 (/ (pow p 3) (pow x 3)))
(* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))
(* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))
(* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))
(* -2 (/ (pow p 3) (pow x 3)))
(/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))
(/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))
(/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))
(* 2 (/ p x))
(/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)
(/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)
(/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)
(* 2 (/ p x))
(* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))
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1
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1
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1
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1
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1
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1
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(/ 1/2 x)
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(/ 1/2 x)
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(/ 1/2 x)
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(/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))
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(* p (+ (* -32 (/ (pow p 2) (pow x 3))) (* 4 (/ 1 x))))
(* p (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))) (* 4 (/ 1 x))))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -2048 (/ (pow p 2) (pow x 7))) (* 256 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))) (* 4 (/ 1 x))))
(* 1/2 (/ x p))
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/ (- (+ (* 1/128 (/ (pow x 5) (pow p 4))) (* 1/2 x)) (* 1/16 (/ (pow x 3) (pow p 2)))) p)
(/ (- (+ (* -1/1024 (/ (pow x 7) (pow p 6))) (* 1/2 x)) (+ (* -1/128 (/ (pow x 5) (pow p 4))) (* 1/16 (/ (pow x 3) (pow p 2))))) p)
(* 1/2 (/ x p))
(* -1 (/ (+ (* -1/2 x) (* 1/16 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (- (+ (* -1/2 x) (* -1/128 (/ (pow x 5) (pow p 4)))) (* -1/16 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (- (+ (* -1/2 x) (* 1/1024 (/ (pow x 7) (pow p 6)))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/128 (/ (pow x 5) (pow p 4))))) p))
(* 1/16 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 4))) (* 1/16 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* 3/1024 (/ (pow x 2) (pow p 6))) (* 1/64 (/ 1 (pow p 4))))) (* 1/16 (/ 1 (pow p 2)))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2048 (/ (pow x 2) (pow p 8))) (* 3/1024 (/ 1 (pow p 6))))) (* 1/64 (/ 1 (pow p 4))))) (* 1/16 (/ 1 (pow p 2)))))
(* 4 (/ (pow p 2) (pow x 2)))
(/ (+ (* -64 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -1024 (pow p 6)) (* 256 (pow p 6))) (pow x 4))) (* 4 (pow p 2))) (* 64 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -4096 (pow p 8)) (* -16 (* (pow p 2) (+ (* -1024 (pow p 6)) (* 256 (pow p 6)))))) (pow x 6))) (* 4 (pow p 2))) (+ (* -1024 (/ (pow p 6) (pow x 4))) (+ (* 64 (/ (pow p 4) (pow x 2))) (* 256 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* 4 (/ (pow p 2) (pow x 2)))
(/ (+ (* -64 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -1024 (pow p 6)) (* 256 (pow p 6))) (pow x 4))) (* 4 (pow p 2))) (* 64 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -4096 (pow p 8)) (* -16 (* (pow p 2) (+ (* -1024 (pow p 6)) (* 256 (pow p 6)))))) (pow x 6))) (* 4 (pow p 2))) (+ (* -1024 (/ (pow p 6) (pow x 4))) (+ (* 64 (/ (pow p 4) (pow x 2))) (* 256 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(* 4 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* 768 (/ (pow p 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -8192 (/ (pow p 2) (pow x 8))) (* 768 (/ 1 (pow x 6))))) (* 64 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(* 1/16 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))) (pow p 2))
(/ (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2)))) (pow p 2))
(/ (+ (* -1/4 (/ (+ (* -1/4 (* (pow x 2) (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))))) (* -1/1024 (pow x 8))) (pow p 6))) (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))))) (pow p 2))
(* 1/16 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))) (pow p 2))
(/ (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2)))) (pow p 2))
(/ (+ (* -1/4 (/ (+ (* -1/4 (* (pow x 2) (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))))) (* -1/1024 (pow x 8))) (pow p 6))) (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))))) (pow p 2))
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)
(/ (pow x 2) p)

