Metrics for Given's Rotation SVD example, simplified

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 14 to 10 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

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

const: 0.0ms (0% of total)

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

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

compiled-spec: 0.0ms (0% of total)

sample9.0s (48.3%)

Results

6.4s	8000×	5	exit
882.0ms	8256×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.8s

backward-pass: 1.4s (21.3% of total)

compiled-spec: 1.4s (21% of total)

ival-sqrt: 1.2s (17.5% of total)

ival-mult: 942.0ms (13.9% of total)

ival-div: 685.0ms (10.1% of total)

ival-add: 573.0ms (8.5% of total)

ival-sub: 437.0ms (6.5% of total)

const: 85.0ms (1.3% of total)

Bogosity

preprocess35.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

128×	`fnmsub-define`
128×	`fmsub-define`
128×	`fnmadd-define`
86×	`fma-define`
80×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	53	30
2	99	30
3	160	30
4	268	30
5	412	30
6	518	30
7	564	30
8	576	30
0	12	11
1	32	10
2	40	10
3	48	10
4	56	10
5	69	10
6	86	10
7	100	10
8	112	10
9	113	10
0	113	10

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

Outputs

(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))

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

Call 2

Inputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x)))))))
(neg (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x))))))))

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

Symmetry

(abs x)

explain127.0ms (0.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
0	-	-	`x`
0	-	-	`#s(literal 1/2 binary64)`
0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
0	-	-	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
0	-	-	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
0	-	-	`(hypot.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`

Results

82.0ms

512×

valid

Compiler

Compiled 115 to 29 computations (74.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

compiled-spec: 18.0ms (35.4% of total)

ival-mult: 11.0ms (21.6% of total)

ival-sqrt: 9.0ms (17.7% of total)

ival-add: 5.0ms (9.8% of total)

ival-div: 4.0ms (7.9% of total)

ival-sub: 3.0ms (5.9% of total)

const: 1.0ms (2% of total)

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

eval0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

32×	`sum3-define`
32×	`+-lowering-+.f64`
32×	`+-lowering-+.f32`
18×	`--lowering--.f32`
18×	`--lowering--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	19	36
2	24	36
3	30	36
4	38	36
5	51	36
6	68	36
7	82	36
8	94	36
9	95	36
0	95	36

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize81.0ms (0.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	accuracy	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

35.0ms

256×

valid

Compiler

Compiled 38 to 9 computations (76.3% saved)

Precisions

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

compiled-spec: 8.0ms (36.3% of total)

ival-mult: 4.0ms (18.1% of total)

ival-sqrt: 4.0ms (18.1% of total)

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

ival-div: 2.0ms (9.1% of total)

ival-sub: 1.0ms (4.5% of total)

const: 1.0ms (4.5% of total)

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

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
1.0ms	x	@	0	(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
0.0ms	x	@	inf	(sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))))
0.0ms	x	@	-inf	(- 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))
0.0ms	x	@	inf	(+ 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))

rewrite264.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3000×	`-lowering-.f32`
3000×	`-lowering-.f64`
2846×	`/-lowering-/.f32`
2846×	`/-lowering-/.f64`
1192×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	67	30
2	542	30
3	6579	30
0	8361	30

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 198

Calls

Call 1

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

Outputs
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (neg.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(neg.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)))
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(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64))) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/64 binary64) (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1/64 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/2 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/16 binary64) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))))))
(/.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64)))) (+.f64 #s(literal 1/64 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64)))) (-.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (+.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 3/2 binary64))))) (+.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(neg.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(.f64 #s(literal -1/2 binary64) (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))))))
(.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

simplify245.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2628×	`-lowering-.f32`
2628×	`-lowering-.f64`
1684×	`+-lowering-+.f64`
1684×	`+-lowering-+.f32`
1572×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	619
1	515	526
2	1480	510
3	4246	508
0	8047	508

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
1/2
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))

Outputs
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(+.f64 (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (/.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x))))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x))))
(- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 11/128 binary64) (.f64 x (.f64 x #s(literal -69/1024 binary64))))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x)) (/.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) #s(literal 3/16 binary64)))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 3/16 binary64) (.f64 (.f64 x x) #s(literal -5/32 binary64)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) #s(literal 3/16 binary64)))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 3/16 binary64) (.f64 (.f64 x x) #s(literal -5/32 binary64)))))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (/.f64 #s(literal -5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal -5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))) x)

eval32.0ms (0.2%)

Compiler: Compiled 6645 to 963 computations (85.5% saved)

prune41.0ms (0.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	232	14	246
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	232	15	247

Accuracy

100.0%

Counts

247 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
	98.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
	4.5%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
	1.2%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
▶	97.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
	97.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
	96.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	95.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶	3.1%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
	99.8%	(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))) (-.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
▶	1.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
	4.1%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
▶	1.2%	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
	4.5%	(.f64 #s(literal 1/8 binary64) (.f64 x x))

Compiler

Compiled 441 to 278 computations (37% saved)

simplify231.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
✓	cost-diff	128	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(hypot.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Rules

2202×	`-lowering-.f32`
2202×	`-lowering-.f64`
2002×	`fma-lowering-fma.f32`
2002×	`fma-lowering-fma.f64`
1848×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	240
1	101	225
2	312	225
3	748	225
4	1643	225
5	3171	225
6	3547	225
7	3830	225
8	4641	225
9	5444	225
0	8515	225

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))))
(+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))
1/2
(/ -1/2 (sqrt (+ (* 1 1) (* x x))))
-1/2
(sqrt (+ (* 1 1) (* x x)))
1
x
(+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))
(sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))
(- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))
(- 1 1)
1
(* x (* x (+ 1/8 (* (* x x) -11/128))))
x
(* x (+ 1/8 (* (* x x) -11/128)))
(+ 1/8 (* (* x x) -11/128))
1/8
(* (* x x) -11/128)
(* x x)
-11/128
(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))))
(* x x)
x
(+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))))
1/8
(* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))
(+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))
-11/128
(* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))
(+ 69/1024 (* (* x x) -1843/32768))
69/1024
(* (* x x) -1843/32768)
-1843/32768
(- 1 (sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))))
1
(sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x)))
(+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))
1/2
(/ (- 1/2 (/ 1/4 (* x x))) x)
(- 1/2 (/ 1/4 (* x x)))
(/ 1/4 (* x x))
1/4
(* x x)
x

