Metrics for Given's Rotation SVD example

analyze631.0ms (5.5%)

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: 392.0ms

ival-mult: 126.0ms (32.1% of total)

...c/correct-round.rkt:119:19: 105.0ms (26.8% of total)

ival-sqrt: 50.0ms (12.7% of total)

ival-add: 31.0ms (7.9% of total)

ival-<: 24.0ms (6.1% of total)

ival-div: 23.0ms (5.9% of total)

ival-fabs: 22.0ms (5.6% of total)

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

const: 3.0ms (0.8% of total)

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

sample2.8s (24.5%)

Results

1.2s	6168×	0	valid
595.0ms	1236×	2	valid
323.0ms	664×	1	valid
113.0ms	188×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-mult: 434.0ms (25.3% of total)

...c/correct-round.rkt:119:19: 303.0ms (17.7% of total)

ival-sqrt: 232.0ms (13.5% of total)

ival-add: 200.0ms (11.7% of total)

backward-pass: 169.0ms (9.9% of total)

ival-<: 163.0ms (9.5% of total)

ival-div: 115.0ms (6.7% of total)

ival-fabs: 67.0ms (3.9% of total)

ival-and: 17.0ms (1% of total)

const: 16.0ms (0.9% of total)

Bogosity

preprocess130.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

2096×	`fnmadd-define`
1548×	`fma-define`
1454×	`fnmsub-define`
1440×	`fmsub-define`
1054×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	96
1	109	86
2	223	80
3	487	80
4	1042	80
5	2062	80
6	3428	80
7	4605	80
8	5316	80
9	5882	80
10	6167	80
11	6320	80
12	6378	80
13	6382	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)

explain223.0ms (1.9%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
64	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))`
34	-	4	(1.0801095361757979e-105 -9.55054109035127e+53)	`(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)))))))`
33	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
0	-	0	-	`x`
0	-	0	-	`#s(literal 1/2 binary64)`
0	-	0	-	`(*.f64 #s(literal 4 binary64) p)`
0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) p) p)`
0	-	0	-	`(+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))`
0	-	0	-	`p`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(.f64 #s(literal 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

72.0ms	374×	0	valid
57.0ms	92×	2	valid
12.0ms	30×	1	valid
11.0ms	16×	3	valid

Compiler

Compiled 213 to 44 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-mult: 23.0ms (35.7% of total)

ival-sqrt: 15.0ms (23.3% of total)

backward-pass: 10.0ms (15.5% of total)

ival-add: 9.0ms (14% of total)

ival-div: 7.0ms (10.9% of total)

const: 2.0ms (3.1% 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
▶	77.8%	(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)

simplify23.0ms (0.2%)

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)

localize109.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 #s(literal 4 binary64) (.f64 p p))
✓	accuracy	89.4%	(+.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	88.9%	(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	76.8%	(sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))

Results

39.0ms	186×	0	valid
38.0ms	47×	2	valid
6.0ms	8×	3	valid
5.0ms	15×	1	valid

Compiler

Compiled 87 to 14 computations (83.9% saved)

Precisions

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

ival-mult: 26.0ms (59.4% of total)

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

backward-pass: 4.0ms (9.1% of total)

ival-add: 4.0ms (9.1% of total)

ival-div: 3.0ms (6.9% of total)

const: 1.0ms (2.3% of total)

series25.0ms (0.2%)

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
10.0ms	x	@	-inf	(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
2.0ms	p	@	0	(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	@	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))))))

rewrite206.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1038×	`-lowering-.f32`
1038×	`-lowering-.f64`
1000×	`/-lowering-/.f32`
1000×	`/-lowering-/.f64`
722×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	37	50
2	115	50
3	401	50
4	1511	50
0	4407	50

Stop Event

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

Counts

6 → 194

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 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.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 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 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))
(exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 x #s(literal 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 -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (/.f64 x #s(literal -2 binary64)) (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 x #s(literal 2 binary64)) (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 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (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 x #s(literal 2 binary64)) (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 x #s(literal 2 binary64)) #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))
(fma.f64 #s(literal -1 binary64) (/.f64 (/.f64 x #s(literal -2 binary64)) (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 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal -1 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) x #s(literal 1/2 binary64))
(fma.f64 (/.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))
(neg.f64 (+.f64 (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) #s(literal 1/2 binary64))
(.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(+.f64 (.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 0 binary64)) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(+.f64 (.f64 (/.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) #s(literal 0 binary64)) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(+.f64 (.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal -2 binary64))) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(exp.f64 (log.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal -1/2 binary64))) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 1/2 binary64))) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 0 binary64) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))
(neg.f64 (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) x))
(/.f64 x (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) #s(literal 1/2 binary64)))
(/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))
(/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))))
(/.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 1 binary64))
(/.f64 (/.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
(/.f64 (-.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 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))) (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) (/.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) (/.f64 (/.f64 x #s(literal 2 binary64)) (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 #s(literal -2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) (/.f64 (/.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))))) (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 -1/2 binary64)) (/.f64 #s(literal 2 binary64) x))
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) (/.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal -2 binary64) x))
(/.f64 (/.f64 (/.f64 x #s(literal -2 binary64)) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (pow.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64))
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(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (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 (exp.f64 (log.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 #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)

simplify297.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

6066×	`-lowering-.f32`
6066×	`-lowering-.f64`
3762×	`+-lowering-+.f64`
3762×	`+-lowering-+.f32`
1702×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	381	2053
1	1209	1828
2	4337	1782
0	8541	1782

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 #s(literal -1/64 binary64) (/.f64 (/.f64 x (*.f64 p p)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal 1/8 binary64) (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 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (.f64 x (-.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (-.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))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1/128 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 p p)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) 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 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64))))
(+ 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))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)) (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (+.f64 (.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))))))) (pow.f64 x #s(literal 6 binary64))))) #s(literal 1 binary64)))
(* -1 (/ p x))
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))))) (+.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)) (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal -1/64 binary64)) (.f64 p p))))) (.f64 p (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (+.f64 p (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x))) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))))) (+.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)) (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal -1/64 binary64)) (.f64 p p)))) (.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 (+.f64 (.f64 (.f64 p p) (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 2 binary64) (.f64 p p))) (+.f64 (.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)))))) (/.f64 (.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))))) (+.f64 (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)) (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) #s(literal -1/64 binary64)) (.f64 p p))))) #s(literal -1/8 binary64)) (.f64 p p))) (*.f64 p (pow.f64 x #s(literal 6 binary64)))))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) 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 (.f64 (*.f64 p p) #s(literal 11/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+.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) (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))
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(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(.f64 p (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(.f64 p (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(.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 (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))) (-.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 (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))) (/.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 x (.f64 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 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(* 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 #s(literal 2 binary64) (.f64 p p)) x) x) (+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))))
(* -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 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (-.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 #s(literal 2 binary64) (.f64 p p)) x) x) (+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))) (-.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))

eval58.0ms (0.5%)

Compiler: Compiled 7281 to 1208 computations (83.4% saved)

prune44.0ms (0.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	303	11	314
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	303	12	315

Accuracy

99.9%

Counts

315 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	24.7%	(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
	29.3%	(/.f64 p (-.f64 #s(literal 0 binary64) x))
▶	26.4%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
▶	77.5%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
	16.6%	(sqrt.f64 (/.f64 (/.f64 (*.f64 p p) x) x))
▶	53.9%	(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)))))))
	54.0%	(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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))))
	53.3%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x)))))
✓	77.8%	(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))))))
▶	49.1%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
	53.4%	(sqrt.f64 #s(literal 1/2 binary64))
▶	35.5%	#s(literal 1 binary64)

Compiler

Compiled 347 to 247 computations (28.8% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 16 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) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (/.f64 #s(literal 1/4 binary64) p)))))
✓	cost-diff	(+.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	(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	(/.f64 #s(literal 1/4 binary64) p)
✓	cost-diff	(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
✓	cost-diff	(/.f64 (*.f64 p p) x)
✓	cost-diff	(/.f64 (/.f64 (*.f64 p p) x) x)
✓	cost-diff	(.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
✓	cost-diff	(/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))))))
✓	cost-diff	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))

Rules

162×	`-lowering-.f32`
162×	`-lowering-.f64`
84×	`fma-define`
70×	`fma-lowering-fma.f32`
70×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	212
1	64	207
2	106	204
3	143	204
4	193	204
5	215	204
6	216	204
0	216	204

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize167.0ms (1.5%)

Localize:

Found 16 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	99.7%	(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
✓	accuracy	96.1%	(/.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%	(/.f64 #s(literal 1/4 binary64) p)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
✓	accuracy	99.7%	(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
✓	accuracy	98.5%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x))
✓	accuracy	95.2%	(/.f64 (/.f64 (*.f64 p p) x) x)
✓	accuracy	95.2%	(/.f64 (*.f64 p p) x)
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x))
✓	accuracy	100.0%	(.f64 #s(literal 4 binary64) (.f64 p p))
✓	accuracy	99.6%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	76.8%	(sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (*.f64 x x)))

Results

88.0ms	185×	0	valid
32.0ms	71×	0	invalid

Compiler

Compiled 253 to 34 computations (86.6% saved)

Precisions

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

ival-mult: 17.0ms (38.4% of total)

ival-div: 10.0ms (22.6% of total)

ival-sqrt: 9.0ms (20.4% of total)

ival-add: 7.0ms (15.8% of total)

const: 1.0ms (2.3% of total)

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

series46.0ms (0.4%)

Counts

21 → 456

Calls

Call 1

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

Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))>
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#<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 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 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 (/ (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 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))>
#<alt (pow x 2)>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 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 (* 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

114 calls:

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

rewrite242.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2406×	`-lowering-.f32`
2406×	`-lowering-.f64`
1842×	`/-lowering-/.f32`
1842×	`/-lowering-/.f64`
1494×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	166
1	106	158
2	426	155
3	1965	155
4	6226	155
0	8255	155