Outputs
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(.f64 p (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(.f64 p (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(* p (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(.f64 p (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 p p)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))
(* -2 (/ (pow p 3) (pow x 3)))
(/.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 x (*.f64 x x)))
(* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (.f64 p (.f64 p p)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 p p))) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (.f64 p (.f64 p p)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 p p))) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* (pow p 3) (- (* 2 (/ 1 (* (pow p 2) x))) (* 2 (/ 1 (pow x 3)))))
(.f64 (.f64 p (.f64 p p)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 p p))) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x)))))
(* -2 (/ (pow p 3) (pow x 3)))
(/.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 x (*.f64 x x)))
(* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))
(.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -2 binary64) (.f64 x (.f64 p p)))) (.f64 #s(literal -1 binary64) (.f64 p (.f64 p p))))
(* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))
(.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -2 binary64) (.f64 x (.f64 p p)))) (.f64 #s(literal -1 binary64) (.f64 p (.f64 p p))))
(* -1 (* (pow p 3) (- (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (* (pow p 2) x))))))
(.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -2 binary64) (.f64 x (.f64 p p)))) (.f64 #s(literal -1 binary64) (.f64 p (.f64 p p))))
(* -2 (/ (pow p 3) (pow x 3)))
(/.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 x (*.f64 x x)))
(/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(/ (+ (* -2 (pow p 3)) (* 2 (* p (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 p (.f64 #s(literal 2 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (*.f64 #s(literal 2 binary64) p)) x)
(/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (*.f64 #s(literal 2 binary64) p)) x)
(/ (+ (* -2 (/ (pow p 3) (pow x 2))) (* 2 p)) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p p))) (.f64 x x)) (*.f64 #s(literal 2 binary64) p)) x)
(* 2 (/ p x))
(/.f64 (*.f64 #s(literal 2 binary64) p) x)
(* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (+.f64 (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 p (.f64 p p))) (*.f64 x x))) (neg.f64 x))
(* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (+.f64 (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 p (.f64 p p))) (*.f64 x x))) (neg.f64 x))
(* -1 (/ (+ (* -2 p) (* 2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (+.f64 (.f64 p #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 p (.f64 p p))) (*.f64 x x))) (neg.f64 x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (pow.f64 p #s(literal 4 binary64)))))
(+ (sqrt 1/2) (* (pow x 4) (- (* -1/8 (/ (pow x 2) (* (pow p 6) (sqrt 1/2)))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))) (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 4 binary64)))))))
(+ (sqrt 1/2) (* (pow x 4) (- (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (+ (* 1/64 (/ 1 (* (pow p 8) (pow (sqrt 1/2) 2)))) (* 3/8 (/ 1 (pow p 8))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 6) (sqrt 1/2)))))) (* 1/8 (/ 1 (* (pow p 4) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/2 binary64) (pow.f64 p #s(literal 8 binary64)))) (/.f64 #s(literal 3/8 binary64) (pow.f64 p #s(literal 8 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))) (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 4 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 x (.f64 x (*.f64 x x)))))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/2 (+ (* -2 (* (pow p 2) (+ (* -4 (pow p 4)) (* -2 (pow p 4))))) (* 4 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/2 (+ (* -4 (pow p 4)) (* -2 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 (.f64 #s(literal -1/4 binary64) (+.f64 (.f64 #s(literal -2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -6 binary64))))) (-.f64 (.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 (.f64 p p) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -1/4 binary64))))))) (pow.f64 x #s(literal 6 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (.f64 p p) (.f64 x x)))))
(+ 1 (+ (* -1/2 (/ (+ (* -1/2 (+ (* -4 (pow p 6)) (* -2 (* (pow p 2) (+ (* 2 (pow p 4)) (* 4 (pow p 4))))))) (* 1/2 (* (pow p 2) (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))) (+ (* -1/2 (/ (+ (* -1/2 (+ (* 2 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* -1/2 (/ (pow p 2) (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (.f64 p p) (.f64 x x))) (/.f64 (+.f64 (+.f64 (.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64))) (.f64 (.f64 p p) #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3 binary64)) (.f64 (.f64 p p) #s(literal -2 binary64)))) (pow.f64 x #s(literal 6 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -53/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 #s(literal -53/16 binary64) (.f64 p p)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (pow.f64 p #s(literal 4 binary64)))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))
(+.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -3/8 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/2 binary64)) #s(literal -1/64 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 8 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (pow.f64 p #s(literal 4 binary64)))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (pow x 4) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/8 (/ (pow x 6) (* (pow p 6) (sqrt 1/2)))) (* 1/2 (/ (- (* -1/2 (+ (* 1/4 (pow x 8)) (* 1/2 (pow x 8)))) (* 1/64 (/ (pow x 8) (pow (sqrt 1/2) 2)))) (* (pow p 8) (sqrt 1/2)))))))
(+.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 6 binary64)))))) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -3/8 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/2 binary64)) #s(literal -1/64 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 p #s(literal 8 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ (pow x 4) (pow p 4))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/4 binary64)) (pow.f64 p #s(literal 4 binary64))))
(+ 1/2 (* (pow x 4) (- (* -1/4 (/ (pow x 2) (pow p 6))) (* 1/4 (/ 1 (pow p 4))))))
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1/2
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1/2
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(* -1 (/ (- (+ (* -4 p) (* 2048 (/ (pow p 7) (pow x 6)))) (+ (* -32 (/ (pow p 3) (pow x 2))) (* 256 (/ (pow p 5) (pow x 4))))) x))
(/.f64 (-.f64 (-.f64 (+.f64 (.f64 p #s(literal -4 binary64)) (/.f64 (.f64 #s(literal 2048 binary64) (pow.f64 p #s(literal 7 binary64))) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (.f64 #s(literal 256 binary64) (pow.f64 p #s(literal 5 binary64))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 #s(literal -32 binary64) (.f64 p (.f64 p p))) (.f64 x x))) (neg.f64 x))
(* 4 (/ p x))
(/.f64 (*.f64 p #s(literal 4 binary64)) x)
(* p (+ (* -32 (/ (pow p 2) (pow x 3))) (* 4 (/ 1 x))))
(.f64 p (+.f64 (/.f64 (.f64 #s(literal -32 binary64) (.f64 p p)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 4 binary64) x)))
(* p (+ (* (pow p 2) (- (* 256 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))) (* 4 (/ 1 x))))
(.f64 p (+.f64 (/.f64 #s(literal 4 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 #s(literal 256 binary64) (.f64 p p)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -32 binary64) (.f64 x (*.f64 x x)))))))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -2048 (/ (pow p 2) (pow x 7))) (* 256 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))) (* 4 (/ 1 x))))
(.f64 p (+.f64 (/.f64 #s(literal 4 binary64) x) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 #s(literal -2048 binary64) (.f64 p p)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 256 binary64) (pow.f64 x #s(literal 5 binary64))))) (/.f64 #s(literal -32 binary64) (.f64 x (*.f64 x x)))))))
(* 1/2 (/ x p))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) p)
(/ (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/2 x)) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (*.f64 x #s(literal 1/2 binary64))) p)
(/ (- (+ (* 1/128 (/ (pow x 5) (pow p 4))) (* 1/2 x)) (* 1/16 (/ (pow x 3) (pow p 2)))) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/128 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 p #s(literal 4 binary64))) (+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (.f64 x #s(literal 1/2 binary64)))) p)
(/ (- (+ (* -1/1024 (/ (pow x 7) (pow p 6))) (* 1/2 x)) (+ (* -1/128 (/ (pow x 5) (pow p 4))) (* 1/16 (/ (pow x 3) (pow p 2))))) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/1024 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 p #s(literal 6 binary64))) (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (.f64 x #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal -1/128 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 p #s(literal 4 binary64))))) p)
(* 1/2 (/ x p))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) p)
(* -1 (/ (+ (* -1/2 x) (* 1/16 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (*.f64 x #s(literal -1/2 binary64))) (neg.f64 p))
(* -1 (/ (- (+ (* -1/2 x) (* -1/128 (/ (pow x 5) (pow p 4)))) (* -1/16 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/128 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 p #s(literal 4 binary64))) (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (.f64 x #s(literal -1/2 binary64)))) (neg.f64 p))
(* -1 (/ (- (+ (* -1/2 x) (* 1/1024 (/ (pow x 7) (pow p 6)))) (+ (* -1/16 (/ (pow x 3) (pow p 2))) (* 1/128 (/ (pow x 5) (pow p 4))))) p))
(/.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (/.f64 (.f64 #s(literal 1/1024 binary64) (pow.f64 x #s(literal 7 binary64))) (pow.f64 p #s(literal 6 binary64))) (+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (/.f64 (*.f64 #s(literal 1/128 binary64) (pow.f64 x #s(literal 5 binary64))) (pow.f64 p #s(literal 4 binary64)))))) (neg.f64 p))
(* 1/16 (/ (pow x 2) (pow p 2)))
(/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (*.f64 p p))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 4))) (* 1/16 (/ 1 (pow p 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (pow.f64 p #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 p p))))
(* (pow x 2) (+ (* (pow x 2) (- (* 3/1024 (/ (pow x 2) (pow p 6))) (* 1/64 (/ 1 (pow p 4))))) (* 1/16 (/ 1 (pow p 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 p p)) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal 3/1024 binary64) (*.f64 x x)) (pow.f64 p #s(literal 6 binary64))) (/.f64 #s(literal -1/64 binary64) (pow.f64 p #s(literal 4 binary64)))))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2048 (/ (pow x 2) (pow p 8))) (* 3/1024 (/ 1 (pow p 6))))) (* 1/64 (/ 1 (pow p 4))))) (* 1/16 (/ 1 (pow p 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 p p)) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -1/2048 binary64) (*.f64 x x)) (pow.f64 p #s(literal 8 binary64))) (/.f64 #s(literal 3/1024 binary64) (pow.f64 p #s(literal 6 binary64))))) (/.f64 #s(literal -1/64 binary64) (pow.f64 p #s(literal 4 binary64)))))))
(* 4 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (*.f64 x x))
(/ (+ (* -64 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/.f64 (-.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (*.f64 x x))
(/ (- (+ (* -1 (/ (+ (* -1024 (pow p 6)) (* 256 (pow p 6))) (pow x 4))) (* 4 (pow p 2))) (* 64 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (-.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -768 binary64)) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 #s(literal -64 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (*.f64 x x))
(/ (- (+ (* -1 (/ (+ (* -4096 (pow p 8)) (* -16 (* (pow p 2) (+ (* -1024 (pow p 6)) (* 256 (pow p 6)))))) (pow x 6))) (* 4 (pow p 2))) (+ (* -1024 (/ (pow p 6) (pow x 4))) (+ (* 64 (/ (pow p 4) (pow x 2))) (* 256 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -4096 binary64)) (.f64 (.f64 p p) (.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -768 binary64)) #s(literal -16 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -1024 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x)) (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 256 binary64)) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x x))
(* 4 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (*.f64 x x))
(/ (+ (* -64 (/ (pow p 4) (pow x 2))) (* 4 (pow p 2))) (pow x 2))
(/.f64 (-.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (*.f64 x x))
(/ (- (+ (* -1 (/ (+ (* -1024 (pow p 6)) (* 256 (pow p 6))) (pow x 4))) (* 4 (pow p 2))) (* 64 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (-.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -768 binary64)) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 #s(literal -64 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x))) (*.f64 x x))
(/ (- (+ (* -1 (/ (+ (* -4096 (pow p 8)) (* -16 (* (pow p 2) (+ (* -1024 (pow p 6)) (* 256 (pow p 6)))))) (pow x 6))) (* 4 (pow p 2))) (+ (* -1024 (/ (pow p 6) (pow x 4))) (+ (* 64 (/ (pow p 4) (pow x 2))) (* 256 (/ (pow p 6) (pow x 4)))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 8 binary64)) #s(literal -4096 binary64)) (.f64 (.f64 p p) (.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -768 binary64)) #s(literal -16 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -1024 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 4 binary64))) (.f64 x x)) (/.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 256 binary64)) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x x))
(* 4 (/ (pow p 2) (pow x 2)))
(/.f64 (.f64 p (.f64 p #s(literal 4 binary64))) (*.f64 x x))
(* (pow p 2) (+ (* -64 (/ (pow p 2) (pow x 4))) (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (+.f64 (/.f64 (.f64 #s(literal -64 binary64) (.f64 p p)) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 4 binary64) (.f64 x x))))
(* (pow p 2) (+ (* (pow p 2) (- (* 768 (/ (pow p 2) (pow x 6))) (* 64 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 #s(literal 768 binary64) (.f64 p p)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -64 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -8192 (/ (pow p 2) (pow x 8))) (* 768 (/ 1 (pow x 6))))) (* 64 (/ 1 (pow x 4))))) (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 #s(literal -8192 binary64) (.f64 p p)) (pow.f64 x #s(literal 8 binary64))) (/.f64 #s(literal 768 binary64) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal -64 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(* 1/16 (/ (pow x 2) (pow p 2)))
(/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (*.f64 p p))
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))) (pow p 2))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 p p)) (.f64 (.f64 x x) #s(literal 1/16 binary64))) (.f64 p p))
(/ (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2)))) (pow p 2))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 p p)) (+.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -3/256 binary64))) (pow.f64 p #s(literal 4 binary64))))) (.f64 p p))
(/ (+ (* -1/4 (/ (+ (* -1/4 (* (pow x 2) (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))))) (* -1/1024 (pow x 8))) (pow p 6))) (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))))) (pow p 2))
(/.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -3/256 binary64)) #s(literal -1/4 binary64))) (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -1/1024 binary64))) (pow.f64 p #s(literal 6 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -3/256 binary64)) (pow.f64 p #s(literal 4 binary64))))) (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 p p)) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (*.f64 p p))
(* 1/16 (/ (pow x 2) (pow p 2)))
(/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (*.f64 p p))
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))) (pow p 2))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 p p)) (.f64 (.f64 x x) #s(literal 1/16 binary64))) (.f64 p p))
(/ (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2)))) (pow p 2))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 p p)) (+.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -3/256 binary64))) (pow.f64 p #s(literal 4 binary64))))) (.f64 p p))
(/ (+ (* -1/4 (/ (+ (* -1/4 (* (pow x 2) (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))))) (* -1/1024 (pow x 8))) (pow p 6))) (+ (* -1/4 (/ (+ (* -1/64 (pow x 6)) (* 1/256 (pow x 6))) (pow p 4))) (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/16 (pow x 2))))) (pow p 2))
(/.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -3/256 binary64)) #s(literal -1/4 binary64))) (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -1/1024 binary64))) (pow.f64 p #s(literal 6 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -3/256 binary64)) (pow.f64 p #s(literal 4 binary64))))) (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 p p)) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (*.f64 p p))
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)