Outputs
(/ (+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
1/2
#s(literal 1/2 binary64)
(/ -1/2 (sqrt (+ (* 1 1) (* x x))))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
-1/2
#s(literal -1/2 binary64)
(sqrt (+ (* 1 1) (* x x)))
(hypot.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(- 1 1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
(* x (* x (+ 1/8 (* (* x x) -11/128))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
x
(* x (+ 1/8 (* (* x x) -11/128)))
(.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64))))
(+ 1/8 (* (* x x) -11/128))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
1/8
#s(literal 1/8 binary64)
(* (* x x) -11/128)
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* x x)
(*.f64 x x)
-11/128
#s(literal -11/128 binary64)
(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(* x x)
(*.f64 x x)
x
(+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))
1/8
#s(literal 1/8 binary64)
(* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))
(.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))
(+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))
(+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))
-11/128
#s(literal -11/128 binary64)
(* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(+ 69/1024 (* (* x x) -1843/32768))
(+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))
69/1024
#s(literal 69/1024 binary64)
(* (* x x) -1843/32768)
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
-1843/32768
#s(literal -1843/32768 binary64)
(- 1 (sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
(+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
1/2
#s(literal 1/2 binary64)
(/ (- 1/2 (/ 1/4 (* x x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(- 1/2 (/ 1/4 (* x x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/ 1/4 (* x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
x

localize183.0ms (1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)))
✓	accuracy	98.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
✓	accuracy	98.3%	(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
✓	accuracy	99.2%	(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
✓	accuracy	99.5%	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

117.0ms	254×	0	valid
3.0ms	2×	0	invalid

Compiler

Compiled 274 to 36 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 16.0ms (28.3% of total)

ival-add: 10.0ms (17.7% of total)

compiled-spec: 9.0ms (15.9% of total)

ival-div: 8.0ms (14.2% of total)

ival-sub: 7.0ms (12.4% of total)

ival-sqrt: 6.0ms (10.6% of total)

const: 1.0ms (1.8% of total)

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

series19.0ms (0.1%)

Counts

22 → 252

Calls

Call 1

Inputs
#<alt (/ (+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))))>
#<alt (+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))>
#<alt (/ -1/2 (sqrt (+ (* 1 1) (* x x))))>
#<alt (sqrt (+ (* 1 1) (* x x)))>
#<alt (- 1 1)>
#<alt (* x (* x (+ 1/8 (* (* x x) -11/128))))>
#<alt (* x (+ 1/8 (* (* x x) -11/128)))>
#<alt (+ 1/8 (* (* x x) -11/128))>
#<alt (* (* x x) -11/128)>
#<alt (* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))))>
#<alt (* x x)>
#<alt (+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))))>
#<alt (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))>
#<alt (- 1 (sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))))>
#<alt (sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x)))>
#<alt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))>
#<alt (/ (- 1/2 (/ 1/4 (* x x))) x)>
#<alt (+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))>
#<alt (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))>
#<alt (* (* x x) -1843/32768)>
#<alt (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))>
#<alt (/ 1/4 (* x x))>

Outputs
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))>
#<alt (- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))>
#<alt (+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)>
#<alt (/ -1/2 x)>
#<alt (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)>
#<alt (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)>
#<alt (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))>
#<alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* x (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (* -1843/32768 (pow x 8))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 8))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))>
#<alt (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4)))>
#<alt (/ (- (pow x 2) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (/ (- (* (pow x 2) (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (/ (- (* (pow x 2) (+ 1 (* x (- (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 5)) (/ 1 (sqrt -1/4)))) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/4) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (/ -1/4 (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (/ -1/4 (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt 2>
#<alt (+ 2 (* -1/8 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* -1843/32768 (pow x 4))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* -1843/32768 (pow x 4))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ 1/4 (pow x 2))>

Calls

63 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ (+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))))
1.0ms	x	@	inf	(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))))
1.0ms	x	@	0	(- 1 (sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))))
1.0ms	x	@	-inf	(/ (+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))))
1.0ms	x	@	0	(sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x)))

rewrite360.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4226×	`-lowering-.f32`
4226×	`-lowering-.f64`
2380×	`/-lowering-/.f32`
2380×	`/-lowering-/.f64`
2112×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	189
1	255	177
2	2425	177
0	8990	177

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 446

Calls

Call 1

Inputs
(/ (+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))))
(+ 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))
(/ -1/2 (sqrt (+ (* 1 1) (* x x))))
(sqrt (+ (* 1 1) (* x x)))
(- 1 1)
(* x (* x (+ 1/8 (* (* x x) -11/128))))
(* x (+ 1/8 (* (* x x) -11/128)))
(+ 1/8 (* (* x x) -11/128))
(* (* x x) -11/128)
(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))))
(* x x)
(+ 1/8 (* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))))
(* (* x x) (+ -11/128 (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))))
(- 1 (sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))))
(sqrt (+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x)))
(+ 1/2 (/ (- 1/2 (/ 1/4 (* x x))) x))
(/ (- 1/2 (/ 1/4 (* x x))) x)
(+ 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))
(sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))
(* (* x x) -1843/32768)
(* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))
(/ 1/4 (* x x))

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

simplify339.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

4516×	`-lowering-.f32`
4516×	`-lowering-.f64`
2482×	`+-lowering-+.f64`
2482×	`+-lowering-+.f32`
2022×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	396	3174
1	1332	2647
2	4643	2589
0	8363	2589

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(/ -1/2 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))
(* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))
(* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4)))
(/ (- (pow x 2) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(/ (- (* (pow x 2) (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(/ (- (* (pow x 2) (+ 1 (* x (- (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))))))) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))
(/ (+ (* 1/4 (* (sqrt (pow x 5)) (/ 1 (sqrt -1/4)))) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/4) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(/ -1/4 (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(/ -1/4 (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
2
(+ 2 (* -1/8 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+ 1 (sqrt 1/2))
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* 69/1024 (pow x 2))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 2))