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 574

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64))))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x)) #s(literal -1/2 binary64))))))
(pow.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x)) #s(literal -1/2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x)) #s(literal -1/2 binary64))))))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x)) #s(literal -1/2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x)) #s(literal -1/2 binary64))))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x)) #s(literal -1/2 binary64))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64)))))
(pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64)))))
(+.f64 #s(literal 1 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64))))
(+.f64 (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(exp.f64 (log1p.f64 (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
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(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (.f64 x x)) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 p p)) #s(literal 1/4 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p p) #s(literal -1/4 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) p)) (/.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1/4 binary64) p)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1/4 binary64) p)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 p p)) #s(literal 1/4 binary64)))
(neg.f64 (/.f64 (*.f64 p p) #s(literal -1/4 binary64)))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 p #s(literal 1/4 binary64))))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 p p)) #s(literal 4 binary64)))
(neg.f64 (*.f64 (/.f64 p #s(literal -1/4 binary64)) p))
(neg.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 0 binary64) (.f64 p p))))
(neg.f64 (*.f64 p (/.f64 p #s(literal -1/4 binary64))))
(neg.f64 (*.f64 (/.f64 p #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) p)))
(neg.f64 (/.f64 p (/.f64 #s(literal -1/4 binary64) p)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) p) p))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 p p)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 p p))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1 binary64) p)))
(/.f64 p (/.f64 #s(literal 1/4 binary64) p))
(/.f64 (*.f64 p p) #s(literal 1/4 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 p p)) #s(literal -1/4 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal -1/4 binary64) p))
(/.f64 (/.f64 p #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p))
(.f64 #s(literal 4 binary64) (.f64 p p))
(*.f64 p (/.f64 p #s(literal 1/4 binary64)))
(.f64 (.f64 p p) #s(literal 4 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 p p)) #s(literal -4 binary64))
(*.f64 (/.f64 p #s(literal 1/4 binary64)) p)
(+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x))
(+.f64 (*.f64 x x) (/.f64 p (/.f64 #s(literal 1/4 binary64) p)))
(exp.f64 (log.f64 (+.f64 (/.f64 p (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (/.f64 p (/.f64 #s(literal 1/4 binary64) p)))
(fma.f64 x x (/.f64 p (/.f64 #s(literal 1/4 binary64) p)))
(fma.f64 #s(literal 4 binary64) (.f64 p p) (.f64 x x))
(fma.f64 p (/.f64 p #s(literal 1/4 binary64)) (*.f64 x x))
(fma.f64 (.f64 p p) #s(literal 4 binary64) (.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (/.f64 p (/.f64 #s(literal 1/4 binary64) p)))
(fma.f64 (/.f64 p #s(literal 1/4 binary64)) p (*.f64 x x))
(+.f64 #s(literal 0 binary64) (*.f64 p p))
(+.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) p)) (.f64 p p))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 0 binary64)) (.f64 p p))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 p)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 p p))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 p) #s(literal -2 binary64)) #s(literal -1 binary64)))
(exp.f64 (+.f64 (log.f64 p) (log.f64 p)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 p p)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 p p)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 p p)))
(/.f64 p (/.f64 #s(literal 1 binary64) p))
(/.f64 (*.f64 p p) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 p p)) #s(literal -1 binary64))
(pow.f64 p #s(literal 2 binary64))
(pow.f64 (*.f64 p p) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 p p)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 p))
(.f64 #s(literal 1 binary64) (.f64 p p))
(*.f64 p p)
(.f64 (.f64 p p) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 p p)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) p))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 p p)))
(exp.f64 (+.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 p #s(literal 1/4 binary64))))))
(exp.f64 (+.f64 (.f64 #s(literal -1 binary64) (log.f64 (/.f64 p #s(literal 1/4 binary64)))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 p (*.f64 x #s(literal -1/4 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 4 binary64) (/.f64 x p))) (/.f64 x (/.f64 p (*.f64 x #s(literal -1/4 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 p #s(literal -1/4 binary64))) (/.f64 x (/.f64 p (*.f64 x #s(literal -1/4 binary64)))))
(neg.f64 (/.f64 x (/.f64 p (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (/.f64 x p)) x))
(/.f64 #s(literal 1 binary64) (/.f64 p (/.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 4 binary64) (/.f64 x p)) (/.f64 #s(literal 1 binary64) x)))
(/.f64 x (/.f64 #s(literal 4 binary64) (/.f64 x p)))
(/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 p (*.f64 x #s(literal -1/4 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal 4 binary64) (/.f64 x p)) #s(literal -1 binary64)))
(/.f64 (/.f64 x #s(literal 4 binary64)) (/.f64 p x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 p #s(literal -1/4 binary64)))
(/.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) p)
(/.f64 (.f64 x (.f64 x #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) p))
(/.f64 (*.f64 x (/.f64 (-.f64 #s(literal 0 binary64) x) p)) #s(literal -4 binary64))
(/.f64 (/.f64 x (/.f64 p x)) #s(literal 4 binary64))
(/.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal 1 binary64)) p)
(/.f64 (neg.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) p))
(pow.f64 (/.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p x))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 4 binary64) (/.f64 x p))))
(*.f64 x (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 p x)))
(.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x x))
(*.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) x)
(*.f64 (/.f64 x (/.f64 #s(literal 4 binary64) (/.f64 x p))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 x #s(literal -1/4 binary64)) p))
(.f64 #s(literal -1/4 binary64) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) x) p)))
(.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 (.f64 x x) #s(literal 4 binary64)))
(*.f64 (/.f64 x #s(literal 4 binary64)) (/.f64 x p))
(.f64 #s(literal -1 binary64) (/.f64 x (/.f64 p (.f64 x #s(literal -1/4 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal -1/4 binary64) p))
(*.f64 (/.f64 x p) (/.f64 x #s(literal 4 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) p) (.f64 x (*.f64 x #s(literal -1/4 binary64))))
(.f64 (/.f64 #s(literal -1/4 binary64) p) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) p))
(.f64 (.f64 x (*.f64 x #s(literal -1/4 binary64))) (/.f64 #s(literal -1 binary64) p))
(.f64 (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) x) p)) #s(literal -1/4 binary64))
(*.f64 (/.f64 x (/.f64 p x)) #s(literal 1/4 binary64))
(.f64 (/.f64 (.f64 x #s(literal -1/4 binary64)) p) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) p))

simplify390.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

6704×	`-lowering-.f32`
6704×	`-lowering-.f64`
4150×	`+-lowering-+.f64`
4150×	`+-lowering-+.f32`
1850×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	879	6265
1	2872	5482
0	8598	5482

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 456

Calls

Call 1

Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))
(+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2))))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow x 6) (sqrt 2)))))))
(* -1 (/ (* p (sqrt 2)) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 4) (sqrt 2))))) (* p (sqrt 2)))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 4) (sqrt 2))))) (* p (sqrt 2))))) x))
(sqrt 2)
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(+ (sqrt 2) (* (pow p 2) (- (* 1/2 (/ (* (pow p 2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 2))))))
(+ (sqrt 2) (* (pow p 2) (- (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6))))) (sqrt 2))) (* 1/2 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (sqrt 2))))) (/ 1 (* (pow x 2) (sqrt 2))))))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (* 1/4 (/ x p))))
(+ 1 (+ (* -1/32 (/ (pow x 2) (pow p 2))) (+ (* 1/4 (/ x p)) (* 1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) (pow p 3))))))
1
(+ 1 (* -1/4 (/ x p)))
(+ 1 (* -1 (/ (+ (* 1/32 (/ (pow x 2) p)) (* 1/4 x)) p)))
(+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3))) p)) (* -1/32 (pow x 2))) p)) (* 1/4 x)) p)))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (* x (+ (* -1/16 (/ (pow x 2) (pow p 3))) (* 1/2 (/ 1 p)))))
(+ 1 (* x (+ (* (pow x 2) (- (* 3/256 (/ (pow x 2) (pow p 5))) (* 1/16 (/ 1 (pow p 3))))) (* 1/2 (/ 1 p)))))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 2 (+ (* -2 (/ (pow p 2) (pow x 2))) (+ (* -1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(* 2 (/ (pow p 2) (pow x 2)))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (* 2 (pow p 2))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2)))) (pow x 2))
(/ (+ (* 1/2 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/2 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/2 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (* 2 (pow p 2))))) (pow x 2))
2
(+ 2 (* -2 (/ (pow p 2) (pow x 2))))
(+ 2 (* (pow p 2) (- (* 6 (/ (pow p 2) (pow x 4))) (* 2 (/ 1 (pow x 2))))))
(+ 2 (* (pow p 2) (- (* (pow p 2) (+ (* -20 (/ (pow p 2) (pow x 6))) (* 6 (/ 1 (pow x 4))))) (* 2 (/ 1 (pow x 2))))))
1
(+ 1 (* 1/2 (/ x p)))
(+ 1 (+ (* -1/16 (/ (pow x 3) (pow p 3))) (* 1/2 (/ x p))))
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(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(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)
(* 1/4 (/ (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))
(* 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
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* x (+ (* -1/32 (/ (* x (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (sqrt 1/2) p)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (.f64 p p)) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p))))
(+ (sqrt 1/2) (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (* x (+ (* -1/32 (/ (sqrt 1/2) (pow p 2))) (* -3/128 (/ (* x (sqrt 1/2)) (pow p 3))))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 p p)) (.f64 (/.f64 #s(literal -3/128 binary64) (.f64 p p)) (.f64 x (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))))))))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(-.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p)) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2))))
(-.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p)) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (* (pow x 4) (sqrt 2)))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 6) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64))) (/.f64 (.f64 (.f64 p p) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)))) #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))))))) (-.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p)) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (/ (* p (* (sqrt 1/2) (sqrt 2))) x))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2))))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))))) (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) p))))) x))
(* -1 (/ (+ (* 1/4 (/ (* (sqrt 1/2) (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 6) (sqrt 2))))) (+ (* 1/2 (/ (* (sqrt 1/2) (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2)))))) (* p (* (pow x 4) (sqrt 2))))) (* p (* (sqrt 1/2) (sqrt 2)))))) x))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (+.f64 (.f64 #s(literal -128 binary64) (pow.f64 p #s(literal 8 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (.f64 (+.f64 (.f64 (.f64 p p) (.f64 #s(literal 2 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (.f64 #s(literal 2 binary64) (.f64 p p)))))) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (+.f64 (.f64 #s(literal 1 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))))) (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))))) (.f64 p p))))) (.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 p (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))))) (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) p)))))) (+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))))) (-.f64 #s(literal 0 binary64) x))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1 (/ (* (pow p 2) (sqrt 1/2)) (* (pow x 2) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(-.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p)) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (* (pow p 2) (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 p p) (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p)) (+.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))))))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow p 2) (+ (* -1 (/ (sqrt 1/2) (* (pow x 2) (sqrt 2)))) (* (pow p 2) (+ (* -1/2 (/ (* (pow p 2) (* (sqrt 1/2) (+ (* -1 (/ (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2)))) (* (pow x 2) (pow (sqrt 2) 2)))) (* 20 (/ 1 (pow x 6)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- (* 6 (/ 1 (pow x 4))) (/ 1 (* (pow x 4) (pow (sqrt 2) 2))))) (sqrt 2))))))))
(+.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 p p) (-.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 p p))) (-.f64 (/.f64 #s(literal 20 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))))) (.f64 #s(literal 2 binary64) (.f64 x x))))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (* 1/4 (/ (* x (sqrt 1/2)) p))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (.f64 p p)) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p))))
(+ (sqrt 1/2) (+ (* -1/32 (/ (* (pow x 2) (sqrt 1/2)) (pow p 2))) (+ (* 1/4 (/ (* x (sqrt 1/2)) p)) (* 1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) (pow p 3))))))
(+.f64 (.f64 x (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (.f64 p p)) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p))) (+.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal -3/64 binary64)))) (.f64 p (.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 x (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal -1/4 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/32 (/ (* (pow x 2) (sqrt 1/2)) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) p) #s(literal 1/32 binary64))) (.f64 x (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (- (* -1/16 (pow x 3)) (* -1/64 (pow x 3)))) p)) (* -1/32 (* (pow x 2) (sqrt 1/2)))) p)) (* 1/4 (* x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 (.f64 x x) #s(literal -3/64 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) p) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal -1/32 binary64))))) p)) p))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ x p)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) x) p))
(+ 1 (* x (+ (* -1/32 (/ x (pow p 2))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/32 binary64) x) (*.f64 p p)) (/.f64 #s(literal 1/4 binary64) p))))
(+ 1 (* x (+ (* x (- (* -3/128 (/ x (pow p 3))) (* 1/32 (/ 1 (pow p 2))))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 x (+.f64 (/.f64 (.f64 #s(literal -3/128 binary64) x) (.f64 p (.f64 p p))) (/.f64 #s(literal -1/32 binary64) (.f64 p p)))))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))))
(-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 p p) (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 p p) (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (+ (* -1 (/ (pow p 2) (* (pow x 2) (sqrt 2)))) (+ (* 1/2 (/ (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2))) (* (pow x 4) (sqrt 2)))) (* 1/2 (/ (- (* -1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1 (/ (* (pow p 2) (- (* -1/2 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (/ (pow p 4) (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow x 6) (sqrt 2)))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (+.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64))) (.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -32 binary64))) (/.f64 (.f64 (.f64 p p) (+.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 6 binary64)) (/.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -2 binary64)))) #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (/.f64 (.f64 p p) (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(* -1 (/ (* p (sqrt 2)) x))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (sqrt.f64 #s(literal 2 binary64))) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (* p (sqrt 2))) x))
(/.f64 (+.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x x) p)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (* 1/2 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 2) (pow (sqrt 2) 2))))) (* p (* (pow x 4) (sqrt 2))))) (* p (sqrt 2)))) x))
(/.f64 (+.f64 (.f64 p (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 #s(literal 1 binary64) (.f64 p (.f64 p (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))))) (-.f64 (.f64 #s(literal 32 binary64) (pow.f64 p #s(literal 6 binary64))) (.f64 #s(literal 1/32 binary64) (/.f64 (pow.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64)) (.f64 p p)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) p))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 x x) p))))) (-.f64 #s(literal 0 binary64) x))
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(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)