eval294.0ms (2.6%)

Compiler: Compiled 67687 to 5072 computations (92.5% saved)

prune189.0ms (1.7%)

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	1546	4	1550
Fresh	0	3	3
Picked	4	1	5
Done	0	5	5
Total	1550	13	1563

Accuracy

100.0%

Counts

1563 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.2%	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)))))) (.f64 p (.f64 p (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
✓	24.6%	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
▶	26.1%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
▶	17.8%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
▶	10.4%	(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	57.3%	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))))
▶	52.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
✓	57.3%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
	49.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x))))))))))))
✓	78.4%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))
✓	56.7%	(sqrt.f64 #s(literal 1/2 binary64))
▶	27.7%	(neg.f64 (/.f64 p x))
✓	34.4%	#s(literal 1 binary64)

Compiler

Compiled 487 to 266 computations (45.4% saved)

simplify223.0ms (2%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
✓	cost-diff	256	(.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
✓	cost-diff	0	(/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	0	(.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 p p))
✓	cost-diff	0	(+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	256	(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	cost-diff	-64	(neg.f64 (/.f64 p x))
✓	cost-diff	0	(/.f64 p x)
✓	cost-diff	0	(*.f64 x #s(literal 1/4 binary64))
✓	cost-diff	0	(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))

Rules

4212×	`-lowering-.f32`
4212×	`-lowering-.f64`
2450×	`/-lowering-/.f32`
2450×	`/-lowering-/.f64`
1614×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	292
1	117	264
2	322	263
3	864	245
4	2224	240
5	4543	240
6	6974	240
0	8208	240