Outputs
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64))))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) x))
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(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal -3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (.f64 x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(/ -1/4 (pow x 3))
(/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x)))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64))) x) (/.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x x))))
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64))) x) (/.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(/ -1/4 (pow x 3))
(/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x)))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
2
#s(literal 2 binary64)
(+ 2 (* -1/8 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))))
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal 11/128 binary64)))))))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) x) x))))
(+ 1 (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal -3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (.f64 x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x)))
(+ 1 (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(-.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal 11/128 binary64)))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 (+.f64 #s(literal 11/128 binary64) (.f64 (.f64 x x) #s(literal -69/1024 binary64))) x) x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal -3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (.f64 x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* 69/1024 (pow x 2))
(.f64 x (.f64 x #s(literal 69/1024 binary64)))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* -1843/32768 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* -1843/32768 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))

eval154.0ms (0.8%)

Compiler: Compiled 22052 to 2569 computations (88.4% saved)

prune91.0ms (0.5%)

Pruning

19 alts after pruning (15 fresh and 4 done)

	Pruned	Kept	Total
New	863	8	871
Fresh	2	7	9
Picked	2	3	5
Done	0	1	1
Total	867	19	886

Accuracy

100.0%

Counts

886 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.6%	(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
	98.2%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
✓	99.9%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
	98.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
	96.8%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	4.5%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
	1.2%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
✓	97.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
	97.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
▶	96.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	95.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	96.5%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
▶	1.2%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
▶	1.4%	(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
✓	1.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
	4.1%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
	4.5%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
▶	3.1%	#s(literal 0 binary64)

Compiler

Compiled 497 to 317 computations (36.2% saved)

simplify151.0ms (0.8%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
✓	cost-diff	256	(+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
✓	cost-diff	128	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))

Rules

1678×	`sum3-define`
1492×	`-lowering-.f32`
1492×	`-lowering-.f64`
1480×	`sum5-define`
1266×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	234
1	89	218
2	273	218
3	859	216
4	1782	216
5	2693	216
6	3202	216
7	4516	216
0	8101	216

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
(- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
1
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
1/2
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(+ 1/2 (/ -1/4 (* x x)))
(/ -1/4 (* x x))
-1/4
(* x x)
x
(+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
0
(* (+ 1/8 (* (* x x) -11/128)) (* x x))
(+ 1/8 (* (* x x) -11/128))
1/8
(* (* x x) -11/128)
(* x x)
x
-11/128
(* (* x x) (+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8)))
(* x x)
x
(+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8))
(* (* x x) -11/128)
-11/128
(+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8)
(* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))
(* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))
(+ 69/1024 (* (* x x) -1843/32768))
69/1024
(* (* x x) -1843/32768)
-1843/32768
1/8
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
1
(sqrt (+ 1/2 (/ 1/2 x)))
(+ 1/2 (/ 1/2 x))
1/2
(/ 1/2 x)
x

Outputs
(/ (- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
1
#s(literal 1 binary64)
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
1/2
#s(literal 1/2 binary64)
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(+ 1/2 (/ -1/4 (* x x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/ -1/4 (* x x))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
-1/4
#s(literal -1/4 binary64)
(* x x)
(*.f64 x x)
x
(+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
0
#s(literal 0 binary64)
(* (+ 1/8 (* (* x x) -11/128)) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(+ 1/8 (* (* x x) -11/128))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
1/8
#s(literal 1/8 binary64)
(* (* x x) -11/128)
(.f64 (.f64 x x) #s(literal -11/128 binary64))
(* x x)
(*.f64 x x)
x
-11/128
#s(literal -11/128 binary64)
(* (* x x) (+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8)))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))))
(* x x)
(*.f64 x x)
x
(+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))
(* (* x x) -11/128)
(.f64 (.f64 x x) #s(literal -11/128 binary64))
-11/128
#s(literal -11/128 binary64)
(+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8)
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))
(* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))
(* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(+ 69/1024 (* (* x x) -1843/32768))
(+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))
69/1024
#s(literal 69/1024 binary64)
(* (* x x) -1843/32768)
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
-1843/32768
#s(literal -1843/32768 binary64)
1/8
#s(literal 1/8 binary64)
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ 1/2 x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(+ 1/2 (/ 1/2 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
x

localize165.0ms (0.9%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	98.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
✓	accuracy	99.5%	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	accuracy	99.2%	(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
✓	accuracy	99.9%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
✓	accuracy	99.5%	(.f64 (.f64 x x) #s(literal -11/128 binary64))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
✓	accuracy	98.3%	(/.f64 #s(literal -1/4 binary64) (*.f64 x x))

Results

112.0ms	254×	0	valid
1.0ms	2×	0	invalid

Compiler

Compiled 281 to 33 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-add: 16.0ms (34.8% of total)

ival-mult: 12.0ms (26.1% of total)

ival-div: 10.0ms (21.8% of total)

ival-sqrt: 4.0ms (8.7% of total)

ival-sub: 3.0ms (6.5% of total)

const: 1.0ms (2.2% of total)

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

series13.0ms (0.1%)

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))>
#<alt (/ (- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))>
#<alt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))>
#<alt (/ (+ 1/2 (/ -1/4 (* x x))) x)>
#<alt (* (+ 1/8 (* (* x x) -11/128)) (* x x))>
#<alt (+ 1/8 (* (* x x) -11/128))>
#<alt (* (* x x) -11/128)>
#<alt (* x x)>
#<alt (+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8))>
#<alt (* (* x x) (+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8)))>
#<alt (- 1 (sqrt (+ 1/2 (/ 1/2 x))))>
#<alt (sqrt (+ 1/2 (/ 1/2 x)))>
#<alt (+ 1/2 (/ 1/2 x))>
#<alt (/ 1/2 x)>
#<alt (/ -1/4 (* x x))>
#<alt (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))>
#<alt (* (* x x) -1843/32768)>
#<alt (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))>
#<alt (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))>