eval190.0ms (1.7%)

Compiler: Compiled 20792 to 3774 computations (81.8% saved)

prune117.0ms (1%)

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	1164	1	1165
Fresh	0	6	6
Picked	0	5	5
Done	0	1	1
Total	1164	13	1177

Accuracy

99.9%

Counts

1177 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	24.7%	(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
▶	29.3%	(/.f64 p (-.f64 #s(literal 0 binary64) x))
✓	26.4%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
▶	49.0%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	77.5%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
▶	16.6%	(sqrt.f64 (/.f64 (/.f64 (*.f64 p p) x) x))
✓	53.9%	(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)))))))
▶	54.0%	(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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))))
	53.3%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x)))))
✓	77.8%	(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))))))
✓	49.1%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
▶	53.4%	(sqrt.f64 #s(literal 1/2 binary64))
✓	35.5%	#s(literal 1 binary64)

Compiler

Compiled 305 to 218 computations (28.5% saved)

simplify166.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 1/4 binary64) x)
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) x) p))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 p p)
✓	cost-diff	0	(/.f64 (*.f64 p p) x)
✓	cost-diff	0	(/.f64 (/.f64 (*.f64 p p) x) x)
✓	cost-diff	256	(sqrt.f64 (/.f64 (/.f64 (*.f64 p p) x) x))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) x)
✓	cost-diff	0	(/.f64 p (-.f64 #s(literal 0 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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p 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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p 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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))))
✓	cost-diff	128	(.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (*.f64 p p)))))

Rules

2972×	`fma-define`
2592×	`-lowering-.f32`
2592×	`-lowering-.f64`
1552×	`fma-lowering-fma.f32`
1552×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	227
1	77	216
2	193	213
3	538	207
4	1060	201
5	1406	201
6	3159	201
7	3924	201
8	4655	201
0	8109	201

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))))))
1/2
(/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))
(* 1/2 x)
x
(+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))))
(* p 2)
p
2
(* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))
(* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))
(+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))
(/ 1/4 p)
1/4
(/ (* (* x x) -1/64) (* p (* p p)))
(* (* x x) -1/64)
(* x x)
-1/64
(* p (* p p))
(* p p)
(/ p (- 0 x))
p
(- 0 x)
0
x
(sqrt 1/2)
1/2
(sqrt (/ (/ (* p p) x) x))
(/ (/ (* p p) x) x)
(/ (* p p) x)
(* p p)
p
x
(* (+ 1 (/ (* 1/4 x) p)) (sqrt 1/2))
(+ 1 (/ (* 1/4 x) p))
1
(/ (* 1/4 x) p)
(* 1/4 x)
1/4
x
p
(sqrt 1/2)
1/2

Outputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p 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 (.f64 x (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) p) p))) p))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) p) p))) p)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))
(/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) p) p))) p))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))))
(+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x (*.f64 x #s(literal -1/64 binary64))) p) p))) p)))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))
(.f64 x (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) p) p))) p))
(* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 x (*.f64 x #s(literal -1/64 binary64))) p) p))) p)
(+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) p) p) p))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
1/4
#s(literal 1/4 binary64)
(/ (* (* x x) -1/64) (* p (* p p)))
(/.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) p) p) p)
(* (* x x) -1/64)
(.f64 x (.f64 x #s(literal -1/64 binary64)))
(* x x)
(*.f64 x x)
-1/64
#s(literal -1/64 binary64)
(* p (* p p))
(.f64 p (.f64 p p))
(* p p)
(*.f64 p p)
(/ p (- 0 x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
p
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (/ (/ (* p p) x) x))
(fabs.f64 (/.f64 p x))
(/ (/ (* p p) x) x)
(/.f64 (/.f64 (*.f64 p p) x) x)
(/ (* p p) x)
(/.f64 (*.f64 p p) x)
(* p p)
(*.f64 p p)
p
x
(* (+ 1 (/ (* 1/4 x) p)) (sqrt 1/2))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(+ 1 (/ (* 1/4 x) p))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
1
#s(literal 1 binary64)
(/ (* 1/4 x) p)
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
x
p
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize163.0ms (1.4%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) x) p))
✓	accuracy	100.0%	(*.f64 #s(literal 1/4 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.7%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 p p)
✓	accuracy	93.9%	(/.f64 (*.f64 p p) x)
✓	accuracy	93.7%	(/.f64 (/.f64 (*.f64 p p) x) x)
✓	accuracy	65.9%	(sqrt.f64 (/.f64 (/.f64 (*.f64 p p) x) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 p (-.f64 #s(literal 0 binary64) x))
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) x)
✓	accuracy	98.3%	(.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (*.f64 p p)))))
✓	accuracy	98.0%	(/.f64 (.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 p #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))
✓	accuracy	97.6%	(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))
✓	accuracy	93.3%	(/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p)))

Results

114.0ms

256×

valid

Compiler

Compiled 276 to 34 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 15.0ms (36.2% of total)

ival-div: 14.0ms (33.8% of total)

ival-add: 5.0ms (12.1% of total)

ival-sqrt: 5.0ms (12.1% of total)

ival-sub: 1.0ms (2.4% of total)

const: 1.0ms (2.4% of total)

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

series29.0ms (0.3%)

Counts

17 → 348

Calls

Call 1

Inputs
#<alt (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))>
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))))))>
#<alt (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))>
#<alt (/ p (- 0 x))>
#<alt (- 0 x)>
#<alt (sqrt 1/2)>
#<alt (sqrt (/ (/ (* p p) x) x))>
#<alt (/ (/ (* p p) x) x)>
#<alt (/ (* p p) x)>
#<alt (* p p)>
#<alt (* (+ 1 (/ (* 1/4 x) p)) (sqrt 1/2))>
#<alt (+ 1 (/ (* 1/4 x) p))>
#<alt (/ (* 1/4 x) p)>
#<alt (* 1/4 x)>
#<alt (/ (* (* x x) -1/64) (* p (* p p)))>
#<alt (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))>

Outputs
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* -1/64 (/ (pow x 3) (pow p 3)))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 3) (pow p 3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))>
#<alt (* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))>
#<alt (* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))>
#<alt (* -1/64 (/ (pow x 3) (pow p 3)))>
#<alt (/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (* 1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (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) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (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) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))>
#<alt (+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))))>
#<alt (+ 1/2 (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))))>
#<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 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (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 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 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) (- (* 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) (+ (* -1/1024 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))>
#<alt (/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))) (pow x 4)))) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 16 (* (pow p 2) (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))))) (* 65536 (pow p 9))) (pow x 6)))) (+ (* 512 (/ (pow p 5) (pow x 2))) (+ (* 4096 (/ (pow p 7) (pow x 4))) (* 8192 (/ (pow p 7) (pow x 4)))))) (pow x 3))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (/ (+ (* 32 (pow p 3)) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* -8192 (pow p 7)) (* -4096 (pow p 7))) (pow x 4))) (* 32 (pow p 3))) (* -512 (/ (pow p 5) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* -65536 (pow p 9)) (* 16 (* (pow p 2) (+ (* -8192 (pow p 7)) (* -4096 (pow p 7)))))) (pow x 6))) (* 32 (pow p 3))) (+ (* -8192 (/ (pow p 7) (pow x 4))) (+ (* -4096 (/ (pow p 7) (pow x 4))) (* -512 (/ (pow p 5) (pow x 2)))))) (pow x 3)))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* (pow p 2) (- (* (pow p 2) (- (* -262144 (/ (pow p 2) (pow x 9))) (* 12288 (/ 1 (pow x 7))))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))))) (* 1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 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 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))))) (* -1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))>
#<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 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 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 (/ 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 (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<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) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (* 1/4 (/ (* x (sqrt 1/2)) p))>
#<alt (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))>
#<alt (* 1/4 (/ (* x (sqrt 1/2)) p))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))>
#<alt (* 1/4 (/ (* x (sqrt 1/2)) p))>
#<alt (/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)>
#<alt (/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)>
#<alt (/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt (+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ p (* 1/4 x)) p)>
#<alt (/ (+ p (* 1/4 x)) p)>
#<alt (/ (+ p (* 1/4 x)) p)>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* 1/4 (/ x p)))>
#<alt (+ 1 (* 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 (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* -1/64 (/ (pow x 2) (pow p 3)))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>

Calls

87 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))
3.0ms	x	@	0	(/ (* (* x x) -1/64) (* p (* p p)))
1.0ms	x	@	inf	(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))))
1.0ms	x	@	inf	(* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))
1.0ms	p	@	0	(* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))

rewrite337.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4252×	`-lowering-.f32`
4252×	`-lowering-.f64`
2718×	`/-lowering-/.f32`
2718×	`/-lowering-/.f64`
2094×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	158
1	136	149
2	795	146
3	7040	146
0	8959	146