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ 1/2 (/ (* x 1/4) p)))
(+ 1/2 (/ (* x 1/4) p))
1/2
(/ (* x 1/4) p)
(* x 1/4)
x
1/4
p
(neg (/ p x))
(/ p x)
p
x
(* (* p p) (+ (/ 1 (* p p)) (/ -1/2 (* x x))))
(* p p)
p
(+ (/ 1 (* p p)) (/ -1/2 (* x x)))
(/ 1 (* p p))
1
(/ -1/2 (* x x))
-1/2
(* x x)
x
(+ 1 (* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))))
1
(* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x)))
(* p p)
p
(/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))
(+ (/ (* (* p p) 11/8) (* x x)) -1/2)
(/ (* (* p p) 11/8) (* x x))
(* (* p p) 11/8)
11/8
(* x x)
x
-1/2
(+ 1 (* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))))
1
(* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x))))
(* p p)
p
(+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))
(* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x)))))
(/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))
(+ 11/8 (/ (* (* p p) -69/16) (* x x)))
11/8
(/ (* (* p p) -69/16) (* x x))
(* (* p p) -69/16)
-69/16
(* x x)
x
(* x (* x (* x x)))
(* x (* x x))
(/ -1/2 (* x x))
-1/2

Outputs
(sqrt (+ 1/2 (/ (* x 1/4) p)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(+ 1/2 (/ (* x 1/4) p))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
1/2
#s(literal 1/2 binary64)
(/ (* x 1/4) p)
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* x 1/4)
(*.f64 x #s(literal 1/4 binary64))
x
1/4
#s(literal 1/4 binary64)
p
(neg (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/ p x)
(/.f64 p x)
p
x
(* (* p p) (+ (/ 1 (* p p)) (/ -1/2 (* x x))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(* p p)
(*.f64 p p)
p
(+ (/ 1 (* p p)) (/ -1/2 (* x x)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/ 1 (* p p))
(/.f64 #s(literal 1 binary64) (*.f64 p p))
1
#s(literal 1 binary64)
(/ -1/2 (* x x))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
x
(+ 1 (* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))))
(+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x))) (/.f64 (.f64 p p) (.f64 x x))))
1
#s(literal 1 binary64)
(* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x)))
(.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x))) (/.f64 (.f64 p p) (.f64 x x)))
(* p p)
(*.f64 p p)
p
(/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x))) (.f64 x x))
(+ (/ (* (* p p) 11/8) (* x x)) -1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (*.f64 x x)))
(/ (* (* p p) 11/8) (* x x))
(/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (*.f64 x x))
(* (* p p) 11/8)
(.f64 (.f64 p p) #s(literal 11/8 binary64))
11/8
#s(literal 11/8 binary64)
(* x x)
(*.f64 x x)
x
-1/2
#s(literal -1/2 binary64)
(+ 1 (* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 x x)))) (.f64 x x)))) (*.f64 x x)))
1
#s(literal 1 binary64)
(* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x))))
(/.f64 (.f64 (.f64 p p) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 x x)))) (.f64 x x)))) (*.f64 x x))
(* p p)
(*.f64 p p)
p
(+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 x x))) (/.f64 (.f64 p p) (.f64 x (.f64 x (*.f64 x x))))))
(* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x)))))
(.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 x x))) (/.f64 (.f64 p p) (.f64 x (.f64 x (.f64 x x)))))
(/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))
(/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(+ 11/8 (/ (* (* p p) -69/16) (* x x)))
(+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (*.f64 x x)))
11/8
#s(literal 11/8 binary64)
(/ (* (* p p) -69/16) (* x x))
(/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (*.f64 x x))
(* (* p p) -69/16)
(.f64 p (.f64 p #s(literal -69/16 binary64)))
-69/16
#s(literal -69/16 binary64)
(* x x)
(*.f64 x x)
x
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
(* x (* x x))
(.f64 x (.f64 x x))
(/ -1/2 (* x x))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)

localize267.0ms (2.4%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	94.4%	(.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
✓	accuracy	92.2%	(/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (*.f64 x x))
✓	accuracy	90.9%	(/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
✓	accuracy	87.6%	(.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))
✓	accuracy	99.9%	(.f64 (.f64 p p) #s(literal 11/8 binary64))
✓	accuracy	93.6%	(/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))
✓	accuracy	93.4%	(.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x)))
✓	accuracy	92.1%	(/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (*.f64 x x))
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	99.7%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 p p))
✓	accuracy	82.9%	(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	accuracy	100.0%	(/.f64 p x)
✓	accuracy	100.0%	(neg.f64 (/.f64 p x))
✓	accuracy	100.0%	(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/4 binary64))
✓	accuracy	97.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))

Results

170.0ms	191×	0	valid
36.0ms	65×	0	invalid

Compiler

Compiled 369 to 37 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 18.0ms (39.6% of total)

ival-div: 15.0ms (33% of total)

ival-add: 9.0ms (19.8% of total)

ival-sqrt: 2.0ms (4.4% of total)

const: 1.0ms (2.2% of total)

ival-neg: 1.0ms (2.2% of total)

backward-pass: 0.0ms (0% of total)

series26.0ms (0.2%)

Counts

22 → 468

Calls

Call 1

Inputs
#<alt (sqrt (+ 1/2 (/ (* x 1/4) p)))>
#<alt (+ 1/2 (/ (* x 1/4) p))>
#<alt (/ (* x 1/4) p)>
#<alt (* x 1/4)>
#<alt (/ p x)>
#<alt (neg (/ p x))>
#<alt (* (* p p) (+ (/ 1 (* p p)) (/ -1/2 (* x x))))>
#<alt (* p p)>
#<alt (+ (/ 1 (* p p)) (/ -1/2 (* x x)))>
#<alt (/ 1 (* p p))>
#<alt (+ 1 (* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))))>
#<alt (* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x)))>
#<alt (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))>
#<alt (* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x))))>
#<alt (+ 1 (* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))))>
#<alt (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))>
#<alt (/ -1/2 (* x x))>
#<alt (/ (* (* p p) 11/8) (* x x))>
#<alt (* (* p p) 11/8)>
#<alt (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x)))))>
#<alt (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))>
#<alt (/ (* (* p p) -69/16) (* x x))>

Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (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)))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))>
#<alt (* 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))))))))>
#<alt (* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))>
#<alt (* -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)))))))>
#<alt (* -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))))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)>
#<alt (/ (+ (* 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)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (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)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (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)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
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#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (* 11/8 (/ (pow p 2) (pow x 4)))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))>
#<alt (/ 11/8 (pow x 4))>
#<alt (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))>
#<alt (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))>
#<alt (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))>
#<alt (* -69/16 (/ (pow p 2) (pow x 6)))>
#<alt (/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))>
#<alt (/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))>
#<alt (/ 11/8 (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ 11/8 (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>
#<alt (* -69/16 (/ (pow p 2) (pow x 2)))>