Outputs
#<alt (/ 1/4 (pow x 3))>
#<alt (/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))>
#<alt (/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4))))>
#<alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)>
#<alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)>
#<alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (+ (* -1 (* x (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3)))) (* (sqrt (/ 1 x)) (/ (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))) (sqrt -1/4)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))>
#<alt (- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* x (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/4 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (/ -1/4 (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (/ -1/4 (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (* -11/128 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))>
#<alt (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (* -1843/32768 (pow x 8))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 8))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))>
#<alt (/ (- x (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 x)) (sqrt 1/2))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 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 (/ 1/2 x)>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4))))))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* x (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* -1843/32768 (pow x 4))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* -1843/32768 (pow x 4))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* 69/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>

Calls

57 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
1.0ms	x	@	-inf	(/ (- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
1.0ms	x	@	0	(/ (- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
0.0ms	x	@	0	(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
0.0ms	x	@	0	(sqrt (+ 1/2 (/ 1/2 x)))

rewrite425.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

5148×	`-lowering-.f32`
5148×	`-lowering-.f64`
2852×	`/-lowering-/.f32`
2852×	`/-lowering-/.f64`
2832×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	174
1	233	151
2	2275	151
0	10389	151

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 488

Calls

Call 1

Inputs
(- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(/ (- 1 (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(* (+ 1/8 (* (* x x) -11/128)) (* x x))
(+ 1/8 (* (* x x) -11/128))
(* (* x x) -11/128)
(* x x)
(+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8))
(* (* x x) (+ (* (* x x) -11/128) (+ (* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))) 1/8)))
(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
(sqrt (+ 1/2 (/ 1/2 x)))
(+ 1/2 (/ 1/2 x))
(/ 1/2 x)
(/ -1/4 (* x x))
(+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
(* (* x x) -1843/32768)
(* (* x x) (+ 69/1024 (* (* x x) -1843/32768)))
(* (* x x) (* (* x x) (+ 69/1024 (* (* x x) -1843/32768))))

Outputs
(+.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
(+.f64 #s(literal 1 binary64) (.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
(+.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) x)))
(+.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
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(+.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) #s(literal -1843/32768 binary64)) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal -1843/32768 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 69/1024 binary64) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 69/1024 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))
(fma.f64 #s(literal 69/1024 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) #s(literal -1843/32768 binary64)) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1843/32768 binary64)) (.f64 x (.f64 x (.f64 x x))) (.f64 #s(literal 69/1024 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 69/1024 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 69/1024 binary64)))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 328509/1073741824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -6260024107/35184372088832 binary64))))) (+.f64 #s(literal 4761/1048576 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1843/32768 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal -1843/32768 binary64)) #s(literal 69/1024 binary64)))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 4761/1048576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64)))) (+.f64 #s(literal 69/1024 binary64) (.f64 #s(literal 1843/32768 binary64) (.f64 x x))))
(.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))
(.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))
(.f64 (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) (.f64 x x))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) x)
(.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))

simplify286.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

4818×	`-lowering-.f32`
4818×	`-lowering-.f64`
1896×	`/-lowering-/.f32`
1896×	`/-lowering-/.f64`
1828×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	2798
1	1255	2411
2	4510	2366
0	8208	2366

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))
(/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (+ (* -1 (* x (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3)))) (* (sqrt (/ 1 x)) (/ (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))) (sqrt -1/4)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* x (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/4 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(/ -1/4 (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
(/ (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4) (pow x 3))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(/ -1/4 (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(* -11/128 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))
(/ (- x (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) x)
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 x)) (sqrt 1/2))
(/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 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)
(/ 1/2 x)
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))
(/ (+ (* (sqrt x) (sqrt -1/4)) (pow x 2)) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4))))))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* x (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* -1843/32768 (pow x 2))
(* 69/1024 (pow x 2))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* 69/1024 (pow x 4))
(* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))

Outputs
(/ 1/4 (pow x 3))
(/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) x)
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/ -1/4 (pow x 2))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))
(.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (sqrt.f64 #s(literal -1/4 binary64)))
(/ (+ (* (sqrt x) (sqrt -1/4)) (pow x 2)) (pow x 2))
(/.f64 (+.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal -1/4 binary64)) (sqrt.f64 x))) (*.f64 x x))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4))))))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1/4 binary64)) (sqrt.f64 x)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 #s(literal -1/4 binary64)))))) (*.f64 x x))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* x (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1/4 binary64)) (sqrt.f64 x)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))))) (*.f64 x x))
(+ 1 (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal -3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (.f64 x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x)))
(+ 1 (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(-.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) #s(literal 1 binary64)))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* -1843/32768 (pow x 2))
(.f64 (.f64 x x) #s(literal -1843/32768 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* -1843/32768 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))))
(* -1843/32768 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))))
(* 69/1024 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 69/1024 binary64))
(* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* (pow x 4) (+ 69/1024 (* -1843/32768 (pow x 2))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))
(* -1843/32768 (pow x 6))
(*.f64 #s(literal -1843/32768 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))))
(* -1843/32768 (pow x 6))
(*.f64 #s(literal -1843/32768 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))))

eval442.0ms (2.4%)

Compiler: Compiled 35428 to 2678 computations (92.4% saved)

prune160.0ms (0.9%)

Pruning

22 alts after pruning (14 fresh and 8 done)

	Pruned	Kept	Total
New	1017	6	1023
Fresh	2	8	10
Picked	1	4	5
Done	0	4	4
Total	1020	22	1042

Accuracy

100.0%

Counts

1042 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
▶	98.6%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
	0.8%	(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1331/2097152 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))))) (-.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))))))
✓	99.9%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
	98.2%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
	0.9%	(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
	98.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
▶	96.8%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	4.5%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
	1.2%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
✓	97.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
▶	97.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	96.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	95.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	98.6%	(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 3/2 binary64)))) (-.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
✓	1.2%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
✓	1.4%	(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
✓	1.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
▶	4.1%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
▶	4.5%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	3.1%	#s(literal 0 binary64)