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1045

Calls

Call 1

Inputs
(* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p)))))))))
(/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))))
(/ p (- 0 x))
(- 0 x)
(sqrt 1/2)
(sqrt (/ (/ (* p p) x) x))
(/ (/ (* p p) x) x)
(/ (* p p) x)
(* p p)
(* (+ 1 (/ (* 1/4 x) p)) (sqrt 1/2))
(+ 1 (/ (* 1/4 x) p))
(/ (* 1/4 x) p)
(* 1/4 x)
(/ (* (* x x) -1/64) (* p (* p p)))
(* x (* x (+ (/ 1/4 p) (/ (* (* x x) -1/64) (* p (* p p))))))

Outputs
(+.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (.f64 p p)) #s(literal -1/64 binary64))))) (fma.f64 (/.f64 #s(literal 1/4 binary64) p) x (*.f64 (/.f64 #s(literal -1/4 binary64) p) x)))
(+.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (.f64 p p)) #s(literal -1/64 binary64))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) p)) (-.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal 1/4 binary64) p) (-.f64 #s(literal 0 binary64) x))))
(+.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) p) (/.f64 (/.f64 (.f64 x x) p) (/.f64 (/.f64 p (/.f64 x p)) #s(literal -1/64 binary64))))
(+.f64 (/.f64 (/.f64 (.f64 x x) p) (/.f64 (/.f64 p (/.f64 x p)) #s(literal -1/64 binary64))) (/.f64 (.f64 x #s(literal 1/4 binary64)) p))
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(/.f64 (.f64 (+.f64 (/.f64 p #s(literal 1/4 binary64)) (/.f64 (.f64 p p) (/.f64 #s(literal -1/64 binary64) (/.f64 p (.f64 x x))))) (.f64 x x)) (/.f64 (.f64 p (/.f64 (.f64 p (.f64 p p)) (.f64 x x))) #s(literal -1/256 binary64)))
(/.f64 (.f64 (+.f64 (.f64 p (-.f64 #s(literal 0 binary64) (.f64 p p))) (/.f64 (.f64 x (.f64 (.f64 x #s(literal -1/64 binary64)) p)) #s(literal -1/4 binary64))) (.f64 x x)) (/.f64 (.f64 p (.f64 p (.f64 p p))) #s(literal -1/4 binary64)))
(/.f64 (.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (/.f64 p (/.f64 p (.f64 x (.f64 x #s(literal -1/64 binary64)))))) (.f64 x x)) (.f64 p (.f64 p p)))
(/.f64 (.f64 (+.f64 (.f64 p p) (/.f64 p (.f64 (/.f64 p (.f64 x (.f64 x #s(literal -1/64 binary64)))) #s(literal 1/4 binary64)))) (.f64 x x)) (/.f64 (.f64 p (.f64 p p)) #s(literal 1/4 binary64)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 p p) #s(literal -1/4 binary64)) (/.f64 (.f64 p (.f64 (.f64 x x) #s(literal 1/64 binary64))) p)) (.f64 x x)) (.f64 p (-.f64 #s(literal 0 binary64) (*.f64 p p))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64)))))) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 p (.f64 p (.f64 p p)))))
(/.f64 (.f64 (/.f64 (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64))))) p) (.f64 x x)) (.f64 p (*.f64 p p)))
(/.f64 (.f64 (.f64 x (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64)))))) x) (.f64 p (.f64 p (.f64 p p))))
(/.f64 (/.f64 (.f64 (.f64 x x) (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64)))))) p) (.f64 p (*.f64 p p)))
(/.f64 (/.f64 (.f64 (.f64 x x) (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64)))))) (.f64 p p)) (*.f64 p p))
(/.f64 (/.f64 (.f64 (.f64 x x) (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64)))))) (.f64 p (*.f64 p p))) p)
(.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (*.f64 p p)) #s(literal -1/64 binary64))))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (*.f64 p p)) #s(literal -1/64 binary64)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (.f64 p p)) #s(literal -1/64 binary64)))) (*.f64 x x))
(.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (*.f64 p p)) #s(literal -1/64 binary64))))) x)
(.f64 (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 p (.f64 p (.f64 p p)))) (*.f64 x x)))
(.f64 (/.f64 (.f64 x x) p) (/.f64 (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64))))) (.f64 p (*.f64 p p))))
(.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64))))) (*.f64 p p)))
(.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (neg.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (.f64 p p)) #s(literal -1/64 binary64)))))))
(.f64 (.f64 (.f64 x x) (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (.f64 x #s(literal -1/64 binary64)))))) (/.f64 #s(literal 1 binary64) (.f64 p (.f64 p (*.f64 p p)))))
(.f64 (/.f64 (.f64 x x) (.f64 p (.f64 p p))) (/.f64 (.f64 p (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 p p)) (.f64 x (*.f64 x #s(literal -1/64 binary64))))) p))
(.f64 (.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 x x) (/.f64 (.f64 p (.f64 p p)) #s(literal -1/64 binary64))))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))

simplify359.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

5270×	`-lowering-.f32`
5270×	`-lowering-.f64`
2448×	`/-lowering-/.f32`
2448×	`/-lowering-/.f64`
2262×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	439	3371
1	1287	3079
2	4297	3001
0	8204	3001

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(* 1/4 (/ x p))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(* 1/4 (/ x p))
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(* 1/4 (/ x p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(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 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) 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)))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))
(+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))))
(+ 1/2 (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (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 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) 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) (+ (* -1/1024 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* -32 (/ (pow p 3) (pow x 3)))
(/ (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))
(/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))) (pow x 4)))) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3))
(/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 16 (* (pow p 2) (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))))) (* 65536 (pow p 9))) (pow x 6)))) (+ (* 512 (/ (pow p 5) (pow x 2))) (+ (* 4096 (/ (pow p 7) (pow x 4))) (* 8192 (/ (pow p 7) (pow x 4)))))) (pow x 3))
(* -32 (/ (pow p 3) (pow x 3)))
(* -1 (/ (+ (* 32 (pow p 3)) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ (* -1 (/ (+ (* -8192 (pow p 7)) (* -4096 (pow p 7))) (pow x 4))) (* 32 (pow p 3))) (* -512 (/ (pow p 5) (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ (* -1 (/ (+ (* -65536 (pow p 9)) (* 16 (* (pow p 2) (+ (* -8192 (pow p 7)) (* -4096 (pow p 7)))))) (pow x 6))) (* 32 (pow p 3))) (+ (* -8192 (/ (pow p 7) (pow x 4))) (+ (* -4096 (/ (pow p 7) (pow x 4))) (* -512 (/ (pow p 5) (pow x 2)))))) (pow x 3)))
(* -32 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3)))))
(* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))
(* (pow p 3) (- (* (pow p 2) (- (* (pow p 2) (- (* -262144 (/ (pow p 2) (pow x 9))) (* 12288 (/ 1 (pow x 7))))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)
(/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))))) (* 1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(* 1/4 (/ x p))
(* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p))
(* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))))) (* -1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(/ 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))
(/ 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))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(* 1/4 (/ (* x (sqrt 1/2)) p))
(* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))
(* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))
(* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))
(* 1/4 (/ (* x (sqrt 1/2)) p))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))
(* 1/4 (/ (* x (sqrt 1/2)) p))
(/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(* 1/4 (/ x p))
(/ (+ p (* 1/4 x)) p)
(/ (+ p (* 1/4 x)) p)
(/ (+ p (* 1/4 x)) p)
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* 1/4 (/ x p)))
1
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* 1/4 (/ x p)))
(+ 1 (* 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)
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(* 1/4 (/ (pow x 2) p))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(* 1/4 (/ (pow x 2) p))
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(* 1/4 (/ (pow x 2) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))

Outputs
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
(* -1/64 (/ (pow x 3) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 p (*.f64 p p)))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p))))))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p))))))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p))))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 p (*.f64 p p)))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 p (.f64 p p))) (/.f64 #s(literal -1/4 binary64) (.f64 p (*.f64 x x))))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 p (.f64 p p))) (/.f64 #s(literal -1/4 binary64) (.f64 p (*.f64 x x))))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 p (.f64 p p))) (/.f64 #s(literal -1/4 binary64) (.f64 p (*.f64 x x))))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/.f64 (+.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 p p)))) (.f64 p (.f64 p p)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/.f64 (+.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 p p)))) (.f64 p (.f64 p p)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/.f64 (+.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 p p)))) (.f64 p (.f64 p p)))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x))) (.f64 p p)) (*.f64 #s(literal 1/4 binary64) x)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(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 #s(literal 1/8 binary64) (/.f64 (/.f64 x (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 #s(literal -1/64 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 p p)) (/.f64 (/.f64 #s(literal 1/8 binary64) p) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) p) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (-.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (+.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))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1/128 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 p p)))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal -16 binary64)) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))
(+.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal -16 binary64)) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 (*.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 5 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 x #s(literal 5 binary64)))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (+.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal -16 binary64)) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 (.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 5 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 x #s(literal 5 binary64))))) (/.f64 (.f64 #s(literal -256 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (pow.f64 x #s(literal 6 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal -16 binary64)) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal 256 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (.f64 x (.f64 x x))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal 256 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal 256 binary64) (/.f64 (pow.f64 p #s(literal 6 binary64)) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))))) (.f64 x (.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal -16 binary64)) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 p (.f64 p p)) (+.f64 (/.f64 (.f64 (.f64 p p) #s(literal -256 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -16 binary64) (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))))
(+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 p (.f64 p p)) (+.f64 (.f64 (.f64 p p) (+.f64 (/.f64 (.f64 #s(literal -256 binary64) (/.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -256 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 5 binary64)))))) (/.f64 #s(literal -16 binary64) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 p p)) (/.f64 (/.f64 #s(literal 1/8 binary64) p) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(+.f64 (.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 p p)) (/.f64 (/.f64 #s(literal 1/8 binary64) p) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (.f64 (/.f64 (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/32 binary64))) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 p p)) (/.f64 #s(literal 1/2 binary64) p)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 (*.f64 x x) p) (sqrt.f64 #s(literal 1/2 binary64))))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/32 (pow x 3)) (* 1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 1/32 binary64))))) (.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/32 binary64)) (.f64 p (*.f64 p 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)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal -1/32 binary64) (.f64 p (.f64 p p))) (/.f64 (.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64))))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -32 binary64))) (.f64 x (*.f64 x x))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))
(+.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -32 binary64))) (.f64 x (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal -512 binary64)) (pow.f64 x #s(literal 5 binary64)))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -32 binary64))) (.f64 x (.f64 x x))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 p #s(literal 7 binary64)) #s(literal 24576 binary64))) (pow.f64 x #s(literal 7 binary64))) (/.f64 (.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal -512 binary64)) (pow.f64 x #s(literal 5 binary64))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 p (.f64 (.f64 p p) #s(literal -32 binary64))) (.f64 x (*.f64 x x))))
(+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 p (.f64 (.f64 p p) #s(literal -32 binary64))) (.f64 #s(literal -512 binary64) (/.f64 (/.f64 (pow.f64 p #s(literal 5 binary64)) x) x))) (.f64 x (.f64 x x))))
(+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 p #s(literal 7 binary64)) #s(literal 24576 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (.f64 #s(literal 512 binary64) (/.f64 (/.f64 (pow.f64 p #s(literal 5 binary64)) x) x)) (.f64 (.f64 p (.f64 p p)) #s(literal 32 binary64)))) (.f64 x (.f64 x x))))
1/2
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(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(* 1/4 (/ (* x (sqrt 1/2)) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p)
(* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* x (+ (* 1/4 (/ (sqrt 1/2) p)) (/ (sqrt 1/2) x)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* 1/4 (/ (* x (sqrt 1/2)) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p)
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* -1/4 (/ (sqrt 1/2) p)))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) p) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* 1/4 (/ (* x (sqrt 1/2)) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p)
(/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 p (.f64 #s(literal 1/4 binary64) x))) p)
(/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 p (.f64 #s(literal 1/4 binary64) x))) p)
(/ (+ (* 1/4 (* x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 p (.f64 #s(literal 1/4 binary64) x))) p)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* 1/4 (/ (* x (sqrt 1/2)) p)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* x (+ (* 1/4 (/ 1 p)) (/ 1 x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(/ (+ p (* 1/4 x)) p)
(/.f64 (+.f64 p (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ p (* 1/4 x)) p)
(/.f64 (+.f64 p (*.f64 #s(literal 1/4 binary64) x)) p)
(/ (+ p (* 1/4 x)) p)
(/.f64 (+.f64 p (*.f64 #s(literal 1/4 binary64) x)) p)
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ x p)))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) p) #s(literal 1 binary64))
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 #s(literal 1/4 binary64) x) p)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* -1/64 (/ (pow x 2) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p)))
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 x x)) (.f64 p (.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p (*.f64 p p)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p (*.f64 p p)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 p (.f64 x x))) (/.f64 #s(literal -1/64 binary64) (.f64 p (*.f64 p p)))) (pow.f64 x #s(literal 4 binary64)))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/.f64 (+.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 p p))) x)) (.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/.f64 (+.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 p p))) x)) (.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/.f64 (+.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 p p))) x)) (.f64 p (*.f64 p p)))
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p p)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p p)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p p)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) p)
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 p p))) (-.f64 #s(literal 0 binary64) p))