Calls

117 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x)))
1.0ms	x	@	-inf	(sqrt (+ 1/2 (/ (* x 1/4) p)))
1.0ms	x	@	inf	(sqrt (+ 1/2 (/ (* x 1/4) p)))
1.0ms	p	@	inf	(* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x)))))
0.0ms	p	@	0	(* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x))))

rewrite383.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3190×	`-lowering-.f32`
3190×	`-lowering-.f64`
2790×	`fma-lowering-fma.f32`
2790×	`fma-lowering-fma.f64`
2196×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	227
1	256	203
2	2740	202
0	8672	202

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 540

Calls

Call 1

Inputs
(sqrt (+ 1/2 (/ (* x 1/4) p)))
(+ 1/2 (/ (* x 1/4) p))
(/ (* x 1/4) p)
(* x 1/4)
(/ p x)
(neg (/ p x))
(* (* p p) (+ (/ 1 (* p p)) (/ -1/2 (* x x))))
(* p p)
(+ (/ 1 (* p p)) (/ -1/2 (* x x)))
(/ 1 (* p p))
(+ 1 (* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))))
(* (* p p) (/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x)))
(/ (+ (/ (* (* p p) 11/8) (* x x)) -1/2) (* x x))
(* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x))))
(+ 1 (* (* p p) (+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))))
(+ (* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))) (/ -1/2 (* x x)))
(/ -1/2 (* x x))
(/ (* (* p p) 11/8) (* x x))
(* (* p p) 11/8)
(* (* p p) (/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x)))))
(/ (+ 11/8 (/ (* (* p p) -69/16) (* x x))) (* x (* x (* x x))))
(/ (* (* p p) -69/16) (* x x))

Outputs
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (-.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64)))))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) #s(literal 1/2 binary64)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p)) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (-.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) 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 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p))) (/.f64 (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/4 binary64) p) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (-.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p)) (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (*.f64 x #s(literal 1/4 binary64)))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p)))) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (-.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p)))) (+.f64 (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64))))) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (-.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64)))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))))
(/.f64 (-.f64 (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64)))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (-.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p)) (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (*.f64 x #s(literal 1/4 binary64)))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (.f64 p (.f64 p p)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (-.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64))))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 p (.f64 x #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p))))
(exp.f64 (.f64 (log.f64 (/.f64 p (.f64 x #s(literal 1/4 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) p)))
(neg.f64 (/.f64 (*.f64 x #s(literal -1/4 binary64)) p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 x #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64)))))
(/.f64 (*.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) p))
(/.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) p)
(/.f64 (neg.f64 (*.f64 x #s(literal -1/4 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) p)))
(pow.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
(.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) p))
(.f64 (.f64 x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)))
(.f64 (/.f64 #s(literal 1 binary64) p) (.f64 x #s(literal 1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) p) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/4 binary64) p) x)
(*.f64 x #s(literal 1/4 binary64))
(*.f64 #s(literal 1/4 binary64) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x p)) #s(literal -1 binary64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 p x)
(/.f64 #s(literal 1 binary64) (/.f64 x p))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x p) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x p)))
(/.f64 (-.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 p #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(pow.f64 (/.f64 x p) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x p) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 p x))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.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 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x p)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) p))
(/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) p)))
(/.f64 #s(literal -1 binary64) (/.f64 x p))
(/.f64 (-.f64 #s(literal 0 binary64) p) x)
(/.f64 (-.f64 #s(literal 0 binary64) p) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (.f64 p (.f64 p p)) (.f64 x (.f64 x x)))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (/.f64 p x) (/.f64 p x)) (.f64 #s(literal 0 binary64) (/.f64 p x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 p x) (/.f64 p x))) (+.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) p)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (neg.f64 (/.f64 x p)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) p) #s(literal -1 binary64))
(pow.f64 (/.f64 x (-.f64 #s(literal 0 binary64) p)) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 p (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 p x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 p x))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(+.f64 (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 p (.f64 p (/.f64 #s(literal -1/2 binary64) (.f64 x x))) #s(literal 1 binary64))
(fma.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(fma.f64 (.f64 p p) (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (.f64 p p) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 p p)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 p p) #s(literal 1 binary64))
(fma.f64 (.f64 p (.f64 p #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) p) p #s(literal 1 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p (.f64 p p)) (.f64 p (.f64 p p))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64)))))))
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(/.f64 (.f64 (+.f64 #s(literal 1331/512 binary64) (/.f64 (.f64 (.f64 (.f64 p (.f64 p p)) (.f64 p (.f64 p p))) (/.f64 #s(literal -328509/4096 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 121/64 binary64) (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)) (-.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)) #s(literal 11/8 binary64)))) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (.f64 (-.f64 #s(literal 121/64 binary64) (/.f64 (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) x) (.f64 (.f64 p p) #s(literal -69/16 binary64))) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) #s(literal -11/8 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (neg.f64 (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) x)) (neg.f64 (.f64 x (*.f64 x x))))
(/.f64 (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (*.f64 x x))) x)
(/.f64 (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x x)) (*.f64 x x))
(/.f64 (.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) #s(literal 1 binary64)) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (.f64 (+.f64 #s(literal 1331/512 binary64) (/.f64 (.f64 (.f64 (.f64 p (.f64 p p)) (.f64 p (.f64 p p))) (/.f64 #s(literal -328509/4096 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 121/64 binary64) (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)) (-.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (*.f64 x x)) #s(literal 11/8 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 121/64 binary64) (/.f64 (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) x) (.f64 (.f64 p p) #s(literal -69/16 binary64))) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))))
(/.f64 (/.f64 (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) x) x) (.f64 x x))
(/.f64 (/.f64 (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) x) (.f64 x x)) x)
(pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 x (.f64 x x)) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (*.f64 x x))) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (+.f64 (neg.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) #s(literal -11/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (*.f64 x x)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1331/512 binary64) (/.f64 (.f64 (.f64 (.f64 p (.f64 p p)) (.f64 p (.f64 p p))) (/.f64 #s(literal -328509/4096 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 121/64 binary64) (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)) (-.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (*.f64 x x)) #s(literal 11/8 binary64))))))
(.f64 (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 121/64 binary64) (/.f64 (.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) x) (.f64 (.f64 p p) #s(literal -69/16 binary64))) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)))))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 (.f64 p p) #s(literal -69/16 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (.f64 (.f64 p p) #s(literal 69/16 binary64)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -69/16 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -69/16 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) x)))
(/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -69/16 binary64)))))
(/.f64 (.f64 (.f64 p p) #s(literal 69/16 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) x) x)
(/.f64 (.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (.f64 (.f64 p p) #s(literal 69/16 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (/.f64 (.f64 p p) x) #s(literal -69/16 binary64)) x)
(pow.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -69/16 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x x) (.f64 (*.f64 p p) #s(literal -69/16 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) x)) #s(literal -1 binary64))
(.f64 p (.f64 p (/.f64 #s(literal -69/16 binary64) (*.f64 x x))))
(.f64 p (.f64 (.f64 p #s(literal -69/16 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 p (/.f64 (.f64 p #s(literal -69/16 binary64)) (*.f64 x x)))
(.f64 (/.f64 p x) (/.f64 (.f64 p #s(literal -69/16 binary64)) x))
(.f64 (/.f64 p x) (pow.f64 (/.f64 x (.f64 p #s(literal -69/16 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 p p) (/.f64 #s(literal -69/16 binary64) (*.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x)))
(.f64 #s(literal -69/16 binary64) (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 #s(literal -69/16 binary64) (.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 (.f64 p p) #s(literal 69/16 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (/.f64 (.f64 p p) x) (/.f64 #s(literal -69/16 binary64) x))
(.f64 (/.f64 #s(literal -69/16 binary64) x) (/.f64 (.f64 p p) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 p p) #s(literal -69/16 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 p p) #s(literal -69/16 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 (*.f64 p p) #s(literal -69/16 binary64)) x))
(.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -69/16 binary64)) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal -69/16 binary64) (.f64 x x)) (*.f64 p p))