Compiler

Compiled 1080 to 437 computations (59.5% saved)

simplify174.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x)
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x)))
✓	cost-diff	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))
✓	cost-diff	(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
✓	cost-diff	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
✓	cost-diff	(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
✓	cost-diff	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))

Rules

1864×	`sum5-define`
1626×	`-lowering-.f32`
1626×	`-lowering-.f64`
1518×	`fma-lowering-fma.f32`
1518×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	293
1	89	266
2	213	266
3	439	266
4	755	266
5	1039	266
6	1591	266
7	2726	266
8	4768	266
0	8251	266

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
(- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
1/2
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(+ 1/2 (/ -1/4 (* x x)))
(/ -1/4 (* x x))
-1/4
(* x x)
x
(+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
1
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(* (* x x) 1/8)
(* x x)
x
1/8
(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024))))))
(* x x)
x
(+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024)))))
1/8
(* (* x x) (+ -11/128 (* x (* x 69/1024))))
(+ -11/128 (* x (* x 69/1024)))
-11/128
(* x (* x 69/1024))
(* x 69/1024)
69/1024
(/ 1/2 (+ 1 (sqrt 1/2)))
1/2
(+ 1 (sqrt 1/2))
1
(sqrt 1/2)
(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))))
1
(sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)))
(+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))
1/2
(/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)
(+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x))))
(+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))
(/ 3/16 (* x (* x (* x x))))
3/16
(* x (* x (* x x)))
x
(* x (* x x))
(* x x)
(/ -1/4 (* x x))
-1/4

Outputs
(/ (- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
1/2
#s(literal 1/2 binary64)
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)
(+ 1/2 (/ -1/4 (* x x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(/ -1/4 (* x x))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
-1/4
#s(literal -1/4 binary64)
(* x x)
(*.f64 x x)
x
(+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
(+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))
(* (* x x) 1/8)
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* x x)
(*.f64 x x)
x
1/8
#s(literal 1/8 binary64)
(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))))))
(* x x)
(*.f64 x x)
x
(+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024)))))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64))))))
1/8
#s(literal 1/8 binary64)
(* (* x x) (+ -11/128 (* x (* x 69/1024))))
(.f64 x (.f64 x (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))))
(+ -11/128 (* x (* x 69/1024)))
(+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) #s(literal 69/1024 binary64)))
-11/128
#s(literal -11/128 binary64)
(* x (* x 69/1024))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* x 69/1024)
(*.f64 x #s(literal 69/1024 binary64))
69/1024
#s(literal 69/1024 binary64)
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1 (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (*.f64 x x)))) x))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (*.f64 x x)))) x)))
(+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (*.f64 x x)))) x))
1/2
#s(literal 1/2 binary64)
(/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (*.f64 x x)))) x)
(+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x))))
(+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (*.f64 x x))))
(+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))
(+.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (*.f64 x x))))
(/ 3/16 (* x (* x (* x x))))
(/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (.f64 x x)))
3/16
#s(literal 3/16 binary64)
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
x
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(/ -1/4 (* x x))
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
-1/4
#s(literal -1/4 binary64)

localize204.0ms (1.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.5%	(/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
✓	accuracy	98.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	accuracy	98.3%	(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x #s(literal 69/1024 binary64))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 69/1024 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))
✓	accuracy	98.3%	(/.f64 #s(literal -1/4 binary64) (*.f64 x x))

Results

145.0ms	254×	0	valid
1.0ms	2×	0	invalid

Compiler

Compiled 343 to 37 computations (89.2% saved)

Precisions

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

ival-mult: 17.0ms (35.5% of total)

ival-div: 11.0ms (22.9% of total)

ival-add: 11.0ms (22.9% of total)

ival-sqrt: 6.0ms (12.5% of total)

ival-sub: 3.0ms (6.3% of total)

const: 1.0ms (2.1% of total)

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

series11.0ms (0.1%)

Counts

23 → 240

Calls

Call 1

Inputs
#<alt (/ (- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))>
#<alt (- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))>
#<alt (/ (+ 1/2 (/ -1/4 (* x x))) x)>
#<alt (+ 1/2 (/ -1/4 (* x x)))>
#<alt (* (* x x) 1/8)>
#<alt (* x x)>
#<alt (* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024))))))>
#<alt (+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024)))))>
#<alt (* (* x x) (+ -11/128 (* x (* x 69/1024))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (- 1 (sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))))>
#<alt (sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)))>
#<alt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))>
#<alt (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)>
#<alt (/ -1/4 (* x x))>
#<alt (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))>
#<alt (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))>
#<alt (* x (* x 69/1024))>
#<alt (* x 69/1024)>
#<alt (/ 3/16 (* x (* x (* x x))))>
#<alt (* x (* x x))>