eval269.0ms (2.4%)

Compiler: Compiled 42399 to 6826 computations (83.9% saved)

prune161.0ms (1.4%)

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	1419	3	1422
Fresh	0	2	2
Picked	2	3	5
Done	0	6	6
Total	1421	14	1435

Accuracy

99.9%

Counts

1435 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	24.7%	(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
▶	29.3%	(/.f64 p (neg.f64 x))
▶	7.4%	(/.f64 p x)
✓	26.4%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
▶	29.3%	(*.f64 (/.f64 #s(literal -1 binary64) x) p)
✓	49.0%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	77.5%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	53.9%	(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)))))))
✓	54.0%	(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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))))
▶	53.3%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x)))))
✓	77.8%	(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))))))
✓	49.1%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
✓	53.4%	(sqrt.f64 #s(literal 1/2 binary64))
✓	35.5%	#s(literal 1 binary64)

Compiler

Compiled 259 to 185 computations (28.6% saved)

simplify165.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))
✓	cost-diff	0	(+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x))))
✓	cost-diff	128	(.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))
✓	cost-diff	128	(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) x)
✓	cost-diff	0	(*.f64 (/.f64 #s(literal -1 binary64) x) p)
✓	cost-diff	-64	(neg.f64 x)
✓	cost-diff	0	(/.f64 p (neg.f64 x))
✓	cost-diff	0	(/.f64 p x)
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x)))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x))))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x)))))
✓	cost-diff	384	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x))

Rules

3360×	`-lowering-.f32`
3360×	`-lowering-.f64`
1516×	`times-frac`
1396×	`fnmadd-define`
952×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	34	199
1	77	189
2	231	171
3	742	163
4	1959	160
5	5085	159
0	8355	159

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))))
(+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))))
1/2
(/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))
(* 1/2 x)
x
(* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))
(+ 1 (/ (/ (* 2 (* p p)) x) x))
1
(/ (/ (* 2 (* p p)) x) x)
(/ (* 2 (* p p)) x)
(* 2 (* p p))
2
(* p p)
p
(- 0 x)
0
(/ p x)
p
x
(/ p (neg x))
p
(neg x)
x
(* (/ -1 x) p)
(/ -1 x)
-1
x
p
(/ (+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))) (- 0 x))
(+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x))))
p
(/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))
(* 1/8 (* (pow p 4) -12))
1/8
(* (pow p 4) -12)
(pow p 4)
4
-12
(* p (* x x))
(* x x)
x
(- 0 x)
0

Outputs
(sqrt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 (/.f64 p x) #s(literal -2 binary64))) x)))))
(+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 (/.f64 p x) #s(literal -2 binary64))) x))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 (/.f64 p x) #s(literal -2 binary64))) x)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))
(-.f64 (.f64 p (.f64 (/.f64 p x) #s(literal -2 binary64))) x)
(+ 1 (/ (/ (* 2 (* p p)) x) x))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x)))
1
#s(literal 1 binary64)
(/ (/ (* 2 (* p p)) x) x)
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (*.f64 x x))
(/ (* 2 (* p p)) x)
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)
(* 2 (* p p))
(.f64 #s(literal 2 binary64) (.f64 p p))
2
#s(literal 2 binary64)
(* p p)
(*.f64 p p)
p
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
(/ p x)
(/.f64 p x)
p
x
(/ p (neg x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
p
(neg x)
(-.f64 #s(literal 0 binary64) x)
x
(* (/ -1 x) p)
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
-1
#s(literal -1 binary64)
x
p
(/ (+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))) (- 0 x))
(/.f64 (-.f64 (*.f64 (/.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) x) x) #s(literal 3/2 binary64)) p) x)
(+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x))))
(-.f64 p (*.f64 (/.f64 (/.f64 (/.f64 (pow.f64 p #s(literal 4 binary64)) p) x) x) #s(literal 3/2 binary64)))
p
(/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))
(/.f64 (/.f64 (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3/2 binary64)) p) (.f64 x x))
(* 1/8 (* (pow p 4) -12))
(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -3/2 binary64))
1/8
#s(literal 1/8 binary64)
(* (pow p 4) -12)
(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))
(pow p 4)
(pow.f64 p #s(literal 4 binary64))
4
#s(literal 4 binary64)
-12
#s(literal -12 binary64)
(* p (* x x))
(.f64 x (.f64 x p))
(* x x)
(*.f64 x x)
x
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)

localize387.0ms (3.4%)

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))
✓	accuracy	99.7%	(.f64 p (.f64 x x))
✓	accuracy	98.5%	(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
✓	accuracy	70.2%	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))
✓	accuracy	100.0%	(/.f64 #s(literal -1 binary64) x)
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal -1 binary64) x) p)
✓	accuracy	100.0%	(/.f64 p (neg.f64 x))
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(/.f64 p x)
✓	accuracy	93.9%	(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)
✓	accuracy	93.7%	(/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)
✓	accuracy	79.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x)))))
✓	accuracy	77.2%	(+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x))))

Results

153.0ms	69×	2	valid
88.0ms	123×	0	valid
60.0ms	64×	1	valid

Compiler

Compiled 230 to 35 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-pow: 40.0ms (33.6% of total)

ival-div: 24.0ms (20.2% of total)

ival-mult: 24.0ms (20.2% of total)

backward-pass: 15.0ms (12.6% of total)

ival-add: 7.0ms (5.9% of total)

ival-sqrt: 4.0ms (3.4% of total)

const: 2.0ms (1.7% of total)

ival-sub: 2.0ms (1.7% of total)

ival-neg: 2.0ms (1.7% of total)

series22.0ms (0.2%)

Counts

17 → 360

Calls

Call 1

Inputs
#<alt (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))>
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))))>
#<alt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))))>
#<alt (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))>
#<alt (/ p x)>
#<alt (/ p (neg x))>
#<alt (neg x)>
#<alt (* (/ -1 x) p)>
#<alt (/ -1 x)>
#<alt (/ (+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))) (- 0 x))>
#<alt (* 1/8 (* (pow p 4) -12))>
#<alt (+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x))))>
#<alt (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))>
#<alt (/ (/ (* 2 (* p p)) x) x)>
#<alt (/ (* 2 (* p p)) x)>
#<alt (* p (* x x))>
#<alt (* (pow p 4) -12)>