simplify367.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

5590×	`-lowering-.f32`
5590×	`-lowering-.f64`
2212×	`/-lowering-/.f32`
2212×	`/-lowering-/.f64`
1672×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	310	5298
1	857	4602
2	2696	4409
3	7473	4373
0	8205	4373

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

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 (- (* 1/1024 (/ 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)))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 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)
(* -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
(+ 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 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)
(/ 1 (pow p 2))
(/ (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (pow p 2))
(/ (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (pow p 2))
(/ (+ 1 (* -1/2 (/ (pow p 2) (pow x 2)))) (pow p 2))
(/ -1/2 (pow x 2))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(/ -1/2 (pow x 2))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(/ -1/2 (pow x 2))
(/ (- (/ (pow x 2) (pow p 2)) 1/2) (pow x 2))
(/ (- (/ (pow x 2) (pow p 2)) 1/2) (pow x 2))
(/ (- (/ (pow x 2) (pow p 2)) 1/2) (pow x 2))
(/ 1 (pow p 2))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(/ 1 (pow p 2))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2))))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
(/ 1 (pow p 2))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(* 11/8 (/ (pow p 4) (pow x 4)))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))
(* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))
(* 11/8 (/ (pow p 4) (pow x 4)))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))
(* (pow p 4) (- (+ (/ 1 (pow p 4)) (* 11/8 (/ 1 (pow x 4)))) (/ 1/2 (* (pow p 2) (pow x 2)))))
(* 11/8 (/ (pow p 4) (pow x 4)))
(/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))
(/ (+ (* 11/8 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow p 2)) (pow x 2)))) (pow x 4))
(/ (+ (* 11/8 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow p 2)) (pow x 2)))) (pow x 4))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 11/8 (/ (pow p 4) (pow x 4)))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* 11/8 (/ (pow p 4) (pow x 4)))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 4) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* 11/8 (/ (pow p 4) (pow x 4)))
(/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))
(/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))
(/ (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))) (pow x 4))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ -1/2 (pow x 2))
(- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))
(- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))
(- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))
(* 11/8 (/ (pow p 2) (pow x 4)))
(* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* 11/8 (/ (pow p 2) (pow x 4)))
(* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* (pow p 2) (- (* 11/8 (/ 1 (pow x 4))) (* 1/2 (/ 1 (* (pow p 2) (pow x 2))))))
(* 11/8 (/ (pow p 2) (pow x 4)))
(/ (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))) (pow x 4))
(/ (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))) (pow x 4))
(/ (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))) (pow x 4))
(/ -1/2 (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(/ -1/2 (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (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)))))
(* (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)))))
(* -69/16 (/ (pow p 6) (pow x 6)))
(* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))
(* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))
(* -69/16 (/ (pow p 6) (pow x 6)))
(* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))
(* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (/ 1/2 (* (pow p 4) (pow x 2))) (* 69/16 (/ 1 (pow x 6))))))
(* -69/16 (/ (pow p 6) (pow x 6)))
(/ (+ (* -69/16 (pow p 6)) (* 11/8 (* (pow p 4) (pow x 2)))) (pow x 6))
(/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))))) (pow x 6))
(/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))))) (pow x 6))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2)))) (pow x 2))
(/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (+ (* -69/16 (/ (pow p 6) (pow x 4))) (+ (* -1/2 (pow p 2)) (* 11/8 (/ (pow p 4) (pow x 2))))) (pow x 2))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(* -69/16 (/ (pow p 6) (pow x 6)))
(* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))
(* (pow p 6) (- (+ (/ 1 (pow p 6)) (/ 11/8 (* (pow p 2) (pow x 4)))) (+ (* 69/16 (/ 1 (pow x 6))) (* 1/2 (/ 1 (* (pow p 4) (pow x 2)))))))
(* -69/16 (/ (pow p 6) (pow x 6)))
(* (pow p 6) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 6) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))
(* (pow p 6) (- (+ (/ 1 (pow p 6)) (/ 11/8 (* (pow p 2) (pow x 4)))) (+ (* 69/16 (/ 1 (pow x 6))) (* 1/2 (/ 1 (* (pow p 4) (pow x 2)))))))
(* -69/16 (/ (pow p 6) (pow x 6)))
(/ (+ (* -69/16 (pow p 6)) (* 11/8 (* (pow p 4) (pow x 2)))) (pow x 6))
(/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* -1/2 (* (pow p 2) (pow x 2))) (* 11/8 (pow p 4))))) (pow x 6))
(/ (+ (* -69/16 (pow p 6)) (* (pow x 2) (+ (* 11/8 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow p 2)) (pow x 2)))))) (pow x 6))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -69/16 (/ (pow p 6) (pow x 6))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4)))))
(+ 1 (+ (* -69/16 (/ (pow p 6) (pow x 6))) (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 11/8 (/ (pow p 4) (pow x 4))))))
(/ -1/2 (pow x 2))
(- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))
(- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))
(- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))
(* -69/16 (/ (pow p 4) (pow x 6)))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))
(* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))
(* -69/16 (/ (pow p 4) (pow x 6)))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))
(* (pow p 4) (- (/ 11/8 (* (pow p 2) (pow x 4))) (+ (* 69/16 (/ 1 (pow x 6))) (/ 1/2 (* (pow p 4) (pow x 2))))))
(* -69/16 (/ (pow p 4) (pow x 6)))
(/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))
(/ (+ (* -69/16 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))))) (pow x 6))
(/ (+ (* -69/16 (pow p 4)) (* (pow x 2) (+ (* -1/2 (pow x 2)) (* 11/8 (pow p 2))))) (pow x 6))
(/ -1/2 (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))
(/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))
(/ -1/2 (pow x 2))
(/ (- (* 11/8 (/ (pow p 2) (pow x 2))) 1/2) (pow x 2))
(/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))
(/ (- (+ (* -69/16 (/ (pow p 4) (pow x 4))) (* 11/8 (/ (pow p 2) (pow x 2)))) 1/2) (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (/ (pow p 2) (pow x 2)))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (pow p 2))
(* 11/8 (/ (pow p 2) (pow x 4)))
(* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4)))))
(* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4)))))
(* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4)))))
(* -69/16 (/ (pow p 4) (pow x 6)))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* -69/16 (/ (pow p 4) (pow x 6)))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 4) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* -69/16 (/ (pow p 4) (pow x 6)))
(/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))
(/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))
(/ (+ (* -69/16 (pow p 4)) (* 11/8 (* (pow p 2) (pow x 2)))) (pow x 6))
(* 11/8 (/ (pow p 2) (pow x 4)))
(/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))
(/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))
(/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))
(* 11/8 (/ (pow p 2) (pow x 4)))
(/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))
(/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))
(/ (+ (* -69/16 (/ (pow p 4) (pow x 2))) (* 11/8 (pow p 2))) (pow x 4))
(/ 11/8 (pow x 4))
(+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))
(+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))
(+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))
(* -69/16 (/ (pow p 2) (pow x 6)))
(* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* -69/16 (/ (pow p 2) (pow x 6)))
(* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* (pow p 2) (- (* 11/8 (/ 1 (* (pow p 2) (pow x 4)))) (* 69/16 (/ 1 (pow x 6)))))
(* -69/16 (/ (pow p 2) (pow x 6)))
(/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))
(/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))
(/ (+ (* -69/16 (pow p 2)) (* 11/8 (pow x 2))) (pow x 6))
(/ 11/8 (pow x 4))
(/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))
(/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))
(/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))
(/ 11/8 (pow x 4))
(/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))
(/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))
(/ (+ 11/8 (* -69/16 (/ (pow p 2) (pow x 2)))) (pow x 4))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))
(* -69/16 (/ (pow p 2) (pow x 2)))

Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (.f64 (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (*.f64 p p)) (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p))))
(+ (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)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (.f64 x (+.f64 (/.f64 (.f64 x (/.f64 #s(literal 1/1024 binary64) (.f64 p (.f64 p p)))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 p p)))))))
(* 1/2 (sqrt (/ x p)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (sqrt.f64 (/.f64 p (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (.f64 p (.f64 p p)) (pow.f64 x #s(literal 5 binary64)))))))
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(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x p))) (sqrt.f64 (/.f64 p (.f64 x (.f64 x x)))))) (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (.f64 p (.f64 p p)) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 p #s(literal 5 binary64)) (pow.f64 x #s(literal 7 binary64))))))))
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(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))
(* -69/16 (/ (pow p 2) (pow x 2)))
(.f64 (.f64 p (/.f64 (/.f64 p x) x)) #s(literal -69/16 binary64))

eval184.0ms (1.6%)

Compiler: Compiled 33232 to 2708 computations (91.9% saved)

prune177.0ms (1.6%)

Pruning

14 alts after pruning (3 fresh and 11 done)

	Pruned	Kept	Total
New	1182	2	1184
Fresh	1	1	2
Picked	0	5	5
Done	0	6	6
Total	1183	14	1197

Accuracy

100.0%

Counts

1197 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.6%	(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
✓	24.6%	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
✓	26.1%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
✓	17.8%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
	15.1%	(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
✓	10.4%	(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	57.3%	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))))
✓	52.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
✓	57.3%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
	49.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x))))))))))))
✓	78.4%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))
✓	56.7%	(sqrt.f64 #s(literal 1/2 binary64))
✓	27.7%	(neg.f64 (/.f64 p x))
✓	34.4%	#s(literal 1 binary64)

Compiler

Compiled 771 to 313 computations (59.4% saved)

regimes55.0ms (0.5%)

Counts

22 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)))))) (.f64 p (.f64 p (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x))))))))))))
(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 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 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))

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

Calls

7 calls:

13.0ms	p
8.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
8.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
7.0ms	x
6.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Results

Accuracy	Segments	Branch
78.4%	1	`p`
84.8%	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))))`
78.4%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes16.0ms (0.1%)

Counts

20 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)))))) (.f64 p (.f64 p (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (.f64 x (*.f64 x x))))))))))))
(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) (/.f64 x (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) p) #s(literal 1/4 binary64))))) #s(literal 1/4 binary64)) (-.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))))

Outputs

(neg.f64 (/.f64 p x))

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

Calls

2 calls:

6.0ms	p
6.0ms	x

Results

Accuracy	Segments	Branch
77.4%	4	`p`
79.7%	2	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes12.0ms (0.1%)

Counts

15 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)))))) (.f64 p (.f64 p (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))

Outputs

#s(literal 1 binary64)

(neg.f64 (/.f64 p x))

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

Calls

2 calls:

5.0ms	x
5.0ms	p

Results

Accuracy	Segments	Branch
74.5%	3	`p`
71.4%	3	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0.1%)

Counts

14 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)))))) (.f64 p (.f64 p (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
74.2%	3	`p`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

11 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(.f64 (.f64 p p) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(.f64 (.f64 p p) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 p p) #s(literal 11/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (+.f64 (.f64 (.f64 p p) (/.f64 (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 #s(literal 11/8 binary64) (/.f64 (.f64 (.f64 p p) #s(literal -69/16 binary64)) (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 p p) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 p p) (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 p (.f64 p #s(literal -69/16 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 11/8 binary64) (.f64 x x)) (.f64 x x)))))) (.f64 p (.f64 p (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))

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

Calls

2 calls:

4.0ms	x
4.0ms	p

Results

Accuracy	Segments	Branch
54.6%	2	`x`
38.0%	3	`p`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

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

2 calls:

1.0ms	p
1.0ms	x

Results

Accuracy	Segments	Branch
34.4%	1	`p`
34.4%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.02507011590957418

Compiler

Compiled 24 to 18 computations (25% saved)

bsearch30.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
27.0ms	-235236825.74324536	-11986591.427121857

Results

12.0ms	30×	2	valid
6.0ms	63×	0	valid
4.0ms	19×	1	valid

Compiler

Compiled 290 to 193 computations (33.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-sqrt: 5.0ms (32.3% of total)

ival-mult: 5.0ms (32.3% of total)

ival-div: 2.0ms (12.9% of total)

ival-add: 2.0ms (12.9% of total)

backward-pass: 1.0ms (6.5% of total)

const: 0.0ms (0% of total)

bsearch82.0ms (0.7%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
36.0ms	5.0652125150856495e-28	2.2000411085521664e-24
38.0ms	3.9349016007046675e-264	1.5935051674577405e-259