Outputs
#<alt (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4))))>
#<alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)>
#<alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)>
#<alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (+ (* -1 (* x (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3)))) (* (sqrt (/ 1 x)) (/ (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))) (sqrt -1/4)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))>
#<alt (- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* x (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/4 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (/ 1/4 (pow x 3))>
#<alt (/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))>
#<alt (/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (/ -1/4 (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 2))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 2))>
#<alt (/ (- (* 1/2 (pow x 2)) 1/4) (pow x 2))>
#<alt 1/2>
#<alt (- 1/2 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- 1/2 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- 1/2 (* 1/4 (/ 1 (pow x 2))))>
#<alt 1/2>
#<alt (- 1/2 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- 1/2 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- 1/2 (* 1/4 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 6))>
#<alt (* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))>
#<alt (* 69/1024 (pow x 4))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 4))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* -11/128 (pow x 2))>
#<alt (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))>
#<alt (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))>
#<alt (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))>
#<alt (* 69/1024 (pow x 4))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* 69/1024 (pow x 4))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 5))) (sqrt 3/16)))>
#<alt (/ (- (* (pow x 3) (- 1 (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))))) (* (sqrt x) (sqrt 3/16))) (pow x 3))>
#<alt (/ (- (* (pow x 3) (- (+ 1 (* -1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 3/16))))) (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))))) (* (sqrt x) (sqrt 3/16))) (pow x 3))>
#<alt (/ (- (* (pow x 3) (- (+ 1 (* (pow x 2) (- (* -1/2 (* (sqrt x) (/ (- 1/2 (* 1/64 (/ 1 (* x (pow (sqrt 3/16) 2))))) (sqrt 3/16)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16))))))) (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))))) (* (sqrt x) (sqrt 3/16))) (pow x 3))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 (pow x 5))) (sqrt 3/16))>
#<alt (/ (+ (* -1/8 (* (sqrt (pow x 5)) (/ 1 (sqrt 3/16)))) (* (sqrt x) (sqrt 3/16))) (pow x 3))>
#<alt (/ (+ (* (sqrt x) (sqrt 3/16)) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 3/16))))))) (pow x 3))>
#<alt (/ (+ (* (sqrt x) (sqrt 3/16)) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))) (* 1/2 (* (sqrt x) (/ (- 1/2 (* 1/64 (/ 1 (* x (pow (sqrt 3/16) 2))))) (sqrt 3/16))))))))) (pow x 3))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (/ 3/16 (pow x 5))>
#<alt (/ (+ 3/16 (* -1/4 (pow x 2))) (pow x 5))>
#<alt (/ (+ 3/16 (* (pow x 2) (- (* 1/2 (pow x 2)) 1/4))) (pow x 5))>
#<alt (/ (+ 3/16 (* (pow x 2) (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4))) (pow x 5))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)))>
#<alt (/ 3/16 (pow x 5))>
#<alt (/ (+ 3/16 (* -1/4 (pow x 2))) (pow x 5))>
#<alt (/ (+ 3/16 (* (pow x 2) (- (* 1/2 (pow x 2)) 1/4))) (pow x 5))>
#<alt (/ (+ 3/16 (* (pow x 2) (- (* 1/2 (pow x 2)) 1/4))) (pow x 5))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))>
#<alt (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (/ -1/4 (pow x 2))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4))))))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* x (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 5)) (/ 1 (sqrt -1/4)))) (* (sqrt x) (sqrt -1/4))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))) (pow x 2))>
#<alt (/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/4) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 (pow x 2))>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (* 69/1024 x)>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (/ 3/16 (pow x 4))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))))
0.0ms	x	@	0	(/ 3/16 (* x (* x (* x x))))
0.0ms	x	@	inf	(* (* x x) (+ -11/128 (* x (* x 69/1024))))
0.0ms	x	@	inf	(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024))))))
0.0ms	x	@	inf	(* (* x x) 1/8)

rewrite375.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

2876×	`-lowering-.f32`
2876×	`-lowering-.f64`
2130×	`/-lowering-/.f32`
2130×	`/-lowering-/.f64`
2114×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	219
1	258	198
2	2769	198
0	8215	198

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 434

Calls

Call 1

Inputs
(/ (- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)) (+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))))
(- 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))
(/ (+ 1/2 (/ -1/4 (* x x))) x)
(+ 1/2 (/ -1/4 (* x x)))
(* (* x x) 1/8)
(* x x)
(* (* x x) (+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024))))))
(+ 1/8 (* (* x x) (+ -11/128 (* x (* x 69/1024)))))
(* (* x x) (+ -11/128 (* x (* x 69/1024))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ 1 (sqrt 1/2))
(sqrt 1/2)
(- 1 (sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))))
(sqrt (+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)))
(+ 1/2 (/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x))
(/ (+ 1/2 (+ (/ 3/16 (* x (* x (* x x)))) (/ -1/4 (* x x)))) x)
(/ -1/4 (* x x))
(+ 1 (sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x))))
(sqrt (+ 1/2 (/ (+ 1/2 (/ -1/4 (* x x))) x)))
(* x (* x 69/1024))
(* x 69/1024)
(/ 3/16 (* x (* x (* x x))))
(* x (* x x))

Outputs
(+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (neg.f64 (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (neg.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))) (fma.f64 (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))))
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(+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 3/2 binary64))))))) (fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 3/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) #s(literal 3/2 binary64)))))))
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(.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) #s(literal 1/2 binary64)))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))) (-.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))) (.f64 x (.f64 x x))))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))))
(.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))) (-.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))) (.f64 x (.f64 x x)))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x))))))
(.f64 x (.f64 x #s(literal 69/1024 binary64)))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(.f64 #s(literal 69/1024 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 69/1024 binary64)) x)
(*.f64 x #s(literal 69/1024 binary64))
(*.f64 #s(literal 69/1024 binary64) x)
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3/16 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -3/16 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/16 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/16 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 3/16 binary64) x)))
(/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 #s(literal 3/16 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 #s(literal -3/16 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (/.f64 #s(literal 3/16 binary64) x) (.f64 x (.f64 x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/16 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal 3/16 binary64) x)) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))
(/.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x x))) x)
(/.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (*.f64 x x))
(/.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) (*.f64 x x)) x)
(pow.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/16 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/16 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 3/16 binary64) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 #s(literal -3/16 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (.f64 x (*.f64 x x)) #s(literal 3/16 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 3/16 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 (*.f64 x x) #s(literal 3/16 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 3/16 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) (/.f64 #s(literal 3/16 binary64) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

simplify293.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

3572×	`-lowering-.f32`
3572×	`-lowering-.f64`
2006×	`/-lowering-/.f32`
2006×	`/-lowering-/.f64`
1994×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	3042
1	1277	2585
2	4831	2517
0	8230	2517