Outputs
#<alt (* -1 x)>
#<alt (+ (* -2 (/ (pow p 2) x)) (* -1 x))>
#<alt (+ (* -2 (/ (pow p 2) x)) (* -1 x))>
#<alt (+ (* -2 (/ (pow p 2) x)) (* -1 x))>
#<alt (* -2 (/ (pow p 2) x))>
#<alt (* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))>
#<alt (* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))>
#<alt (* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))>
#<alt (* -2 (/ (pow p 2) x))>
#<alt (* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))>
#<alt (* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))>
#<alt (* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))>
#<alt (* -2 (/ (pow p 2) x))>
#<alt (/ (+ (* -2 (pow p 2)) (* -1 (pow x 2))) x)>
#<alt (/ (+ (* -2 (pow p 2)) (* -1 (pow x 2))) x)>
#<alt (/ (+ (* -2 (pow p 2)) (* -1 (pow x 2))) x)>
#<alt (* -1 x)>
#<alt (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))>
#<alt (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))>
#<alt (* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- (* 1/8 (/ 1 (pow p 4))) (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* -1/8 (/ (- (* 1/8 (/ 1 (pow p 4))) (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2))))) (* (pow p 2) (pow (sqrt 1/2) 2)))) (* 1/16 (/ 1 (pow p 6))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 4))) (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))>
#<alt (/ p x)>
#<alt (/ (+ p (* -1 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))))) x)>
#<alt (/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (+ (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))) (* -1/2 (/ (+ (* 8 (pow p 8)) (* (pow p 2) (+ (* -4 (pow p 6)) (pow p 6)))) (* p (pow x 6))))))) x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* -1 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (+ (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))) (* -1/2 (/ (+ (* 8 (pow p 8)) (* (pow p 2) (+ (* -4 (pow p 6)) (pow p 6)))) (* p (pow x 6))))))) x))>
#<alt (/ p x)>
#<alt (* p (+ (* -1 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (+ (* (pow p 2) (- (* 3/2 (/ (pow p 2) (pow x 5))) (/ 1 (pow x 3)))) (/ 1 x)))>
#<alt (* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -5/2 (/ (pow p 2) (pow x 7))) (* 3/2 (/ 1 (pow x 5))))) (/ 1 (pow x 3)))) (/ 1 x)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 2) (pow p 2))))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (- (* -2 (/ (pow p 4) (pow x 2))) (* -1 (pow p 2))) (pow x 2))>
#<alt (/ (- (* 4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (/ (- (* -8 (/ (pow p 8) (pow x 6))) (+ (* -4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))))) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (- (* -2 (/ (pow p 4) (pow x 2))) (* -1 (pow p 2))) (pow x 2))>
#<alt (/ (- (* 4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2))))) (pow x 2))>
#<alt (/ (- (* -8 (/ (pow p 8) (pow x 6))) (+ (* -4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))))) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))>
#<alt (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))>
#<alt (* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 8))) (* 4 (/ 1 (pow x 6))))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 2) (pow p 2))))>
#<alt (- (+ 1/2 (* 1/8 (/ (pow x 4) (pow p 4)))) (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (- (+ 1/2 (* -1/16 (/ (pow x 6) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ (pow x 2) (pow p 2))))>
#<alt (- (+ 1/2 (* 1/8 (/ (pow x 4) (pow p 4)))) (* 1/4 (/ (pow x 2) (pow p 2))))>
#<alt (- (+ 1/2 (* -1/16 (/ (pow x 6) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* -1/4 (/ (pow x 2) (pow p 2)))>
#<alt (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2)))))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow p 8))) (* 1/16 (/ 1 (pow p 6))))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2)))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (* -2 (/ (pow p 4) (pow x 4))) (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))))>
#<alt (- (* 4 (/ (pow p 6) (pow x 6))) (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (* -2 (/ (pow p 4) (pow x 4))) (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))))>
#<alt (- (* 4 (/ (pow p 6) (pow x 6))) (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))) 1/2)>
#<alt (- (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))) 1/2)>
#<alt (* -1/4 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/4 (pow x 2)) (* 1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/4 (pow x 2)) (* -1/16 (/ (pow x 6) (pow p 4)))) (* -1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/4 (pow x 2)) (* 1/32 (/ (pow x 8) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 2))) (* 1/16 (/ (pow x 6) (pow p 4))))) (pow p 2))>
#<alt (* -1/4 (/ (pow x 2) (pow p 2)))>
#<alt (/ (+ (* -1/4 (pow x 2)) (* 1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/4 (pow x 2)) (* -1/16 (/ (pow x 6) (pow p 4)))) (* -1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))>
#<alt (/ (- (+ (* -1/4 (pow x 2)) (* 1/32 (/ (pow x 8) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 2))) (* 1/16 (/ (pow x 6) (pow p 4))))) (pow p 2))>
#<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 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 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 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ p x))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (* -1 (/ p x))>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt p>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt p>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt p>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) (pow x 2)))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* 2 (/ (pow p 2) x))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>
#<alt (* -12 (pow p 4))>

Calls

90 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))))
1.0ms	p	@	inf	(sqrt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))))
1.0ms	x	@	inf	(sqrt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))))
1.0ms	p	@	inf	(/ (+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))) (- 0 x))
1.0ms	x	@	0	(/ (+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))) (- 0 x))

rewrite373.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3576×	`-lowering-.f32`
3576×	`-lowering-.f64`
2730×	`/-lowering-/.f32`
2730×	`/-lowering-/.f64`
1946×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	153
1	134	142
2	725	123
3	5229	116
0	8170	116

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 959

Calls

Call 1

Inputs
(* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))
(sqrt (+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))))
(+ 1/2 (/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x))))
(/ (* 1/2 x) (* (+ 1 (/ (/ (* 2 (* p p)) x) x)) (- 0 x)))
(/ p x)
(/ p (neg x))
(neg x)
(* (/ -1 x) p)
(/ -1 x)
(/ (+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))) (- 0 x))
(* 1/8 (* (pow p 4) -12))
(+ p (/ (* 1/8 (* (pow p 4) -12)) (* p (* x x))))
(/ (* 1/8 (* (pow p 4) -12)) (* p (* x x)))
(/ (/ (* 2 (* p p)) x) x)
(/ (* 2 (* p p)) x)
(* p (* x x))
(* (pow p 4) -12)

Outputs
(+.f64 #s(literal 0 binary64) (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x))
(+.f64 (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x) #s(literal 0 binary64))
(+.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(+.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) (-.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x))) #s(literal 0 binary64)) (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x))
(+.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x)))) (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x))
(-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)))
(-.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x))
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)))
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x) x) x))
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x))))
(-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x)
(fma.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 p (-.f64 #s(literal 0 binary64) p)) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal 2 binary64) (.f64 (/.f64 (.f64 p p) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 p (/.f64 (*.f64 #s(literal 2 binary64) p) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 p (.f64 (.f64 #s(literal 2 binary64) p) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 p p) (/.f64 #s(literal -2 binary64) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 p p) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 p p) (neg.f64 (/.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (.f64 p p) (.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (.f64 p p) (.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (.f64 p p) (.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 x #s(literal -1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(fma.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 x (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) #s(literal 0 binary64) (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x))
(fma.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x))) (-.f64 (/.f64 (.f64 p (*.f64 p #s(literal -2 binary64))) x) x))
(fma.f64 (-.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 p x) (/.f64 (*.f64 #s(literal 2 binary64) p) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (*.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(fma.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal -1 binary64) (+.f64 x (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)) #s(literal 0 binary64))
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(.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x))
(.f64 (.f64 #s(literal 2 binary64) p) (/.f64 p (*.f64 x x)))
(.f64 (.f64 #s(literal 2 binary64) p) (*.f64 (/.f64 p x) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 p (/.f64 x p)) (/.f64 #s(literal 2 binary64) x))
(.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 p (/.f64 x p)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) p) x) (/.f64 p x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) (.f64 p p)))
(*.f64 #s(literal -2 binary64) (/.f64 (/.f64 p (/.f64 x p)) (-.f64 #s(literal 0 binary64) x)))
(.f64 #s(literal -2 binary64) (/.f64 (/.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) x) x))
(.f64 #s(literal -2 binary64) (.f64 (/.f64 p (/.f64 x p)) (/.f64 #s(literal -1 binary64) x)))
(.f64 #s(literal -2 binary64) (/.f64 (.f64 p p) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(.f64 (.f64 p #s(literal -2 binary64)) (/.f64 p (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(.f64 (/.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) x) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (.f64 x x)) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (*.f64 p p))
(.f64 (/.f64 p (.f64 x x)) (*.f64 #s(literal 2 binary64) p))
(.f64 (/.f64 (.f64 p p) (*.f64 x x)) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 1 binary64) (.f64 p p)) (/.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) x) x))
(.f64 (/.f64 (.f64 p p) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) p) #s(literal -1 binary64)) (/.f64 (/.f64 p x) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 p p) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) x))
(*.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (/.f64 p (/.f64 x p)) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) p) #s(literal 1 binary64)) (/.f64 p (*.f64 x x)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)) (.f64 p (*.f64 p #s(literal -2 binary64))))
(.f64 (/.f64 (.f64 p (*.f64 p #s(literal -2 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) x) x))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x))
(*.f64 (/.f64 (/.f64 p (/.f64 x p)) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x))
(*.f64 (/.f64 (/.f64 p (/.f64 x p)) #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 p #s(literal -2 binary64)) x) (/.f64 p (-.f64 #s(literal 0 binary64) x)))
(.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) p)) (/.f64 p (.f64 x x)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) p) x)) (/.f64 p x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 2 binary64) p)) (/.f64 p x))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) x) p) (/.f64 p x))
(.f64 (.f64 (/.f64 (*.f64 #s(literal 2 binary64) p) x) #s(literal 1 binary64)) (/.f64 p x))
(.f64 (.f64 (/.f64 (*.f64 #s(literal 2 binary64) p) x) (/.f64 #s(literal 1 binary64) x)) p)
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal 2 binary64))) (.f64 p p))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (.f64 #s(literal 2 binary64) p))) p)
(exp.f64 (.f64 (log.f64 (/.f64 x (.f64 #s(literal 2 binary64) (*.f64 p p)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(neg.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 2 binary64) (.f64 p p))))
(/.f64 #s(literal 2 binary64) (/.f64 x (*.f64 p p)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x)
(/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 x (.f64 p (.f64 p #s(literal -2 binary64)))))
(/.f64 (/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) x) #s(literal -1 binary64))
(/.f64 (.f64 p (.f64 p #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 p p)))
(/.f64 (*.f64 #s(literal 2 binary64) p) (/.f64 x p))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) p) #s(literal 1 binary64)) (/.f64 x p))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) p) #s(literal -1 binary64)) (/.f64 x (-.f64 #s(literal 0 binary64) p)))
(/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 x (.f64 #s(literal 2 binary64) (.f64 p p))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x))
(*.f64 #s(literal 2 binary64) (/.f64 p (/.f64 x p)))
(.f64 p (/.f64 (.f64 #s(literal 2 binary64) p) x))
(.f64 p (.f64 (/.f64 p x) #s(literal 2 binary64)))
(.f64 (.f64 p p) (/.f64 #s(literal 2 binary64) x))
(.f64 (.f64 p p) (*.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(.f64 (.f64 p p) (*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) x)))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) x) #s(literal 1 binary64))
(.f64 (/.f64 p x) (.f64 #s(literal 2 binary64) p))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 p (*.f64 p #s(literal -2 binary64))) x))
(.f64 (/.f64 #s(literal -1 binary64) x) (.f64 p (*.f64 p #s(literal -2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 p (*.f64 p #s(literal -2 binary64))) x) #s(literal -1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 (.f64 #s(literal 2 binary64) p) (-.f64 #s(literal 0 binary64) x)))
(.f64 (.f64 p (*.f64 p #s(literal -2 binary64))) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 #s(literal 2 binary64) (*.f64 p p)))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 p p)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 2 binary64) p) (/.f64 p x))
(*.f64 (/.f64 p (/.f64 x p)) #s(literal 2 binary64))
(.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x)))
(.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 #s(literal 2 binary64) x) (.f64 p p))
(.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) p) x) p)
(.f64 #s(literal -2 binary64) (/.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) x))
(*.f64 #s(literal -2 binary64) (/.f64 (/.f64 p (/.f64 x p)) #s(literal -1 binary64)))
(.f64 (.f64 p #s(literal -2 binary64)) (/.f64 p (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) x) #s(literal -2 binary64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) p) #s(literal 1 binary64)) (/.f64 p x))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 p p)) (/.f64 #s(literal 2 binary64) x))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 p p)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (.f64 p p) #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) x))
(.f64 (/.f64 (.f64 p p) #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) p) #s(literal -1 binary64)) (/.f64 p (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (.f64 p p) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x))
(.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (.f64 p p) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) p) #s(literal 1 binary64)) (/.f64 p x))
(.f64 (/.f64 (.f64 p (-.f64 #s(literal 0 binary64) p)) #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) x))
(.f64 (/.f64 (.f64 p #s(literal -2 binary64)) #s(literal -1 binary64)) (/.f64 p x))
(.f64 (/.f64 (.f64 p (*.f64 p #s(literal -2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (.f64 p #s(literal -2 binary64)) x) (-.f64 #s(literal 0 binary64) p))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) p)) (/.f64 p x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 2 binary64) p)) p)
(+.f64 (.f64 (.f64 p x) #s(literal 0 binary64)) (.f64 p (.f64 x x)))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 p x)) (.f64 p (.f64 x x)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (.f64 p (.f64 x x))))
(fma.f64 #s(literal 0 binary64) (.f64 p x) (.f64 p (*.f64 x x)))
(fma.f64 (.f64 p x) #s(literal 0 binary64) (.f64 p (*.f64 x x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (.f64 p (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 p x)))
(/.f64 (.f64 p (.f64 x x)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 p (.f64 x x))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 p (*.f64 x x)))
(.f64 p (.f64 x x))
(.f64 p (/.f64 (.f64 x x) #s(literal 1 binary64)))
(.f64 x (.f64 p x))
(.f64 x (/.f64 (.f64 p x) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 p (*.f64 x x))))
(.f64 (.f64 x x) p)
(.f64 (.f64 p (*.f64 x x)) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (.f64 p x) x)
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) p))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 p x)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (*.f64 p x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (*.f64 p x) #s(literal 1 binary64)) x)
(*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))
(*.f64 #s(literal -12 binary64) (pow.f64 p #s(literal 4 binary64)))