Results

35.0ms	72×	2	valid
13.0ms	138×	0	valid
11.0ms	20×	3	valid
5.0ms	26×	1	valid

Compiler

Compiled 336 to 250 computations (25.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 13.0ms (37.6% of total)

ival-sqrt: 8.0ms (23.1% of total)

ival-add: 5.0ms (14.5% of total)

ival-div: 4.0ms (11.6% of total)

backward-pass: 4.0ms (11.6% of total)

const: 1.0ms (2.9% of total)

bsearch142.0ms (1.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
95.0ms	5.0652125150856495e-28	2.2000411085521664e-24
40.0ms	3.9349016007046675e-264	1.5935051674577405e-259

Results

78.0ms	29×	1	valid
25.0ms	58×	2	valid
15.0ms	151×	0	valid
8.0ms	18×	3	valid

Compiler

Compiled 208 to 170 computations (18.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 12.0ms (34.2% of total)

ival-sqrt: 7.0ms (20% of total)

backward-pass: 6.0ms (17.1% of total)

ival-add: 5.0ms (14.3% of total)

ival-div: 4.0ms (11.4% of total)

const: 1.0ms (2.9% of total)

bsearch100.0ms (0.9%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
97.0ms	-3.493795395680604e-142	-1.9840012779527121e-146

Results

84.0ms	94×	0	valid
4.0ms	21×	1	valid
4.0ms	13×	2	valid

Compiler

Compiled 112 to 90 computations (19.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-sqrt: 77.0ms (88.7% of total)

ival-mult: 5.0ms (5.8% of total)

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

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

backward-pass: 1.0ms (1.2% of total)

const: 0.0ms (0% of total)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
20×	`+-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	63	128
1	91	128
2	97	128
3	102	128
4	104	128

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))))
(if (<=.f64 x #s(literal -155000000 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))))))))))
(if (<=.f64 p #s(literal 2105036471864423/2215827865120445285436604169234485268788427414982608644747394113713414456189281304992986194038624093815384393617798347846350945898212351959632084639523021319185153902243763020549247279516306127414463752183841820368271691660401046407456843466086176161485977628013706077372678144 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6690223559559187/1393796574908163946345982392040522594123776 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))))
(if (<=.f64 p #s(literal 9001800702051809/69244620785013915169893880288577664649638356718206520148356066053544201755915040781030818563707002931730762300556198370198467059319135998738502644985094416224536059445117594392163977484884566481701992255745056886508490364387532700233026358315193005046436800875428314917896192 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6132704929595921/11150372599265311570767859136324180752990208 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -8997827589086393/449891379454319638281053850768598185886969711830191663310075557261183758067148787031904068610389085714992091063352089512320826605549429968900851518086516385513472 binary64)) (neg.f64 (/.f64 p x)) #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 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) p) x) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal -155000000 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))))))))))
(if (<=.f64 x #s(literal -155000000 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) p) x) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 p (.f64 p (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -2 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))))))))))
(if (<=.f64 p #s(literal 2105036471864423/2215827865120445285436604169234485268788427414982608644747394113713414456189281304992986194038624093815384393617798347846350945898212351959632084639523021319185153902243763020549247279516306127414463752183841820368271691660401046407456843466086176161485977628013706077372678144 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6690223559559187/1393796574908163946345982392040522594123776 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))))
(if (<=.f64 p #s(literal 2105036471864423/2215827865120445285436604169234485268788427414982608644747394113713414456189281304992986194038624093815384393617798347846350945898212351959632084639523021319185153902243763020549247279516306127414463752183841820368271691660401046407456843466086176161485977628013706077372678144 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6690223559559187/1393796574908163946345982392040522594123776 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) p) x) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))))
(if (<=.f64 p #s(literal 9001800702051809/69244620785013915169893880288577664649638356718206520148356066053544201755915040781030818563707002931730762300556198370198467059319135998738502644985094416224536059445117594392163977484884566481701992255745056886508490364387532700233026358315193005046436800875428314917896192 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6132704929595921/11150372599265311570767859136324180752990208 binary64)) (neg.f64 (/.f64 p x)) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 p #s(literal 9001800702051809/69244620785013915169893880288577664649638356718206520148356066053544201755915040781030818563707002931730762300556198370198467059319135998738502644985094416224536059445117594392163977484884566481701992255745056886508490364387532700233026358315193005046436800875428314917896192 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6132704929595921/11150372599265311570767859136324180752990208 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) p) x) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -8997827589086393/449891379454319638281053850768598185886969711830191663310075557261183758067148787031904068610389085714992091063352089512320826605549429968900851518086516385513472 binary64)) (neg.f64 (/.f64 p x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal -8997827589086393/449891379454319638281053850768598185886969711830191663310075557261183758067148787031904068610389085714992091063352089512320826605549429968900851518086516385513472 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) p) x) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.3s (11.9%)

Rules

6082×	`-lowering-.f32`
6082×	`-lowering-.f64`
4860×	`/-lowering-/.f32`
4860×	`/-lowering-/.f64`
4524×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	178
1	207	166
2	2297	166
0	9390	166
0	381	2053
1	1209	1828
2	4341	1780
0	8565	1780
0	14	15
1	31	14
2	42	13
3	47	13
4	49	13
5	50	13
0	50	13
0	57	454
1	413	389
2	4937	387
0	8250	387

Stop Event

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

Compiler

Compiled 496 to 315 computations (36.5% saved)

preprocess151.0ms (1.3%)

Compiler: Compiled 418 to 220 computations (47.4% saved)

analyze658.0ms (5.9%)

sample2.6s (23.3%)

preprocess179.0ms (1.6%)

explain236.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize136.0ms (1.2%)

series16.0ms (0.1%)

rewrite269.0ms (2.4%)

simplify371.0ms (3.3%)

eval41.0ms (0.4%)

prune40.0ms (0.4%)

simplify59.0ms (0.5%)

localize179.0ms (1.6%)

series45.0ms (0.4%)

rewrite391.0ms (3.5%)

simplify307.0ms (2.7%)

eval135.0ms (1.2%)

prune91.0ms (0.8%)

simplify210.0ms (1.9%)

localize333.0ms (3%)

series48.0ms (0.4%)

rewrite372.0ms (3.3%)

simplify392.0ms (3.5%)

eval294.0ms (2.6%)

prune189.0ms (1.7%)

simplify223.0ms (2%)

localize267.0ms (2.4%)

series26.0ms (0.2%)

rewrite383.0ms (3.4%)

simplify367.0ms (3.3%)

eval184.0ms (1.6%)

prune177.0ms (1.6%)

regimes55.0ms (0.5%)

regimes16.0ms (0.1%)

regimes12.0ms (0.1%)

regimes7.0ms (0.1%)

regimes9.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch30.0ms (0.3%)

bsearch82.0ms (0.7%)

bsearch142.0ms (1.3%)

bsearch100.0ms (0.9%)

simplify14.0ms (0.1%)

soundness1.3s (11.9%)

preprocess151.0ms (1.3%)

end0.0ms (0%)

Profiling