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (+ (* -1 (* x (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3)))) (* (sqrt (/ 1 x)) (/ (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))) (sqrt -1/4)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* x (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* -1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* x (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/4 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))
(/ (+ 1/4 (* (pow x 2) (- (* 1/2 x) 1/2))) (pow x 3))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(/ -1/4 (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 3))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/ -1/4 (pow x 2))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 2))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 2))
(/ (- (* 1/2 (pow x 2)) 1/4) (pow x 2))
1/2
(- 1/2 (* 1/4 (/ 1 (pow x 2))))
(- 1/2 (* 1/4 (/ 1 (pow x 2))))
(- 1/2 (* 1/4 (/ 1 (pow x 2))))
1/2
(- 1/2 (* 1/4 (/ 1 (pow x 2))))
(- 1/2 (* 1/4 (/ 1 (pow x 2))))
(- 1/2 (* 1/4 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))
(* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))
(* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* -1 (* (sqrt (/ 1 (pow x 5))) (sqrt 3/16)))
(/ (- (* (pow x 3) (- 1 (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))))) (* (sqrt x) (sqrt 3/16))) (pow x 3))
(/ (- (* (pow x 3) (- (+ 1 (* -1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 3/16))))) (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))))) (* (sqrt x) (sqrt 3/16))) (pow x 3))
(/ (- (* (pow x 3) (- (+ 1 (* (pow x 2) (- (* -1/2 (* (sqrt x) (/ (- 1/2 (* 1/64 (/ 1 (* x (pow (sqrt 3/16) 2))))) (sqrt 3/16)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16))))))) (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))))) (* (sqrt x) (sqrt 3/16))) (pow x 3))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 (pow x 5))) (sqrt 3/16))
(/ (+ (* -1/8 (* (sqrt (pow x 5)) (/ 1 (sqrt 3/16)))) (* (sqrt x) (sqrt 3/16))) (pow x 3))
(/ (+ (* (sqrt x) (sqrt 3/16)) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 3/16))))))) (pow x 3))
(/ (+ (* (sqrt x) (sqrt 3/16)) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 3/16)))) (* 1/2 (* (sqrt x) (/ (- 1/2 (* 1/64 (/ 1 (* x (pow (sqrt 3/16) 2))))) (sqrt 3/16))))))))) (pow x 3))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(/ 3/16 (pow x 5))
(/ (+ 3/16 (* -1/4 (pow x 2))) (pow x 5))
(/ (+ 3/16 (* (pow x 2) (- (* 1/2 (pow x 2)) 1/4))) (pow x 5))
(/ (+ 3/16 (* (pow x 2) (- (* (pow x 2) (+ 1/2 (* 1/2 x))) 1/4))) (pow x 5))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)))
(/ 3/16 (pow x 5))
(/ (+ 3/16 (* -1/4 (pow x 2))) (pow x 5))
(/ (+ 3/16 (* (pow x 2) (- (* 1/2 (pow x 2)) 1/4))) (pow x 5))
(/ (+ 3/16 (* (pow x 2) (- (* 1/2 (pow x 2)) 1/4))) (pow x 5))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(/ -1/4 (pow x 2))
(* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))
(/ (+ (* (sqrt x) (sqrt -1/4)) (pow x 2)) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4))))))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 2) (+ 1 (* x (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ 1 (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(* (sqrt (/ 1 (pow x 3))) (sqrt -1/4))
(/ (+ (* 1/4 (* (sqrt (pow x 5)) (/ 1 (sqrt -1/4)))) (* (sqrt x) (sqrt -1/4))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt x) (/ 1 (sqrt -1/4)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))) (pow x 2))
(/ (+ (* (sqrt x) (sqrt -1/4)) (* (pow x 3) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/4) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))))))) (pow x 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 (pow x 2))
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(* 69/1024 x)
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(/ 3/16 (pow x 4))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
(* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4))))
(.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1/4 binary64))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) x)))) x)
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (+.f64 (.f64 x (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal -1/4 binary64))))))) (/.f64 #s(literal 1 binary64) x))))) x)
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* (pow x 2) (- (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* x (- (+ (* -1 (* x (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3)))) (* (sqrt (/ 1 x)) (/ (- (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4)))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))) (sqrt -1/4)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/4))))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/4) 3))))))) (* 1/4 (/ 1 (* x (pow (sqrt -1/4) 2))))))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (+.f64 (.f64 x (-.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal -1/4 binary64)))))) (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -1/4 binary64))) #s(literal 1/16 binary64))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/4 binary64))))))) (/.f64 #s(literal 1 binary64) x))))) x)
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) x))
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 x x))) (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))
(+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 x x))) (+.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x x))) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (/.f64 #s(literal -3/64 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))) (.f64 #s(literal 1/32 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) x))
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(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
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(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -3/32 binary64) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/16 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (- 1/4 (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 (pow x 2))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(* 69/1024 x)
(*.f64 x #s(literal 69/1024 binary64))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ 3/16 (pow x 4))
(/.f64 #s(literal 3/16 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

eval132.0ms (0.7%)

Compiler: Compiled 28953 to 2571 computations (91.1% saved)

prune98.0ms (0.5%)

Pruning

24 alts after pruning (11 fresh and 13 done)

	Pruned	Kept	Total
New	910	4	914
Fresh	2	7	9
Picked	0	5	5
Done	0	8	8
Total	912	24	936

Accuracy

100.0%

Counts

936 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
	98.7%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	98.6%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
	98.4%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
	0.8%	(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1331/2097152 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))))) (-.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))))))
✓	99.9%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
	0.9%	(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))))
	98.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
✓	96.8%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	4.5%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
	1.2%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
	97.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x) (-.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (*.f64 x x))))) x) #s(literal 1/2 binary64)))))))
✓	97.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
✓	97.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
✓	98.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	96.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	95.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	1.2%	(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
✓	1.4%	(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
✓	1.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
✓	4.1%	(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
✓	4.5%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	3.1%	#s(literal 0 binary64)

Compiler

Compiled 1648 to 479 computations (70.9% saved)

regimes70.0ms (0.4%)

Counts

34 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1331/2097152 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))))) (-.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x) (-.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (*.f64 x x))))) x) #s(literal 1/2 binary64)))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 3/2 binary64)))) (-.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))) (-.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Outputs

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

Calls

7 calls:

11.0ms	x
10.0ms	(hypot.f64 #s(literal 1 binary64) x)
10.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
9.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
8.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.9%	1	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.9%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.9%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.9%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.9%	1	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes69.0ms (0.4%)

Counts

31 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1331/2097152 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64)))))) (-.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -11/128 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x) (-.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (*.f64 x x))))) x) #s(literal 1/2 binary64)))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) #s(literal 3/2 binary64)))) (-.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))