simplify364.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

5324×	`-lowering-.f32`
5324×	`-lowering-.f64`
2456×	`/-lowering-/.f32`
2456×	`/-lowering-/.f64`
2348×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	3528
1	973	3050
2	3190	2944
0	8234	2944

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

Inputs
(* -1 x)
(+ (* -2 (/ (pow p 2) x)) (* -1 x))
(+ (* -2 (/ (pow p 2) x)) (* -1 x))
(+ (* -2 (/ (pow p 2) x)) (* -1 x))
(* -2 (/ (pow p 2) x))
(* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))
(* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))
(* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))
(* -2 (/ (pow p 2) x))
(* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))
(* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))
(* (pow p 2) (- (* -1 (/ x (pow p 2))) (* 2 (/ 1 x))))
(* -2 (/ (pow p 2) x))
(/ (+ (* -2 (pow p 2)) (* -1 (pow x 2))) x)
(/ (+ (* -2 (pow p 2)) (* -1 (pow x 2))) x)
(/ (+ (* -2 (pow p 2)) (* -1 (pow x 2))) x)
(* -1 x)
(* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))
(* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))
(* x (- (* -2 (/ (pow p 2) (pow x 2))) 1))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- (* 1/8 (/ 1 (pow p 4))) (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
(+ (sqrt 1/2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ (* -1/8 (/ (- (* 1/8 (/ 1 (pow p 4))) (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2))))) (* (pow p 2) (pow (sqrt 1/2) 2)))) (* 1/16 (/ 1 (pow p 6))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 4))) (* 1/64 (/ 1 (* (pow p 4) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* (pow p 2) (sqrt 1/2)))))))
(/ p x)
(/ (+ p (* -1 (/ (pow p 3) (pow x 2)))) x)
(/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))))) x)
(/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (+ (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))) (* -1/2 (/ (+ (* 8 (pow p 8)) (* (pow p 2) (+ (* -4 (pow p 6)) (pow p 6)))) (* p (pow x 6))))))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -1 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* -1 (/ (pow p 3) (pow x 2))) (+ (* -1/2 (/ (+ (* -4 (pow p 6)) (pow p 6)) (* p (pow x 4)))) (* -1/2 (/ (+ (* 8 (pow p 8)) (* (pow p 2) (+ (* -4 (pow p 6)) (pow p 6)))) (* p (pow x 6))))))) x))
(/ p x)
(* p (+ (* -1 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* 3/2 (/ (pow p 2) (pow x 5))) (/ 1 (pow x 3)))) (/ 1 x)))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -5/2 (/ (pow p 2) (pow x 7))) (* 3/2 (/ 1 (pow x 5))))) (/ 1 (pow x 3)))) (/ 1 x)))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2)))) (* (pow p 4) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (pow x 6)) (* 1/8 (/ (* (pow x 2) (+ (* -1/8 (pow x 4)) (* 1/64 (/ (pow x 4) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* (pow p 6) (sqrt 1/2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (sqrt 1/2)))))))
1/2
(+ 1/2 (* -1/4 (/ (pow x 2) (pow p 2))))
(+ 1/2 (* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2))))))
(/ (pow p 2) (pow x 2))
(/ (- (* -2 (/ (pow p 4) (pow x 2))) (* -1 (pow p 2))) (pow x 2))
(/ (- (* 4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (- (* -8 (/ (pow p 8) (pow x 6))) (+ (* -4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))))) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (- (* -2 (/ (pow p 4) (pow x 2))) (* -1 (pow p 2))) (pow x 2))
(/ (- (* 4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2))))) (pow x 2))
(/ (- (* -8 (/ (pow p 8) (pow x 6))) (+ (* -4 (/ (pow p 6) (pow x 4))) (+ (* -1 (pow p 2)) (* 2 (/ (pow p 4) (pow x 2)))))) (pow x 2))
(/ (pow p 2) (pow x 2))
(* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
(* (pow p 2) (+ (* (pow p 2) (- (* (pow p 2) (+ (* -8 (/ (pow p 2) (pow x 8))) (* 4 (/ 1 (pow x 6))))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2))))
1/2
(+ 1/2 (* -1/4 (/ (pow x 2) (pow p 2))))
(- (+ 1/2 (* 1/8 (/ (pow x 4) (pow p 4)))) (* 1/4 (/ (pow x 2) (pow p 2))))
(- (+ 1/2 (* -1/16 (/ (pow x 6) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
1/2
(+ 1/2 (* -1/4 (/ (pow x 2) (pow p 2))))
(- (+ 1/2 (* 1/8 (/ (pow x 4) (pow p 4)))) (* 1/4 (/ (pow x 2) (pow p 2))))
(- (+ 1/2 (* -1/16 (/ (pow x 6) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))
(* -1/4 (/ (pow x 2) (pow p 2)))
(* (pow x 2) (- (* 1/8 (/ (pow x 2) (pow p 4))) (* 1/4 (/ 1 (pow p 2)))))
(* (pow x 2) (- (* (pow x 2) (+ (* -1/16 (/ (pow x 2) (pow p 6))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2)))))
(* (pow x 2) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow p 8))) (* 1/16 (/ 1 (pow p 6))))) (* 1/8 (/ 1 (pow p 4))))) (* 1/4 (/ 1 (pow p 2)))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (* -2 (/ (pow p 4) (pow x 4))) (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))))
(- (* 4 (/ (pow p 6) (pow x 6))) (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (* -2 (/ (pow p 4) (pow x 4))) (+ 1/2 (* -1 (/ (pow p 2) (pow x 2)))))
(- (* 4 (/ (pow p 6) (pow x 6))) (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* 2 (/ (pow p 4) (pow x 4))))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))) 1/2)
(- (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))) 1/2)
(* -1/4 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (pow x 2)) (* 1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/4 (pow x 2)) (* -1/16 (/ (pow x 6) (pow p 4)))) (* -1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/4 (pow x 2)) (* 1/32 (/ (pow x 8) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 2))) (* 1/16 (/ (pow x 6) (pow p 4))))) (pow p 2))
(* -1/4 (/ (pow x 2) (pow p 2)))
(/ (+ (* -1/4 (pow x 2)) (* 1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/4 (pow x 2)) (* -1/16 (/ (pow x 6) (pow p 4)))) (* -1/8 (/ (pow x 4) (pow p 2)))) (pow p 2))
(/ (- (+ (* -1/4 (pow x 2)) (* 1/32 (/ (pow x 8) (pow p 6)))) (+ (* -1/8 (/ (pow x 4) (pow p 2))) (* 1/16 (/ (pow x 6) (pow p 4))))) (pow p 2))
(/ 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 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 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 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* -1 (/ p x))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(* -1 (/ p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
p
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) (pow x 2)))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* 2 (/ (pow p 2) x))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))
(* -12 (pow p 4))

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

eval525.0ms (4.6%)

Compiler: Compiled 23881 to 3787 computations (84.1% saved)

prune180.0ms (1.6%)

Pruning

15 alts after pruning (3 fresh and 12 done)

	Pruned	Kept	Total
New	1316	3	1319
Fresh	0	0	0
Picked	2	3	5
Done	0	9	9
Total	1318	15	1333

Accuracy

99.9%

Counts

1333 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.1%	(/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) p) x)
	29.0%	(/.f64 (-.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) x)
	29.3%	(/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x))
✓	29.3%	(/.f64 p (neg.f64 x))
✓	7.4%	(/.f64 p x)
✓	26.4%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
✓	29.3%	(*.f64 (/.f64 #s(literal -1 binary64) x) p)
✓	49.0%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	77.5%	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	53.9%	(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)))))))
✓	54.0%	(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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))))
✓	77.8%	(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))))))
✓	49.1%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
✓	53.4%	(sqrt.f64 #s(literal 1/2 binary64))
✓	35.5%	#s(literal 1 binary64)

Compiler

Compiled 447 to 241 computations (46.1% saved)

regimes44.0ms (0.4%)

Counts

20 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(/.f64 p x)
(/.f64 p (neg.f64 x))
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
(/.f64 (-.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) x)
(/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) p) x)
(/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) 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 (/.f64 (*.f64 p p) x) x))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(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)))))))
(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) 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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))))
(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))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 p p)) (.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))

Outputs

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

8.0ms	(.f64 (.f64 #s(literal 4 binary64) p) p)
7.0ms	p
6.0ms	x
6.0ms	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))
5.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))

Results

Accuracy	Segments	Branch
77.8%	1	`p`
83.4%	2	`x`
99.9%	2	`(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x)))))))`
99.9%	2	`(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (.f64 x x))))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))`
99.9%	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))`
77.8%	1	`(.f64 (.f64 #s(literal 4 binary64) p) p)`

Compiler

Compiled 80 to 56 computations (30% saved)

regimes13.0ms (0.1%)

Counts

17 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(/.f64 p x)
(/.f64 p (neg.f64 x))
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
(/.f64 (-.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) x)
(/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) p) x)
(/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) 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 (/.f64 (*.f64 p p) x) x))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(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)))))))
(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) 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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (.f64 p p))))))))))

Outputs

(/.f64 (*.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x))

#s(literal 1 binary64)

(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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))))))))))

Calls

2 calls:

5.0ms	x
5.0ms	p

Results

Accuracy	Segments	Branch
72.3%	3	`p`
66.1%	3	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0.1%)