Outputs

(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/16 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) x)))) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/16 binary64) (*.f64 x (*.f64 x (*.f64 x x))))) x)))))

Calls

7 calls:

15.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
11.0ms	(hypot.f64 #s(literal 1 binary64) x)
9.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
9.0ms	x
9.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
98.8%	1	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
98.8%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.8%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.8%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.8%	1	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes354.0ms (1.9%)

Counts

22 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))

Outputs

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

Calls

1 calls:

352.0ms

Results

Accuracy	Segments	Branch
98.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes11.0ms (0.1%)

Counts

20 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) x))))

Outputs

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0%)

Counts

18 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))

Outputs

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes9.0ms (0%)

Counts

17 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))

Outputs

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
98.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0%)

Counts

16 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
97.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes11.0ms (0.1%)

Counts

15 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))

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

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
96.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes10.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

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

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
95.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

12 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 11/128 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x #s(literal 69/1024 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64))))) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -11/128 binary64) (.f64 x (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (.f64 x x) #s(literal -1843/32768 binary64)))))))) (.f64 x x)) (-.f64 (-.f64 (.f64 x (.f64 x #s(literal -11/128 binary64))) #s(literal 1/8 binary64)) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 69/1024 binary64) (.f64 (*.f64 x x) #s(literal -1843/32768 binary64))))))))

Outputs
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
4.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))

Outputs
(.f64 #s(literal 1/8 binary64) (.f64 x x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
4.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Outputs
#s(literal 0 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
3.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify25.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

176×	`unsub-neg_binary64`
144×	`neg-mul-1_binary64`
100×	`+-commutative_binary64`
84×	`*-commutative_binary64`
70×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	189
1	97	189
2	145	189
3	204	189
4	252	189
5	359	189
6	536	189
7	569	189
8	589	189
9	598	189
10	600	189

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
#s(literal 0 binary64)

Outputs
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 3/16 binary64) (.f64 x (.f64 x (.f64 x x))))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
#s(literal 0 binary64)

soundness3.8s (20.3%)

Rules

5148×	`-lowering-.f32`
5148×	`-lowering-.f64`
4818×	`-lowering-.f32`
4818×	`-lowering-.f64`
4516×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	385	3042
1	1277	2585
2	4831	2517
0	8230	2517
0	396	3174
1	1332	2647
2	4643	2589
0	8363	2589
0	11	30
1	67	30
2	542	30
3	6579	30
0	8361	30
0	36	219
1	258	198
2	2769	198
0	8215	198
0	38	189
1	255	177
2	2425	177
0	8990	177
0	31	174
1	233	151
2	2275	151
0	10389	151
0	12	11
1	32	10
2	40	10
3	48	10
4	56	10
5	69	10
6	86	10
7	100	10
8	112	10
9	113	10
0	113	10
0	169	619
1	515	526
2	1480	510
3	4246	508
0	8047	508
0	373	2798
1	1255	2411
2	4510	2366
0	8208	2366

Stop Event

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

Compiler

Compiled 545 to 307 computations (43.7% saved)

preprocess104.0ms (0.6%)

Remove: (abs x)
Compiler: Compiled 520 to 208 computations (60% saved)

Iter	Nodes	Cost
0	17	35
1	53	30
2	99	30
3	160	30
4	268	30
5	412	30
6	518	30
7	564	30
8	576	30
0	12	11
1	32	10
2	40	10
3	48	10
4	56	10
5	69	10
6	86	10
7	100	10
8	112	10
9	113	10
0	113	10

Iter	Nodes	Cost
0	61	189
1	97	189
2	145	189
3	204	189
4	252	189
5	359	189
6	536	189
7	569	189
8	589	189
9	598	189
10	600	189

Iter	Nodes	Cost
0	17	35
1	53	30
2	99	30
3	160	30
4	268	30
5	412	30
6	518	30
7	564	30
8	576	30
0	12	11
1	32	10
2	40	10
3	48	10
4	56	10
5	69	10
6	86	10
7	100	10
8	112	10
9	113	10
0	113	10

Iter	Nodes	Cost
0	61	189
1	97	189
2	145	189
3	204	189
4	252	189
5	359	189
6	536	189
7	569	189
8	589	189
9	598	189
10	600	189

analyze1.0ms (0%)

sample9.0s (48.3%)

preprocess35.0ms (0.2%)

explain127.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0%)

localize81.0ms (0.4%)

series4.0ms (0%)

rewrite264.0ms (1.4%)

simplify245.0ms (1.3%)

eval32.0ms (0.2%)

prune41.0ms (0.2%)

simplify231.0ms (1.2%)

localize183.0ms (1%)

series19.0ms (0.1%)

rewrite360.0ms (1.9%)

simplify339.0ms (1.8%)

eval154.0ms (0.8%)

prune91.0ms (0.5%)

simplify151.0ms (0.8%)

localize165.0ms (0.9%)

series13.0ms (0.1%)

rewrite425.0ms (2.3%)

simplify286.0ms (1.5%)

eval442.0ms (2.4%)

prune160.0ms (0.9%)

simplify174.0ms (0.9%)

localize204.0ms (1.1%)

series11.0ms (0.1%)

rewrite375.0ms (2%)

simplify293.0ms (1.6%)

eval132.0ms (0.7%)

prune98.0ms (0.5%)

regimes70.0ms (0.4%)

regimes69.0ms (0.4%)

regimes354.0ms (1.9%)

regimes11.0ms (0.1%)

regimes8.0ms (0%)

regimes9.0ms (0%)

regimes7.0ms (0%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes5.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify25.0ms (0.1%)

soundness3.8s (20.3%)

preprocess104.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	17	35
1	53	30
2	99	30
3	160	30
4	268	30
5	412	30
6	518	30
7	564	30
8	576	30
0	12	11
1	32	10
2	40	10
3	48	10
4	56	10
5	69	10
6	86	10
7	100	10
8	112	10
9	113	10
0	113	10

Iter	Nodes	Cost
0	61	189
1	97	189
2	145	189
3	204	189
4	252	189
5	359	189
6	536	189
7	569	189
8	589	189
9	598	189
10	600	189