Counts

16 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(/.f64 p x)
(/.f64 p (neg.f64 x))
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
(/.f64 (-.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) x)
(/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) p) x)
(/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) 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 (/.f64 (*.f64 p p) x) x))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) x) p)) (sqrt.f64 #s(literal 1/2 binary64)))
(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)))))))
(/.f64 (+.f64 p (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (.f64 p (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x)))))

Outputs

(/.f64 (*.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x))

#s(literal 1 binary64)

(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

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
72.3%	3	`p`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes5.0ms (0%)

Counts

13 → 3

Calls

Call 1

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

Outputs

(/.f64 (*.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x))

#s(literal 1 binary64)

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
71.8%	3	`p`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes7.0ms (0.1%)

Counts

9 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(/.f64 p x)
(/.f64 p (neg.f64 x))
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (.f64 p p) x) x)))
(/.f64 (-.f64 (/.f64 (.f64 p (.f64 p p)) (*.f64 x x)) p) x)
(/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) p) x)
(/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x))

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

Calls

2 calls:

3.0ms	p
3.0ms	x

Results

Accuracy	Segments	Branch
58.7%	2	`x`
38.6%	2	`p`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	x
1.0ms	p

Results

Accuracy	Segments	Branch
35.5%	1	`p`
37.8%	2	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes1.0ms (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

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
35.5%	1	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999996878184	-0.9999392493375602

Compiler

Compiled 24 to 18 computations (25% saved)

bsearch64.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
44.0ms	7.225308991412635e-59	3.689467272993151e-54
16.0ms	2.0307283010386158e-85	5.811082682787723e-85

Results

32.0ms	135×	0	valid
14.0ms	46×	2	valid
5.0ms	27×	1	valid

Compiler

Compiled 440 to 316 computations (28.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-sqrt: 24.0ms (58.3% of total)

ival-mult: 8.0ms (19.4% of total)

ival-div: 3.0ms (7.3% of total)

ival-add: 3.0ms (7.3% of total)

backward-pass: 2.0ms (4.9% of total)

const: 1.0ms (2.4% of total)

bsearch56.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
35.0ms	7.225308991412635e-59	3.689467272993151e-54
16.0ms	2.0307283010386158e-85	5.811082682787723e-85

Results

24.0ms	43×	2	valid
13.0ms	131×	0	valid
7.0ms	34×	1	valid

Compiler

Compiled 344 to 260 computations (24.4% saved)

Precisions

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

ival-mult: 18.0ms (56.3% of total)

ival-sqrt: 5.0ms (15.6% of total)

ival-div: 3.0ms (9.4% of total)

ival-add: 3.0ms (9.4% of total)

backward-pass: 2.0ms (6.3% of total)

const: 1.0ms (3.1% of total)

bsearch81.0ms (0.7%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
61.0ms	7.225308991412635e-59	3.689467272993151e-54
16.0ms	2.0307283010386158e-85	5.811082682787723e-85

Results

13.0ms	137×	0	valid
13.0ms	40×	2	valid
6.0ms	31×	1	valid

Compiler

Compiled 216 to 180 computations (16.7% saved)

Precisions

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

ival-mult: 8.0ms (36.9% of total)

ival-sqrt: 5.0ms (23.1% of total)

ival-div: 3.0ms (13.8% of total)

ival-add: 3.0ms (13.8% of total)

backward-pass: 2.0ms (9.2% of total)

const: 1.0ms (4.6% of total)

bsearch46.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
43.0ms	-1.5403600132778147e-110	-4.524820741438927e-114

Results

26.0ms	21×	2	valid
9.0ms	89×	0	valid
4.0ms	18×	1	valid

Compiler

Compiled 112 to 90 computations (19.6% saved)

Precisions

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

ival-div: 21.0ms (66.3% of total)

ival-mult: 5.0ms (15.8% of total)

ival-sqrt: 3.0ms (9.5% of total)

ival-add: 2.0ms (6.3% of total)

backward-pass: 1.0ms (3.2% of total)

const: 0.0ms (0% of total)

bsearch29.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
26.0ms	-3.880807519387691e+70	-6.728069105519207e+69

Results

12.0ms	33×	2	valid
4.0ms	21×	1	valid
4.0ms	38×	0	valid
2.0ms	4×	3	valid

Compiler

Compiled 84 to 66 computations (21.4% saved)

Precisions

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

ival-mult: 6.0ms (39.6% of total)

ival-sqrt: 3.0ms (19.8% of total)

ival-div: 2.0ms (13.2% of total)

backward-pass: 2.0ms (13.2% of total)

ival-add: 2.0ms (13.2% of total)

const: 0.0ms (0% of total)

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

62×	`*-commutative_binary64`
62×	`neg-mul-1_binary64`
52×	`unsub-neg_binary64`
42×	`+-commutative_binary64`
32×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	82	190
1	113	190
2	123	190
3	131	190
4	142	190
5	151	190
6	163	187
7	177	187
8	221	187
9	286	187
10	302	187
11	316	187
12	319	187

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 -9006748894778255/9007199254740992 binary64)) (/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) 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 p #s(literal 2362230782765653/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296 binary64)) (/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x)) (if (<=.f64 p #s(literal 7067388259113537/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(literal 1 binary64) (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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (*.f64 p p))))))))))))
(if (<=.f64 p #s(literal 4199521391583383/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592 binary64)) (/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x)) (if (<=.f64 p #s(literal 1725436586697641/862718293348820473429344482784628181556388621521298319395315527974912 binary64)) #s(literal 1 binary64) (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 1268605420374147/4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354046107648 binary64)) (/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x)) (if (<=.f64 p #s(literal 7453886054533809/27606985387162255149739023449108101809804435888681546220650096895197184 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -6065214955889283/173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864 binary64)) (/.f64 p (neg.f64 x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal -17500000000000000119928481027344970939011281806082246507514336083181568 binary64)) (/.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 -9006748894778255/9007199254740992 binary64)) (/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) 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 -9006748894778255/9007199254740992 binary64)) (/.f64 (-.f64 (/.f64 (.f64 (.f64 p (.f64 p p)) #s(literal 3/2 binary64)) (.f64 x x)) 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 p #s(literal 2362230782765653/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296 binary64)) (/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x)) (if (<=.f64 p #s(literal 7067388259113537/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(literal 1 binary64) (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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (*.f64 p p))))))))))))
(if (<=.f64 p #s(literal 2362230782765653/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296 binary64)) (/.f64 (.f64 p (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -3/2 binary64)) x) x))) x) (if (<=.f64 p #s(literal 7067388259113537/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(literal 1 binary64) (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 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (.f64 (.f64 x x) #s(literal -1/64 binary64)) (.f64 p (*.f64 p p))))))))))))
(if (<=.f64 p #s(literal 4199521391583383/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592 binary64)) (/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x)) (if (<=.f64 p #s(literal 1725436586697641/862718293348820473429344482784628181556388621521298319395315527974912 binary64)) #s(literal 1 binary64) (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 4199521391583383/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592 binary64)) (/.f64 (.f64 p (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (.f64 (.f64 p p) #s(literal -3/2 binary64)) x) x))) x) (if (<=.f64 p #s(literal 1725436586697641/862718293348820473429344482784628181556388621521298319395315527974912 binary64)) #s(literal 1 binary64) (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 1268605420374147/4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354046107648 binary64)) (/.f64 (.f64 p (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) (-.f64 #s(literal 0 binary64) x)) (if (<=.f64 p #s(literal 7453886054533809/27606985387162255149739023449108101809804435888681546220650096895197184 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 p #s(literal 1268605420374147/4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354046107648 binary64)) (/.f64 (.f64 p (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (.f64 (*.f64 p p) #s(literal -3/2 binary64)) x) x))) x) (if (<=.f64 p #s(literal 7453886054533809/27606985387162255149739023449108101809804435888681546220650096895197184 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -6065214955889283/173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864 binary64)) (/.f64 p (neg.f64 x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal -6065214955889283/173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631086950685087723239310884864 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal -17500000000000000119928481027344970939011281806082246507514336083181568 binary64)) (/.f64 p x) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.8s (15.3%)

Rules

6066×	`-lowering-.f32`
6066×	`-lowering-.f64`
5324×	`-lowering-.f32`
5324×	`-lowering-.f64`
5270×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	439	3371
1	1287	3079
2	4297	3001
0	8204	3001
0	316	3528
1	973	3050
2	3190	2944
0	8234	2944
0	381	2053
1	1209	1828
2	4337	1782
0	8541	1782
0	33	158
1	136	149
2	795	146
3	7040	146
0	8959	146
0	14	15
1	31	14
2	42	13
3	47	13
4	49	13
5	50	13
0	50	13

Stop Event

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

Compiler

Compiled 593 to 367 computations (38.1% saved)

preprocess63.0ms (0.5%)

Compiler: Compiled 548 to 262 computations (52.2% saved)

Iter	Nodes	Cost
0	82	190
1	113	190
2	123	190
3	131	190
4	142	190
5	151	190
6	163	187
7	177	187
8	221	187
9	286	187
10	302	187
11	316	187
12	319	187

Iter	Nodes	Cost
0	82	190
1	113	190
2	123	190
3	131	190
4	142	190
5	151	190
6	163	187
7	177	187
8	221	187
9	286	187
10	302	187
11	316	187
12	319	187

analyze631.0ms (5.5%)

sample2.8s (24.5%)

preprocess130.0ms (1.1%)

explain223.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify23.0ms (0.2%)

localize109.0ms (0.9%)

series25.0ms (0.2%)

rewrite206.0ms (1.8%)

simplify297.0ms (2.6%)

eval58.0ms (0.5%)

prune44.0ms (0.4%)

simplify26.0ms (0.2%)

localize167.0ms (1.5%)

series46.0ms (0.4%)

rewrite242.0ms (2.1%)

simplify390.0ms (3.4%)

eval190.0ms (1.7%)

prune117.0ms (1%)

simplify166.0ms (1.4%)

localize163.0ms (1.4%)

series29.0ms (0.3%)

rewrite337.0ms (2.9%)

simplify359.0ms (3.1%)

eval269.0ms (2.4%)

prune161.0ms (1.4%)

simplify165.0ms (1.4%)

localize387.0ms (3.4%)

series22.0ms (0.2%)

rewrite373.0ms (3.3%)

simplify364.0ms (3.2%)

eval525.0ms (4.6%)

prune180.0ms (1.6%)

regimes44.0ms (0.4%)

regimes13.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0%)

regimes7.0ms (0.1%)

regimes11.0ms (0.1%)

regimes1.0ms (0%)

bsearch0.0ms (0%)

bsearch64.0ms (0.6%)

bsearch56.0ms (0.5%)

bsearch81.0ms (0.7%)

bsearch46.0ms (0.4%)

bsearch29.0ms (0.3%)

simplify36.0ms (0.3%)

soundness1.8s (15.3%)

preprocess63.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	82	190
1	113	190
2	123	190
3	131	190
4	142	190
5	151	190
6	163	187
7	177	187
8	221	187
9	286	187
10	302	187
11	316	187
12	319	187